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PHOTONICS LABORATORY Manual ECE 5137 Betty Lise Anderson Bradley D. Clymer Stuart A. Collins, Jr. Lawrence J. Pelz Steven Ringel Department of Electrical and Computer Engineering Copyright 2012, The Ohio State University

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Page 1: PHOTONICS) LABORATORY) ) )

PHOTONICS)LABORATORY)

)Manual)

)ECE)5137))

Betty)Lise)Anderson)Bradley)D.)Clymer)Stuart)A.)Collins,)Jr.)Lawrence)J.)Pelz)Steven)Ringel)

)Department)of)Electrical)and)Computer)

Engineering))

Copyright)2012,)The)Ohio)State)University)

Page 2: PHOTONICS) LABORATORY) ) )

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Page 3: PHOTONICS) LABORATORY) ) )

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Page 4: PHOTONICS) LABORATORY) ) )

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H)"'0:50"('":5754';",'95"05,5.0+&",I*44,B"(&5",(3:5)("*,"5=;5+(5:"('":5+*:5)'("')41"&'>"('";506'09"(&5"5=;50*95)(,B"/3("*)",'95",5),5":5+*:5">&.("(&55=;50*95)(,",&'34:"/5B".):"&'>":5(.*45:C"G5":'")'(":56*)5"+')(0.,("0.(*'"'0:*660.+(*')"566*+*5)+1B"(&5",(3:5)("93,(":5+*:5">&.("*,"."95.)*)<634"95.,305"'6;506'09.)+5B".):":56*)5"&*,"'>)"+')(0.,("0.(*'C

Page 8: PHOTONICS) LABORATORY) ) )

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7 * *

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1

PART I: INTRODUCTION TO SEVERAL PHOTONICTECHNOLOGIES

SafetyOptical Sensing

Fiber Optic CommunicationAcousto-Optic Modulation

Laser Diode PhysicsQuantum Well Detection

Liquid CrystalsSolar Cells

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2

SAFETY

"When the beam struck my eye I heard a distinct popping

sound, caused by a laser-induced explosion at the back of my

eyeball.* My vision was obscured almost immediately by streams of

blood floating in the vitreous humor, and by what appeared to be

particulate matter suspended in the vitreous humor. It was like

viewing the world through a round fishbowl full of glycerol into

which a quart of blood and a handful of black pepper have been

partially mixed. There was local pain within a few minutes of the

accident, but it did not become excruciating. The most immediate

response after such an incident is horror. As a Vietnam War

Veteran, I have seen several terrible scenes of human carnage, but

none affected me more than viewing the world through my

bloodfilled eyeball. In the aftermath of the accident I went into

shock, as is typical in personal injury accidents.

"As it turns out, my injury was severe but not nearly as bad

as it might have been. I was not looking directly at the prism from

which the beam had reflected, so the retinal damage is not in the

fovea. The beam struck my retina between the fovea and the optic

nerve, missing the optic nerve by about three millimeters. Had the

focused beam struck the fovea, I would have sustained a blind spot

* The author had been using a relatively low power neodymium-yag laser.

He had not wearing protective goggles, even though they were available in the

laboratory because the goggles tend to result in tunnel vision, they fog up, and

they can become uncomfortable during long hours in the lab.

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EE 737 Photonics Laboratory Manual Safety

3

in the center of my field of vision. Had it struck the optic nerve, I

probably would have lost the sight of that eye.

"The beam did strike so close to the optic nerve, however, that it

severed nerve-fiber bundles radiating from the optic nerve. This has

resulted in a crescent-shaped blind spot many times the size of the

lesion.... The effect of the large blind area is much like having a finger

placed over one's field of view of my damaged eye, although the blood

streamers have disappeared. These "floaters" are more a daily hindrance

than the blind areas, because the brain tries to integrate out the blind area

when the undamaged eye is open. There is also recurrent pain in the eye,

especially when I have been reading too long or when I get tired." [1]

During the course of this laboratory, you will be working with some

dangerous equipment. In order to protect yourself, your classmates and your

beloved instructor, you will want to know what the hazards are, how dangerous

they are, and what precautions to take. While protecting yourself and the people

around you must be your first priority, there are also a variety of interesting

ways to damage the equipment, and we will concern ourselves with that kind of

safety as well.

The dangers to people fall into three primary categories as far as this

laboratory is concerned: radiation hazards (laser beams), electrical hazards (high

voltage), and chemical hazards.

The equipment is also sensitive to radiation, electricity, and chemicals. For

example, a highly focused high-power laser beam can damage the surface of a

mirror. Some of the devices you'll be handling are susceptible to electrostatic

discharges (ESD). The chemical hazards may come from you- the oils on your

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EE 737 Photonics Laboratory Manual Safety

4

skin, for example, can permanently ruin the coatings on a lens if you pick it up

without gloves.

Since people are harder to replace than lenses, we will begin with personal

safety.

lens

anterior

chamber

posterior chamber

ora serrataretina (inside surface)

cornea

optic nerve

iris

Figure 1. Structure of the eye.

RADIATION HAZARDS;

Eye DamageThe structure of the eye is shown in the crude drawing in Figure 1.

The eye has a thin eyelid made of skin (not shown), underneath which is the

cornea, a structure that is transparent to visible wavelengths (so you can see).

The cornea has no blood vessels, and has a refractive index of 1.376. [2] The

cornea absorbs radiation in the wavelength range of 200 nm-315 nm, and this

absoprtion can result in photokeratitis, an inflammation of the cornea. [3] To put

that wavelength range into perspective, the visible range is approximately

between 380 nm and 770 nm. Below 380 nm is the ultraviolet region. The cornea

is also susceptible to infared radiation in the range of 3µm to 1 mm. [3]

Behind the cornea is the anterior chamber, containing the aqueous humor,

a nutrient-bearing fluid that has an index of reaction of 1.336. Beyond this

chamber is the lens, which is also transparent to visible light, but is a different

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EE 737 Photonics Laboratory Manual Safety

5

tissue type than the cornea. The lens has a refractive index of 1.41 (near the

center). [2] The lens is absorbing in the wavelength range of 315-400 nm [2] and

exposure to light at these wavelengths can produce cataracts. [3]

Behind the lens is the posterior chamber, filled with vitreous humor, a

gelatinous material of refractive index 1.336. It is in this chamber that small epics

of cellular material that are not transparent occasionally appear. These look like

squiggles or spots in your field of vision and are called vitreous floaters. If you are

familiar with the principles of Fourier optics, you will see diffraction patterns

around the edges of these (you'll see them anyway, but if you know your Fourier

you'll understand them).

At the back of the eye is the retina, which contains about 100 ! 106 rods

and 10 ! 106 cones. It is the retina that is primarily damaged by visible and near

infrared light, in the 400nm - 1400 nm range. [3] The lens and cornea pass

radiation in this range and focus it onto the retina. High power levels can

therefore result in burns to the retina that do not heal.

DAMAGE THRESHOLDS AND MPE's

It would be nice to give a number and say, "A laser more powerful than

this is dangerous." When you are about to work with a laser, you will want to

figure out the Maximum Permissible Exposure (MPE) for that laser.

Unfortunately, the thing is very complex. Damage thresholds depend on the

wavelength of the light, the time of exposure (how long the beam hits you and

whether or not it's pulsed), and the conditions under which it's viewed

(intrabeam versus extended source viewing).

"Intrabeam" viewing means viewing a laser beam by putting one's eye

directly into the beam. The same conditions can also be achieved by looking at a

specular reflection off an object such as a watchband or an optical post. The term

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EE 737 Photonics Laboratory Manual Safety

6

"extended source" refers to conditions in which the beam is sufficiently divergent

(reflecting off a diffuse surface such as a piece of paper, or an uncollimated

beam). Figure 2 shows some typical situations that result in these types of

viewing.

a

r

!

eye

Figure 2a. Intrabeam viewing- primary beam. After [4]

mirror

eye

direct beam

indirect beam

laser

Figure 2b. Intrabeam viewing- specularly reflected secondary beam. After [4]

Figure 2 continued next page

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EE 737 Photonics Laboratory Manual Safety

7

eye

laser

a

!

r

r1

"vDL

#

Figure 2c. Extended source viewing- normally diffuse reflection. After [4]

!

r

"

Figure 2 d. For a small, but highly divergent beam (such as that emitted from a

semiconductor laser), this is still intrabeam viewing, since it is the angle subtended by the eye , not the source, that is the issue.

The type of viewing one is exposed to is determined by the limiting angle

!min. When the angle is greater than !min, the MPE needed is that for extended

viewing, for angles less than !min, intrabeam viewing MPE's apply. Figure 3

shows the value of !min as a function of exposure time.

Figures 4, 5, and 6 gives the MPE values at the cornea for direct

(intrabeam) viewing, as a function of wavelength and time exposure. For

wavelengths between 0.7 µm and 1.4 µm, you use Figure 4, lower line, but you

must apply a correction factor from Figure 7. For example, you may be using a

940 nm laser diode, operating CW (continuous wave, meaning it's always on).

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EE 737 Photonics Laboratory Manual Safety

8

Suppose you think it would not take you longer than 5 seconds to realize you are

being exposed and jerk your head away. (Radiation at 940 nm is in the infrared

region, so you wouldn't see it.) What is the MPE? Wavelengths between 0.4µm

and 1.4 µm are shown in Figure 4, from which the MPE is 1.8CAt3/4!10-3 J/cm2.

The factor CA must come from Figure 7, where it is found to be 2.9. Therefore the

Maximum Permissible Exposure is (1.8)(2.9)(53/4)(10-3) = 17.4 mJ/cm2.

For extended source (diffuse) viewing, Figure 8 must be used. Again,

correction factors for wavelengths between 0.7 and 1.4 µm must be applied from

Figure 7.

1

2

4

6

810

2

4

Subte

nse

angle

!m

in (

mra

d)

10-8

10-6

10-4

10-2

100

Exposure duration (sec)

Figure 3. Limiting angular subtense ("min), after ANSI. [5] Extended sources lie

above the line; apparent visual angles below the line are considered intrabeam

viewing.

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EE 737 Photonics Laboratory Manual Safety

9

10-7

10-6

10-5

10-4

10-3

10-2

Radia

nt

Exposure

(J/

cm

2)

10-5

10-4

10-3

10-2

10-1

100

101

Exposure Duration (sec)

!=1.06 " 1.4 µm

!=0.4 " 0.7µm

Figure 4. MPE's for eye exposure to visible and near infrared (intrabeam

viewing), single exposure. After [5] Functional form of lower line: Radiant

exposure=1.8!10-3 t3/4 (J/cm2). For wavelengths between these two line (0.7

µm – 1.3 µm), functional form of lower line applies, with correction factors (Figure

7).

0.001

2

4

0.01

2

4

0.1

2

4

1

Radia

nt

Exposure

(J/

cm

2)

0.340.320.300.280.260.240.220.20

Wavelength (µm)

Figure 5. MPE for eye exposure to ultraviolet beams (intrabeam viewing), single

exposure. After [5] .

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EE 737 Photonics Laboratory Manual Safety

10

0.01

2

4

6

80.1

2

4

6

81

Radia

nt

Exposure

(J/

cm

2)

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

101

Exposure Duration (sec)

Figure 6. MPE's for eye exposure to far infrared beams (!-1.4µm – 1mm)

(intrabeam viewing), single exposure. After [5] Funtional form is Radiant

Exposure=0.56 t1/4 (J/cm2)

1

2x100

3

4

5

6

Corr

ecti

on F

acto

r C

A

1.41.31.21.11.00.90.80.7

Wavelength (µm)

Figure 7. Correction factors for wavelengths 0.7-1.4µm (CF8.5.2). After [5]

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11

0.001

0.01

0.1

1

10

100

Inte

gra

ted R

adia

nce (

J•cm

-2/

sr)

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Exposure Duration (sec)

!=1.06 " 1.4 µm

!=0.4 " 0.7 µm

Figure 8. Maximum Permissible Exposure (MPE) for viewing a diffuse reflection

of a laser beam or an extended source laser. After[5]

Skin Damage

Damage to the skin can also result from laser radiation. There is some

feeling in the laser community that laser damage to the skin is not as dangerous

since the skin can heal better than eyes can. Lasers can, however cause

"reddening, blistering, charring, and actual burned-out cavities" in the skin. [4]

Furthermore, the same lasers that can burn the skin can also damage materials

such as glass and plastic, [6] meaning a beam intense enough to burn your skin

can also burn your protective eyewear. Such a beam should be entirely enclosed

and inaccessible to the user. Still higher powers can set fire to clothing.

Gaussian and Elliptical beams: From Table 1, it is clear we will need to calculate

the power density (W/cm2) or energy density (J/cm2) for any lasers we might be

using. For a HeNe laser, which emits a circular Gaussian beam, the beam

diameter a is generally given. This number is actually the diameter of the 1/e

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12

Table 1. MPE's for Skin Exposure to a Laser Beam (Copied with permission from Laser Institute of America[5] Wavelength ! (µm) Exposure Duration t

(sec) Maximum Permissible Explosure (MPE)

Notes for Calculation and Measurement

Ultraviolet 0.200 to 0.302 10-9 to 3 " 104 3 " 10-3 J•cm-2

0.303 10-9 to 3 " 104 4 " 10-3 J•cm-2

0.304 10-9 to 3 " 104 6 " 10-3 J•cm-2

0.305 10-9 to 3 " 104 1.0 " 10 -2 J•cm-2 or 0.56 t1/4 J•cm-2 0.306 10-9 to 3 " 104 1.6 " 10 -2 J•cm-2 whichever is

0.307 10-9 to 3 " 104 2.5 " 10 -2 J•cm-2 lower

0.308 10-9 to 3 " 104 4.0 " 10 -2 J•cm-2

0.309 10-9 to 3 " 104 6.3 " 10 -2 J•cm-2 1 mm limiting

0.310 10-9 to 3 " 104 1.0 " 10 -1 J•cm-2 aperture

0.311 10-9 to 3 " 104 1.6 " 10 -1 J•cm-2

0.312 10-9 to 3 " 104 2.5 " 10 -1 J•cm-2

0.313 10-9 to 3 " 104 4.0 " 10 -1 J•cm-2

0.314 10-9 to 3 " 104 6.3 " 10 -1 J•cm-2

0.315 to 0.400 10-9 to 10 0.56 t1/4 J•cm-2

0.315 to 0.400 10 to 103 1 J•cm-2

0.315 to 0.400 103 to 3 " 104 1 " 10-3 W•cm-2

Visible and Near Infrared

0.400 to 1.400 10 -9 to 10 -7 2CA " 10-2 J•cm-2 1 mm limiting

10-7 to 10 1.1 CAt1/4 J•cm-2 aperture

10 to 3 " 104 0.2 CA W•cm-2

Far Infrared 1 mm limiting

1.4 to 103 10 -9 to 10 -7 10-2 J•cm-2 aperture for

10-7 to 10 0.56 t1/4 J•cm-2 1.4 to 100µm >10 0.1 W•cm-2 11mm limiting

aperture for 0.1 to 1mm

1.54 only 10-9 to 10-6 1.0 J•cm-2

points of the (circular) Gaussian energy profile. The peak power density of the

beam is then given by

E =4!

"a2

[1]

for a single transverse mode laser, where # is the total laser power.

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13

Semiconductor lasers, on the other hand, emit elliptical beams. You'll be

reading more about these if you are doing the lasers experiment, but in this case,

the peak power density is

E =1.27!

b + r"1( ) c + r"

2( ) [2]

where b is the length of the major axis of the elliptical beam cross section, c is the

minor axis, !1 is the beam divergence in the direction corresponding to the major

axis, and !2 is the beam divergence associated with the direction of the minor

axis. These parameters are shown in Figure 9.

cb

!2

!1

Figure 9. Definitions of terms in equation [2] for an elliptical beam.

Lasers used in this course

In this particular course, we will be using two basic types of lasers, HeNe

lasers that emit at 632.8 nm, at powers generally less than 5mW (which is still

dangerous), and semiconductor lasers, which may be visible, or in the infrared

region between 800 nm and 1.55µm. These are all dangerous lasers. How

dangerous? The American National Standards Institute classifies all lasers

according to their hazard potential. There are four categories, From Class 1 lasers

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EE 737 Photonics Laboratory Manual Safety

14

which present essentially no hazard, to Class IV lasers, from which even a diffuse

reflection is hazardous. Class IV lasers can start fires and burn skin. These

classes are detailed in Table 2.

Table 2. Accesible Limits for Selected Continuous-Wave (>0.254 sec) Lasers and Laser

Systems, taken with permission from [5]

Wavelength Range

Emission Duration (sec)

Class I Class II (visible only)

Class 3 Class IV

Ultraviolet 3 ! 104 !0.8 ! 10-9 W to !8 ! 10-6

W depending on Wavelength

NA

>Class I but !0.5 W depending on wavelength

>0.5 W

Visible 0.4 -

0.550 µm 3 ! 104 <0.4 µW >Class I ,but <

1 mW >Class II but < 0.5 W

>0.5 W

Visible and Near Infrared

0.55 - 1.06 µm

3 ! 10-4 < 4 µW to

<200µW, wavelength dependent

NA

> Class I but < 0.5 W, wavelength dependent

>0.5 W

Near Infrared, 1.06 - 1.4 µm

3 ! 104 <200µW NA > 200µW but < 0.5 W

>0.5 W

Far Infrared,

1.4-100 µm

>10 <0.8 mW NA > Class I but < 0.5 W

>0.5 W

Safety Rules

Before you use any laser you will have to determine the type of hazards it

poses. Once that is known, you can establish what kinds of precautions are

necessary. These precautions are detailed in your supplemental laser safety text.

For example, when using a Class III laser, you should always wear goggles,

unless you completely encose the beam or use neutral density filters to reduce

the power of the beam immediately after the laser to levels classified as Class I.

Class I lasers require no special precautions. With a Class III laser, you should in

any case use a beam stop to prevent the laser beam from leaving your bench, so

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EE 737 Photonics Laboratory Manual Safety

15

that a person walking by your table cannot accidently be exposed, and you

should avoid setups that put beams at or near eye level.

ELECTRICAL HAZARDS (to people)

The electrical hazards to people that will come up in this laboratory are

from the high voltage power supplies used to power the gas lasers, and AC line

voltages, particularly those experiments using a variable transformer (solar cells,

quantum wells).

Some good policies to follow for electrical safety are:

1. Assume all circuits are live until you have personally checked that they

are disabled.

2. Metallic or otherwise conductive rings, bracelets, watches, etc. should

not be worn when working with high voltage circuits, power supplies, etc. Also,

metallic pens, rulers, etc. should be avoided during work.

3. It only takes 200mA to kill a person (if it goes through the heart).

Current can go through the heart when travelling from a hand to a foot, or from

on hand to the other. Therefore:

a. Do not stand on a wet floor while working on circuitry. Assume

all floors are conductive and grounded unless special precautions have

been taken (insulating mats, etc.). Do not touch circuitry while hands, feet,

body are wet or perspiring.

b. Use only one hand whenever possible.

c. If you must touch an electrical device (to check for overheating,

for example), use the back of your hand. Electrical current makes the

muscles contract, causing your fingers to close into a fist. By using the

back of your hand, you ensure that your fingers close away from the wire,

naturally removing your contact, instead of causing your fingers to grip

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EE 737 Photonics Laboratory Manual Safety

16

the wire, after which the flow of electricity will prevent you from letting

go.

d) Wear protective goggles if there is a possibility of sparks or

arcing.

If an electrical shock occurs, kill the circuit. Once that is done, it is safe to

touch to victim to administer first aid. This may include cardio-pulmonary

resuscitation to restart breathing and/or the heart.

CHEMICAL HAZARDS (to people)

The liquid crystal experiment requires you to use various chemicals,

including the liquid crystal material itself. The only potentially dangerous

chemical in this process is alcohol, which is flammable, and acetone, which is

carcinogenic. Therefore gloves must be worn to avoid skin exposure.

Furthermore, acetone qualifies as hazardous waste and must be disposed of

properly; it cannot be dumped down the drain. Used acetone must be kept in

special containers, and when the container is full, it will be collected by the

university and disposed of properly.

EQUIPMENT HAZARDS

In this section, we will be talking not about the hazards that the

equipment poses, but rather the ways in which you can damage the equipment

and devices through negligence or ignorance. The key issue in this section is

electro-static discharge (ESD), to which many of the devices are very sensitive.

That is, you can destroy some of the devices merely by picking them up.

Beyond ESD, there are certain rules for care and handling of optics (mirrors,

lenses, fibers) you are expected observe.

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Electro-Static Discharge (ESD)

As you know from petting your cat on a fine winter's day in your living

room with the polyester carpet, you can carry around substantial amounts of

electricity. Your cat is a reasonably large structure and can dissipate the typical

amounts of charge you carry, but some of the semiconductor devices have very

small structures- on the order of microns- and these can be destroyed by

discharges so small you don't even feel them. You have these charges on you all

the time, just from walking and moving around.

For you to feel the shock of an electrostatic discharge, you must discharge

at least 4000V. [7] By contrast, Table 1 shows the damage thresholds for some

common semiconductor devices. You can see why the manufacturer of your

personal computer wants you to have a trained technician install the extra

memory! That technician is presumably taking the proper precautions to protect

those memory chips.

The charge that you carry is generated triboelectrically, tribo from the

Greek for "rub". Any two surfaces that rub together, such as your foot against

the floor, your hand across the table, the pen across the tablet, air blowing across

your work, can exchange charge, leaving both surfaces with a residual charge.

Even just two surfaces separating, without rubbing, can transfer charge from one

to the other. One insidious example is adhesive tape- when you take a peice off

the roll, you are forcibly separating one layer from another, leaving thousands of

volts on the tape. This charge is hard to dissipate since the tape is non-

conducting, but can be transferred to whatever you're taping.

During triboelectric generation, one material is generally left with net

positive charge, and the other with a net negative charge. These depend on what

two materials are involved- materials higher up in Table 2 tend to acquire

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18

positive charge when separated from materials lower down. Things like surface

finish and contamination will also affect relationships on this list.

TABLE 1. Representative Sample of Part Susceptibility Data [7] Device Number Technology Susceptibility

Level Pin Combination

VN98AK VMOS 110V (+) Gate to source 3N170 MOSFET 150V (-) Gate to source Custom IC CMOS 150V (-) Input to

ground 2N4416 JFET 220V (-) Gate to source Custom IC Bipolar op-amp 400V (-) Input to

ground 1N5711 Schottky diode 500V (-) Anode to

cathode MC1660 ECL 500V (+) Output to Vcc CD4001A CMOS 800V (-) Input to Vdd 54S04 Schottky TTL 1000V (+)Input to Vdd RNC50 Thin-film resistor 1000V Lead to lead 5404 TTL 1600V (+) Input to Vdd 54L04 Low-power TTL 3500V (-) Input to

ground 2N2222 Bipolar transistor 15,000V (+) Emitter to base

TABLE 2. Triboelectric Series [7] POSITIVE +

NEGATIVE (-)

Acetate Glass Nylon Wool Silk

Aluminum Polyester

Paper Cotton Steel

Nickel, copper, silver Zinc

Rubber Polyurethane foam

PVC (vinyl) Teflon

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A conductive material can easily be discharged by connecting it to

ground, while insulating materials are difficult to discharge. In general, the

surface resistivity of objects and people will affect how easily the charges can be

removed, and the capacitance combined with the resistance will affect the speed

with which the charge moves. Since there is no such thing as a perfect insulator,

the charge on any object will eventually bleed off. If the charge on object is

transferred instantly, as with a conductor, the instantaneous current can be very

high, and damage parts. On the other hand, insulators can more easily have

extremely high voltages on them to start with, and are therefore also potentially

dangerous. The charges on the insulator will cause en electric field, which can in

turn induce charges onto nearby objects. Nothing is innocuous.

ESD Precautions

In industry, precautions are taken during manufacture of sensitive items

(for example, computers). Depending on the degree of sensitivity, these

precautions may include conductive flooring, conductive smocks, ionized air

blowers, wrist straps, grounding chains hanging from carts, and conductive

packaging and bins for components.

The most dangerous object in the laboratory from the point of view of ESD

is a person, because people move around a great deal and touch everything. The

single most important precaution to take, therefore, is to ground the human. This

is most often done with a conductive wrist strap connected to a good ground.

These wrist straps generally have a 1M! resistor in series with the ground

connection, to prevent electrocution if the person accidentally touches 120V

while grounded.

Another effective and common strategy is to ground the work surface,

which must therefore be conductive. This is useless if the person walking up to

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20

the bench and picking up a board is not also grounded, meaning that wrist straps

are still necessary.

In this laboratory course, you will be using conductive work mats which

must be grounded and wearing a wrist strap which must be grounded when working

with sensitive devices. You should check that the mat is grounded every time

you use it, and check that it is clean. Excessive dust or contamination on the

surface will make it more resistive, therefore compromising its effectiveness.

The wrist strap must fit snugly enough to make good electrical contact

with your skin. It does no good to wear it over your sleeve. Those of us with

hairy arms may have to wear the strap such that the conductive button (some

styles) is on the inside of the wrist, where there is usually less hair.

The components themselves must be kept in a closed , conductive container

until a grounded work surface and grounded worker are available. Then and

only then may the part be removed from the packaging. The component must be

handled only by grounded personnel until it is safely installed in a circuit or

fixture with adequate grounding to protect the device.

In this laboratory course, the most ESD sensitive devices you will handle

are laser diodes. Not only can these devices be instantaneously destroyed by an

ESD event, they can be damaged in subtle ways that don't show up until some

later time. They can suddenly start to degrade faster, or stop lasing.

Transient Protection for Laser Diodes

The laser diodes can also be destroyed by transients that occur, for

example, when a power supply is turned on. For this reason, we have purchased

special laser power supplies with a soft turn-on. These prevent current to the

laser from spiking. When using any other type of power supply, you must 1)

disconnect the laser when plugging in and turning on the supply, then 2) with

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21

the current output set to zero, connect the laser, and only then 3) slowly increase

the current to the operating level.

Chemical Hazards to Equipment

The chemical hazards to the equipment come primarily from you. The

primary source of concern is skin oil and other organic contaminants, which can

ruin the optics, and mirrors and lenses are not cheap.

The mirror in your bathroom at home has a silvered back, with a layer of

glass on top. When the mirror is dirty, you wash it with Windex®. In the optics

laboratory, the mirrors are silvered (or aluminum'ed) on the front surface (why?).

If you touch that surface, your fingerprint, a messy pile of oil, will destroy the

reflectivity, and the mirrors are not much bigger than a fingerprint. Attempting

to wipe your print off may scratch the metallization. You must handle mirrors only

by the edges . As additional precaution, when mounting mirrors, you should

wear gloves. If the mirror is dusty, the preferred cleaning method is to blow the

dust off with N2 (not your breath! more chemicals!), or gently wipe with lens

tissue (not your sleeve).

The lenses and filters you will be using generally have some antireflection

coatings deposited on their surfaces, which can also be destroyed by skin oil. You

must handle lenses and filters only by the edges. You should also wear gloves when

mounting and aligning optics.

SUMMARY

You are the most dangerous component in the lab, since you a) move

around, b) look at things, c) touch things. Fortunately, you are also able to

control your behavior to eliminate all risks to yourself, your classmates, and the

equipment.

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Homework:

1) The acousto-optic experiment uses a HeNe laser that has a wavelength

of 632.8 nm (red), a minimum spot size of 0.59mm , a divergence (assuming no

additional optics) of 1.35 mrad, and a CW power of 1 mW.

a) What is the MPE? Assume a reaction time of a quarter of a second, sine

this is a visible laser. During typical use in the lab, you will be dealing with

intrabeam viewing situations. How close to the laser would you have to be for

the situation to be considered extended source viewing?

b) Classify this laser.

c) What part of your eye is the most susceptible to this laser, and what are

the possible effects of looking at this beam? Is there a potential for skin damage

(give numbers to defend your answer)?

d) How long can you safely look into this beam? Note you cannot use your

previous MPE value to compute this, since that was based on a specific time of

0.25 sec. You will have to use the functional form.

e) What safety precautions must you take?

2) The laser physics experiment uses a semiconductor laser that emits at

788nm (infrared), has a spot size of approximately 10µm by 1µm, a divergence of

10° parallel (HWHM) to the junction plane and 35° perpendicular to the junction

plane (the lit spot on the surface of the laser is an ellipse, and the emission is also

elliptical, figure next page), and a CW power of up to 50 mW.

a) What is the MPE? Assume it would not take you more than 10 seconds

to realize you are being exposed. You'll have to assume a distance from the laser-

how close are you likely to put your eye to the laser? 5 cm? 2 cm? Is this

intrabeam or extended source viewing?

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EE 737 Photonics Laboratory Manual Safety

23

b) Classify this laser.

c) What part of your eye is the most susceptible to this laser, and what are

the possible effects of looking at this beam? Is there a potential for skin damage?

d) How long can you safely look into this beam?

e) What safety precautions must you take?

f) To use this laser, you will have to collimate the beam. Assuming you

use a 40X lens for this purpose, you will reduce the divergence to about .13°, and

increase the spot to a circle of radius about 0.2mm. Now what is the

classification?

g) Have the precautions needed changed? If so, how?

3. We have two kinds of goggles in the lab. Their attenuation curves are

given below. For each of the experiments above, decide which goggles to use.

Will they provide enough protection?

Optical Density (O.D.)=-log(Pout/Pin)

0

4

6

8

10

2

OPTIC

AL D

EN

SIT

Y

200 300 400 500 600 700 800

Wavelength (nm) Curve A.

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EE 737 Photonics Laboratory Manual Safety

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0

15

10

5

OPTIC

AL D

EN

SIT

Y

300 500 700

Wavelength (nm)

900 11001300 1500

Curve B.

LIBRARY PROBLEM:

This write-up addressed the safety issues with lasers, but what about

very bright incoherent light? Specifically, the light source in the solar cell and

quantum well experiments are 300-W quartz halogen, tungsten filament light

bulbs (ANSI designation ELH), with an approximately 1cm diameter emitting

area. They are incoherent sources, but still quite bright. Is there a danger to your

eyes from these?

Hints: You will need first to determine the energy spectrum of this source,

and find out how much energy is in the ultraviolet, visible, and infrared regions.

An incandescent filament acts as a blackbody radiator, and the temperature is a

function of the power of the bulb. Incandescent sources are also remarkably

inefficient; only about 10% of the electrical power into a standard incandescent

bulb is emitted as visible light.

REFERENCES

[1] C. D. Dekker, “Accident victim's view,” Laser Focus, August, p. 6,

1977. With permission.

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EE 737 Photonics Laboratory Manual Safety

25

[2] F. L. Pedrotti and L. S. Pedrotti, Introduction to Optics, Englewood

Cliffs: Prentice Hall, 1987.

[3] J. A. Smith, “Laser Safety Guide,” , 8th ed: Laser Institute of

America, 1992.

[4] A. Mallow and L. Chabot, Laser Safety Handbook. New York: Van

Nostrand Reinhold Company, 1978.

[5] The Laser Insitute of America, “American national standard for the

safe use of lasers ANSI Z136.1-1986,” , 1986.

[6] D. C. Winburn, Practical Laser Safety, vol. 11. New York: Marcel

Dekker, Inc., 1985.

[7] O. J. McAteer, Electrostatic Discharge Control. New York: McGraw-

Hill, 1990. With permission.

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Figure 5. Relationship between " and k.

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Figure 5. Rays of a particular mode.

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Page 41: PHOTONICS) LABORATORY) ) )

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Figure 6. Bessel functions of the first and second kinds.

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Page 42: PHOTONICS) LABORATORY) ) )

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Figure 7. The fundamental mode. Inside a, the function is a Bessel function of the first

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vertical axis is field strength.

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Figure 8. Fiber refractive index profiles: left, step index; right, graded index.

Page 44: PHOTONICS) LABORATORY) ) )

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Figure 9. Congruent rays in a slab waveguide. After [1]

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L3.)(*M8CD".)C".08"+.448C";<(=<>=2$!42(?3@"-*9&("8P+*(*)9"(&8"0.C*.(*')"A'C8,"*,"4',(

.)C"J*44")'("08.+&"(&8"C8(8+('0D".,,3A*)9"."4')9"8)'39&"@*/80"@'0"(&8,8"A'C8,"('

C*8"'3(F

Page 47: PHOTONICS) LABORATORY) ) )

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$:

n1kn k

2

continuum of

radiation modes quantized guided modes no modes

!

STEP

25 24 23 22 21 20 15 10 m=0

n1

kn k2

continuum of

radiation modes quantized guided modes

!

no modes

GRADED

m=0123456789101112131415161718

Figure 10. Mode spacing in !-space for step and index fibers.

!"#$%&"'()*+,

;("*,"6',,*/48"<'0"8)8091"('"/8"(0.),<8008="<0'>"')8">'=8"('".)'(&80?"@'0

8A.>648B"+'),*=80"(&8"/8)("<*/80",*(3.(*')"*)"@*9308"CC?"-*9&("*,"*)*(*.441

60'6.9.(*)9".(",'>8".)948""!B"/3(".<(80"(&8"<*/80"/8)="*,",3==8)41"60'6.9.(*)9".(

.")8D".)948"""?"E8",.1"(&.("(&8"8)8091"&.,"/88)"#$%&'()"('"(&8"'(&80">'=8?"F&8

<*9308",&'D,"."+.,8"D&808"4*9&("*,"+'3648="<0'>"')8"93*=8=">'=8"('".)'(&80

93*=8=">'=8G"*(">*9&("H3,(".,"4*I841"/8"+'3648="('"."0.=*.(*')">'=8"J.)="4',(K?

Page 48: PHOTONICS) LABORATORY) ) )

!!"#$#"%&'(')*+,"-./'0.('01"2.)3.4 56(*+.4" 78),*)9

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!!

!"

Figure 11. Example of mode coupling, in this case due to a bend.

<&808".08"4'(,"'=">.1,"('"*)?3+8"@'?8"+'364*)9A"*)&'@'98)8*(*8,"*)"(&8

08=0.+(*B8"*)?8C"'="(&8"94.,,D"/3//48,D"*@630*(*8,D"B.0*.(*'),"*)"+'08"0.?*3,D

,+0.(+&8,D"8(+E"F)"60.+(*+8D"@'?8"+'364*)9"*,"608((1"&.0?"('".B'*?E

5)8"+'@@')"+.3,8"'="@'?8"+'364*)9"*,"@*+0'/8)?*)9A",@.44"/8)?,".08

3).B'*?./41"*)+3008?">&8)"+./4*)9"."=*/80D"='0"*),(.)+8E""F)"."+./48D"(&8"=*/80G,H"*,

G.08H",300'3)?8?"/1"B.0*'3,",(08)9(&"@8@/80,".)?"(&8"'3(80"+./48A",@.44"9.6,

+.)"'++30"*)">&*+&"(&8"=*/80"@.1")'("4*8",(0.*9&(E""2*+0'/8)?*)9"*,"."08.4"60'/48@

='0"(&',8"*)"(&8"(848+'@@3)*+.(*'),"/3,*)8,,D"/3("='0",8),'0"68'648"*("*,"."/'')E

I",8),'0"/.,8?"')"@*+0'/8)?*)9"4',,"*,",&'>)"*)"J*9308"KLE"M808D"(>'

+'0039.(8?",30=.+8,"&.B8"."=*/80"03))*)9"/8(>88)"(&8@E"I,"(&8",30=.+8,".08

/0'39&("+4',80"('98(&80"G?*,64.+8@8)(",8),'0HD"(&8".@64*(3?8"'="(&8"/8)?,"*)"(&8

=*/80".08"*)+08.,8?D"+.3,*)9"+'364*)9"=0'@"')8"@'?8"('"(&8")8C(E"7'@8"4*9&(">*44

/8"4',("('"0.?*.(*')D".)?".,"(&8"4.,("@'?8"*,"N8@6(*8?N"'="0.?*.(*')D"@'08">*44"/8

/0'39&("*)"=0'@"(&8"4'>80"'0?80"@'?8,E"<&8"('(.4"'3(63("6'>80".("(&8"?8(8+('0

8)?">*44"?8+08.,8E"<&*,"6.0(*+34.0"4',,"@8+&.)*,@"*,"."08,').)("8==8+(D".)?"(&8

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Page 49: PHOTONICS) LABORATORY) ) )

!!"#$#"%&'(')*+,"-./'0.('01"2.)3.4 56(*+.4" 78),*)9

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fiber

direction of force

Figure 12. Microbending sensor

<4(&'39&"(&*,"*,"(8+&)*+.441"."=*,64.+8>8)(",8),'0?"*("+'34="/8"3,8="('

>8.,308"@'0+8"/1"64.+*)9".",60*)9"/8(A88)"(&8"(A'"+'0039.(8=",30@.+8,?"'0

B*/0.(*')?"'0"(8>680.(308"/1"63((*)9"."/4'+C"'@",'>8">.(80*.4".9.*),("')8"'@"(&8

64.(8,D".,"(8>680.(308"+&.)98,"(&8">.(80*.4"8E6.)=,?"+.3,*)9"=*,64.+8>8)(F"G'30

*>.9*).(*')"*,"(&8"4*>*(F

!"#!$%&'()"!

H*/80"'6(*+",8),'0,".08"98)80.441"'@"(A'"(168,I".>64*(3=8".)="6&.,8F

<>64*(3=8",8),'0,".08"(&',8"*)"A&*+&"(&8".>'3)("'@"4*9&("93*=8="/1"(&8"@*/80"*,

.@@8+(8="/1",'>8">8.,30.)="*)"(&8"8)B*0')>8)(D">'(*')?"(8>680.(308?

0.=*.(*')?">'*,(308?"8(+F"%&.,8",8),'0,".08"*)(80@80'>8(0*+?".)="(.C8".=B.)(.98,

'@"6&.,8"+&.)98,"+.3,8="/1"+&.)98,"*)"(&8"8)B*0')>8)(F

*+,-./012&!234564

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,&'A)"*)"H*9308":"J*F8F"@*/80"8>/8==8="*)"."=*B*)9"/'.0=KF"5(&80,".08"/.,8="')

+'364*)9"4',,8,"/8(A88)"(A'"@*/80,F"H'0"8E.>648?"+'),*=80"(&8".00.)98>8)("*)

H*9308";$F"L808?"(&8"=*,(.)+8"/8(A88)"(A'"'/M8+(,"*,">8.,308="/1"8>/8==*)9".

@*/80"*)"8.+&"'/M8+(F"7*)+8"(&8"4*9&("*)"(&8"8>*((*)9"@*/80"+'>8,"'3(".(",'>8".)948?

(&8".>'3)("'@"(&*,"4*9&("(&.("*,"+'3648="*)('"(&8"08+8*B*)9"@*/80"*,"."@3)+(*')"'@"(&8

=*,(.)+8"/8(A88)"(&8>F

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photodiode

light

emitting

diode

lens

fiber

OBJECT 1 OBJECT 2

Figure 13. A proximity sensor.

7'<8(*<8,"(&8"*)63(".)="'3(63(">*/80,".08"(&8",.<8">*/80?"5)8"'>"(&8

/8.3(*8,"'>"4*9&("*,"(&.("(@'"@.A8,"60'6.9.(*)9"*)"'66',*(8"=*08+(*'),"(&0'39&

(&8",.<8",6.+8"&.A8")'"8>>8+("')"')8".)'(&80?""B1"3,*)9".">*/80"'6(*+"=*08+(*').4

+'36480C".,",&'@)"*)"D*9308"E:C"')8"+.)",3<".)="=*A*=8"/8.<,C"F3,("4*G8"3,*)9".

/8.<,64*((80"*)"+')A8)(*').4"H/34GI"'6(*+,?

Figure 14. Use of a directional coupler and a mirror in a proximity sensor

J&808".08"<10*.="@.1,"('"*<648<8)(".<64*(3=8",8),'0,C".)="1'3"@*44"/8

4''G*)9">'0",'<8"8K.<648,"*)"(&8"60'/48<,?

!"#$%&'()*%+,%+-.%*+/01&2%)$-+$

L)(80>80'<8(0*+",8),'0,"98)80.441"&.A8"(@'"4*9&("6.(&,M"')8"*,".>>8+(8="/1

(&8"<8.,30.)=".)="(&8"'(&80"08<.*),"3)+&.)98=?"J&8"(@'"/8.<,".08"*)(80>808=

('98(&80C".)="(&8"08,34(*)9".<64*(3=8"=868)=,"')"(&8"6&.,8"=*>>808)+8"/8(@88)

Page 51: PHOTONICS) LABORATORY) ) )

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.,",&';)"*)"A*9308"BC=

somebody's foot

reference arm

input

beam

splitter

beam

combiner

E1

E2

output

E + E1 2

L

Figure 15. A Mach-Zehnder fiber interferometer

-8(D,",366',8"(&.("(&8"608,,308"8E80(8F"/1"(&8"?''("')"(&8"?*/80

+'<608,,8,"(&8"94.,,".)F"+.3,8,"."4'+.4"+&.)98"*)"08?0.+(*G8"*)F8E"H(&8"+$,-,'."/-0#

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/8.<,64*((80"(&8"8)8091"*,"F*G*F8F"8K3.441@"(&8"(;'"/8.<,".08" E1! A

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2ej!tej" o =">&8"?*84F"*)"(&8"08?808)+8".0<"8)F,"36"(0.G84*)9"."F*,(.)+8"2@".)F

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Page 53: PHOTONICS) LABORATORY) ) )

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,&'<)"*)"=*9308">?/@"A&*,"*,"B)'<)".,"/*.,*)9"*)"!"#$%#&"%'@"C"+&.)98"*)"(&8

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,8+(*')@

0 !!!" #!!" "!

"#

Inte

rfere

nce term

0 !!!" #!!" "!

"#

"I

"# "#

"I

Figure 16. a) interferometric term of phase-sensitive sensor as a function of phase

difference between two arms; b) same sensor biased in quadrature.

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Page 54: PHOTONICS) LABORATORY) ) )

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Displacement, mm

OU

TP

UT

A=2V

B=1VSensor 1

Sensor 2

Figure 17. Sensitivity and dynamic range of two sensors.

;'")'("+')<3,8",8),*(*=*(1">*(&"08,'43(*')?"08,'43(*')"*,"(&8",@.448,(

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Page 65: PHOTONICS) LABORATORY) ) )

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Page 66: PHOTONICS) LABORATORY) ) )

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0-a a

Inte

nsity

Radius

Figure 4. The field distribution of a single mode fiber.

0

Inte

nsity

-a a

first mode

second

mode

Figure 5. First and second modes (fundamental mode is zeroth mode, not shown)

Figure 6. Intensity distribution in a fiber supporting thousands of modes.

Page 67: PHOTONICS) LABORATORY) ) )

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n2

n1

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2a

corecladding cladding

n (0)1

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Figure 7. Fiber refractive index profiles; left: step; right: graded.

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Page 68: PHOTONICS) LABORATORY) ) )

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80'B3+(>

Figure 8. Dispersion.

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+3006)(>

Page 69: PHOTONICS) LABORATORY) ) )

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photodetector

amplifier

decision

circuit

outputlight

Figure 9. Receiver block diagram.

=&6"+':8.0.('0"+':8.06,"(&6"'3(83(",*>).4"('",':6"(&06,&'4?"@'4(.>6

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a)

b)

c)

Figure 10. a) ideal pulse train; b) dispersed pulse train; c) dispersed pulse train with

noise.

7)".??*(*')"('"?*,860,*')C"(&'3>&C"(&6",*>).4"G*44"/6".((6)3.(6?B"2'?60)

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Page 70: PHOTONICS) LABORATORY) ) )

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Figure 11. Eye diagram.

Page 71: PHOTONICS) LABORATORY) ) )

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Page 76: PHOTONICS) LABORATORY) ) )

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?F3441"+'3)(60+4'+CH*,6@"('"./'3("QO":R"?F3441"+4'+CH*,6@D"";&6"&*J&60"(&6

+3006)(G"(&6"&*J&60"(&6"'8(*+.4"8'H60G",'"(&6"4'H60"(&6"/*("600'0"0.(6"H*44"/6D

>3)T"?;'JJ46",H*(+&"F0')("8.)64@"I&6)"(&6",H*(+&"*,"*)"(&6"03)"8',*(*')G

(&6"A6(6+(6A"600'0,".06"8.,,6A"('"(&6"+'3)(60D"I&6)"(&6",H*(+&"*,"*)"(&6",('8

8',*(*')G"/*(,".06",(*44"/6*)J",6)("'B60"(&6"F*/60"'8(*+"4*)CG"/3("(&6"600'0,"A6(6+(6A

.06")'(",6)("('"(&6"+'3)(60D

M'4AT""?;'JJ46",H*(+&"F0')("8.)64@"I&6)"(&*,",H*(+&"*,"*)"(&6"&'4A"8',*(*')G

(&6"A*,84.1"*,"4.(+&6AG".)A"(&6")3:/60"'F"600'0,",'"F.0".("(&6"(*:6"(&6",H*(+&"*,

F4*886A"*,"A*,84.16AG"!"#$%&&'&($)'*#+*"%$#'$!%$,%#%)#%,$-*,$)'"*#%,$+*#%&*-../0""E)"(&6

Page 82: PHOTONICS) LABORATORY) ) )

!!"#$#"%&'(')*+,"-./'0.('01"2.)3.4 5*/60"78(*+"9'::3)*+.(*'),"-./

#;

+')(*)36":'<6="(&6"<*,84.1"*,"+'),(.)(41"38<.(6<".,"(&6")3:/60"'>"600'0,

+&.)?6,@"A&*,">6.(306"*,"3,6>34"*>"')6"*,"(.B*)?"."4')?":6.,306:6)(=".)<"C.)(,

*)(60*:"06,34(,".(",&'0(60"(*:6"*)(60D.4,"C*(&'3("<*,(30/*)?"(&6"(6,(@"7)6"+.)">4*8

(&6"&'4<",C*(+&"6D601">*D6":*)3(6,="06+'0<"(&6")3:/60="(&6)",6("*("('"+')(*)36

3)(*4"(&6")6E("06.<*)?@

F6,6(G"H%3,&"/3((')"')">0')("8.)64I"J6(,"(&6")3:/60"'>"600'0,"+'3)(6<"('

K60'@

ALG"H5*/60"'8(*+"JA"+'))6+('0="/.+B"8.)64I"A&*,"*,"'8(*+.4"'3(83("('"(&6">*/60

4*)B@

FLGH5*/60"'8(*+"JA"+'))6+('0"')"/.+B"8.)64I"A&*,"*,"(&6"'8(*+.4"*)83(">0':

(&6">*/60"4*)B@

MNA"!FF7F"FOA!"A!JANPQG

A'":6.,306"(&6"R3.4*(1"'>"."(0.),:*,,*')"4*)B="(&6"860+6)(.?6"'>"/*(,"(&.(

.06"*)+'006+(41"<6(6+(6<"*,"+.4+34.(6<@"5'0"6E.:846="."STUV"M!F":6.),"(&.(="')"(&6

.D60.?6=",(.(*,(*+.441",86.B*)?="S"/*("*)"STV"*,"*)+'006+(41"<6(6+(6<@"N)"'0<60"('"/6".

,(.(*,(*+.441",*?)*>*+.)("0.(6=".("46.,("STT"600'0,",&'34<"/6"<6(6+(6<=".,"."0346"'>

(&3:/@

A&*,"806,6)(,",':6":6.,306:6)("80'/46:,">'0"4*)B,"'>",4'C"+4'+B"0.(6,=

,*)+6"(&6"(*:6"06R3*06<"('",6)<"6)'3?&"/*(,"('"80'<3+6"STT"600'0,"+.)"/6"D601

4')?="6,86+*.441"C&6)"600'0,".06"0.0641"<6(6+(6<@"A&6"M!F"(6,(60"&.,".)"*)(60).4

+4'+B"0.(6"'>"S2/*(W,6+@"A'"<6(6+("STT"600'0,">0':".",1,(6:"C*(&".""STUVM!F="STSS

/*(,":3,("/6",6)(="06R3*0*)?"STX",6+')<,="'0")6.041"YZ"&'30,@

Page 83: PHOTONICS) LABORATORY) ) )

!!"#$#"%&'(')*+,"-./'0.('01"2.)3.4 5*/60"78(*+"9'::3)*+.(*'),"-./

#;

'LS198 'LS198

QA

QD

(2)QH

(10) (20)

(1)

(23)

S0S1

QA

Q

(20)

(23)

H

(1)S0S1

+5

(11) (11)(13)(13)

RST RST

RI(2)

RI

'86

(2)

(1)(3)

(1)

(2)'14

MOD

OUT

(2)

+

(4)

DS

Q

(11)

REC

IN(12)

DS

Q

+(10)

R

R

(1)

(3)

(3) (4)

'14

'LS74

'LS74

'86(5) (4)

(5)

(9)

CLK

(13)

RST(L)

'00

(6) (1)

(2)10K

RUN/STOP

+ '14

(3)

(11) (10)

ENABLE

'14 '14(6) (5)

(8)

(9)

10K

+

10uF+

-

RESET

5*<306"=>"?4'+@"A*.<0.:"'B"?!C"(6,(60""DA6,*<)E"F>"?066A*)<G

Page 84: PHOTONICS) LABORATORY) ) )

!!"#$#"%&'(')*+,"-./'0.('01"2.)3.4 5*/60"78(*+"9'::3)*+.(*'),"-./

#;

0.1uF

'04(1) (2)

(3)

510 510

'04

100pF

(4)

1MHz

'04(5) (6)

CLK

+5V

0.1uF

'05

MOD

OUT

1K

70

TX(2,6,7)

HFBR-1412(3)

RX

HFBR-2412

Fiber

(2)

(3,7)0.1uF

115

+5

RECVR

IN

LED

CURRENT

ADJUST

5*<306"=>"94'+?@"'8(*+.4"*)(60A.+6"+*0+3*(,>"BC6,*<)D"E>"F066G*)<H

Page 85: PHOTONICS) LABORATORY) ) )

!!"#$#"%&'(')*+,"-./'0.('01"2.)3.4 5*/60"78(*+"9'::3)*+.(*'),"-./

##

DIGIT 4 DIGIT 2DIGIT 3 DIGIT 1

a

b

c

d

e

f

g

74C947

Vcc

(1)

a4

35

a4

20

b4

b4

21

34

c4

c4

7

2

2 d4

d4

6

23

e4

e4 f4

f4

g4

g4

36375

2426

25

a3

a3

b3

b3

c3

c3

d3 e3

d3 e3

f3

f3

g3

g3

3029

1110

931

32

13 1514 16

17 1819

a2

a2 b2

b2

c2

c2

d2

d2

e2

e2

f2

f2

g2

g2

2524

15 1326

2714

67

89

10 1112

a1

a1

b1

b1 c1

c1

d1

d1

e1

e1

f1

f1

g1

g1

2120

1918

1722

23

3738

3940

24

3

backplane5

1com

com

P1

P1 P2

P2

P3

P3

P4

P4

P4

N.C

.

33

38

39

2

3

4

N.C

.N.C

.N.C

.N.C

.N.C

.

+

LZI

29

LZO

30

N.C

.

OSC

N.C

.

+

UP/DOWN

3

627

ENABLE

ENABLE

3

1

+

10K

HOLD

STORE

34

GND

35

'14

CLK

13 14

32

RST(L)

RESET

5*;306"$<"=*,84.1"*)(60>.+6"+*0+3*(<"?=6,*;)@"A<"B066C*);D

!"#$%&'()"!&%"!*

Page 86: PHOTONICS) LABORATORY) ) )

!!"#$#"%&'(')*+,"-./'0.('01"2.)3.4 5*/60"78(*+"9'::3)*+.(*'),"-./

#;

<"=60)*60",+.46"*,".)"*)>6)*'3,"?6@*+6"3,6?"('"06.?":6.,306:6)(,"('"@601

&*>&".++30.+*6,A"B)"(&6"%&'(')*+,"-./C"1'3":.1"3,6"."=60)*60":*+0':6(60C"D'0

6E.:846C"('".?F3,("."8',*(*')"')"(0.),4.(*')",(.>6,A"B)",':6".884*+.(*')C"1'3")66?

')41"(30)"(&6"G)'/"3)(*4":.E*:3:"+'384*)>"*,"'/(.*)6?C"'0",':6(&*)>",*:*4.0C

.)?"(&6".:'3)("'D"(0.),4.(*')"*,")'("8.0(*+34.041"'D"*)(606,(A"B)"'(&60".884*+.(*'),C

&'H6@60C"1'3"H*44"H.)("('"G)'H"(&.("1'3":'@6?"(&6"ID*/60C"46),C"6(+AJ"6E.+(41

KAKK$L"::M"860&.8,"1'3N06"84'((*)>"+'384*)>"6DD*+*6)+1".,"."D3)+(*')"'D

?*,84.+6:6)(A

9'),*?60".":*+0':6(60",3+&".,"(&.("*)"5*>306"OA""<,"(&6"'3(60"G)'/"*,

(30)6?C"*(".?@.)+6,"'0"06+6?6,".4')>"(&6"&'0*P')(.4",+.46A"Q&6"D*0,("'0?60"'D

/3,*)6,,"*,"('"?6+*?6"H&6(&60"*("*,".":6(0*+"'0"!)>4*,&"=60)*60A"R'3"+.)"3,3.441"(644

/1",*:841":6.,30*)>"(&6"?*,(.)+6"/6(H66)":.F'0"(*+G,"')"(&6":.*)"I&'0*P')(.4"*)

(&6"D*>306J".E*,A"BD"(&6"?*,(.)+6"/6(H66)"K".)?"$"*,"$"+:C"(&6)"(&6"3)*(,".06

+6)(*:6(60A"BD"(&6"?*,(.)+6"/6(H66)"K".)?"OK"*,".)"*)+&C"(&6)"*(N,"80'/./41".)

!)>4*,&A"S'(6"(&.("(&6":.F'0"*)+06:6)(,":.1"/6"::C"'0"OTOKN,"'D".)"*)+&A

7)6"D344"06@'43(*')"'D"(&6"'3(60"G)'/".?@.)+6,"*(,"6?>6"/1"O":*)'0

*)+06:6)(A"-6(N,",388',6"(&.("(&6":.F'0"*)+06:6)(,".06"L"::".8.0(C":6.)*)>"(&6

:*)'0"(*+G,".06"KAL"::".8.0(A"U6"'/,60@6"(&.("(&6"6?>6"&.,"+0',,6?"/'(&"(&6"OV

::".)?"(&6"OVAL"::":.0GC",'"(&6"8',*(*')"*,".("46.,("OVAL::A

0 5 10 15

0

45

40

35

30

S6E("H6"4''G".("(&6":.0G*)>,"')"(&6"'3(60"G)'/A"B)"')6"06@'43(*')C"LK"'D

(&6,6":.0G,"H*44"8.,,"(&6":.*)".E*,C",'"LK"'D"(&6,6":.0G,"6W3.4,"KAL::C"'0"')6

Page 87: PHOTONICS) LABORATORY) ) )

!!"#$#"%&'(')*+,"-./'0.('01"2.)3.4 5*/60"78(*+"9'::3)*+.(*'),"-./

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@G?HI>?J@K@G?;@::?

7)",':6":*+0':6(60,L"(&606"*,".)".DD*(*').4",+.46"')"(&6"*))60",&.F(?"MF

(&606"*,L"1'3"+.)"E6("16(".)'(&60"D6+*:.4"84.+6?"M)"(&*,"+.,6L"1'3"4''<"F'0"(&6"4*)6

')"(&6"4.,("N60)*60"O&'0*P')(.4"*)"(&6"D0.B*)EQ"(&.("!"#$"4*)6,"38"B*(&"%&'""4*)6"')

(&6"'3(60"<)'/R,"6DE6?"M)"(&6"F*E306"/64'BL"*("4''<,"4*<6"(&6"4*)6,"4./646D"STS"4*)6,

38"/6,(L",'"(&6"F*).4"D*E*("*,"STS?"U&6"F*).4"06.D*)E"*,"(&606F'06"@G?;@T"::L"E*C*)E

1'3"."06,'43(*')"'F">?>>@"::"'0"@"!:?

30

25

20

15

10

24

6

8

0

Page 88: PHOTONICS) LABORATORY) ) )

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3(*4*A<>"*)".")3@/<0"'B"=.1,C"*)+43>*)D",=*(+&*)DC",+.))*)D".)>",8<+(03@

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*)(<0.+(*'),".)>"(&<",(3><)("*,".44'=<>"('"<G8<0*@<)("=*(&".,8<+(,"'B"'8(*+.4

/<.@"><B4<+(*')"(&.("+.)"/<"3,<>"B'0"<*(&<0",=*(+&*)DC",+.))*)D"'0",8<+(03@

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Page 89: PHOTONICS) LABORATORY) ) )

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>0*B<"(&<"8*<A'<4<+(0*+"><B*+<D";&<",*C).4"*,"GH"*)"'0><0"('"80'>3+<".)".+'3,(*+

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.)>"(&<">*??0.+(*')".)C4<"*,"><(<0=*)<>"/1"(&<".+'3,(*+"?0<I3<)+1"K*)"(&*,"+.,<

LM2NA"'0",'OD

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+'44*=.(<>D"P'3"F*44")<<>"('"/<"./4<"('"='B<"(&<"+01,(.4",*><F.1,"K,<<"?*C30<O"*)

'0><0"('"J<<8"(&<"/<.="C'*)C"(&0'3C&"(&<"(F'".8<0(30<,".,"1'3"+&.)C<"(&<

.)C4<"'?"*)+*><)+<D

laser

crystal

RF signal in

;&<">0*B<0"&.,"(F'"*)83("8'0(,E"')+<"4./<4<>"Q='>*.)>"')<"4./<4<>"Q(0*K?'0

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Page 90: PHOTONICS) LABORATORY) ) )

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+01,(.4"*,"$*4R>$M"(&<",8<<:"'B",'3):"*)"(&<"+01,(.4"*,"$>#E"P=U,M".):"(&<"(&*+P)<,,

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9&505"!!*,"(&5":05;35)+1"':"(&5"4*<&("',+*44.(*')".)7"!"*,"%4.)+=>,"+'),(.)(?"@&5

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E1

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Figure 1. The three optical processes.

F5G(H"+'),*750"(&5"+.,5",&'9)"*)"(&5"+5)(50"':"I*<305"J?"K)"545+(0')"*,

.,,3L57"('",(.0("*)"(&5"&*<&50"5)50<1",(.(5H".)7"(&5"4'950",(.(5"*,"5LE(1?"K,"1'3

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Page 109: PHOTONICS) LABORATORY) ) )

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Ec

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Figure 2. Distribution of electrons and holes in the semiconductor bands.

G&.(":'347"(&5",E5+(03="'B"(&5",E')(.)5'3,"5=*,,*')"4'';"4*;5>"7'"1'3

(&*);H"I45.041":5"+.)"5FE5+(")'"5)50<1"J*75.441K"/54':"(&5"/.)7"<.E@"G&.(

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Page 110: PHOTONICS) LABORATORY) ) )

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ENERGY

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Figure 3. The gain curve !#"! of a semiconductor

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Page 111: PHOTONICS) LABORATORY) ) )

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Figure 4. E-k diagram of a direct-gap semiconductor, showing conservation of k.

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Figure 5. Pumping of a laser diode by injection under forward bias.

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Figure 6. Generic diode laser structure.

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+.00*50,".05"7*<<3,*)>".A.1"<0'@"(&5"B3)+(*')".)7"05+'@/*)*)>",=')(.)5'3,41D

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J44"@'750)",5@*+')73+('0"4.,50"7*'75,"3,5"."7'3/45K&5(50',(03+(305"('"+')<*)5

(&5"+.00*50,".,",&'A)"*)"H*>305"#D"L&5"5)50>1"/.00*50,".("(&5"B3)+(*'),"G55="(&5

545+(0'),".)7"&'45,"<0'@"7*<<3,*)>".A.1C"@.G*)>"*("5.,*50"('"=*45"(&5@"3="*)"')5

=4.+5K"(&*,"*,"G)'A)".,"+.00*50"+')<*)5@5)(D

L&505".05"."+'3=45"'<"*)(505,(*)>",*75"5<<5+(,"'<"3,*)>"(&*,",(03+(305D"H*0,("'<

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+')(*)35"('",55">.*)".,"(&51"(0.?54D"%&'('),"(0.?54*)>".(",'@5".)>45"('"(&5

B3)+(*')"=4.)5"A*44"5?5)(3.441"@'?5"'3(,*75"(&5">.*)".05.".)7"/5"4',(D"J4,'")'(*+5

(&.("/5+.3,5"(&5"(A'"@.(50*.4,"')"(&5"'3(,*75"&.?5"A*75"/.)7">.=,C"(&51".05

5,,5)(*.441"(0.),=.05)("M./,'0=(*')"*,)F("=',,*/45N"('"(&5"=&'('),"/5*)>"+05.(57"*)

Page 115: PHOTONICS) LABORATORY) ) )

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(&5"!"#$%&'(!)&*:"/5+.3,5"(&5*0"5)50;1"<*44"+'),*,(5)("<*(&"(&5"/.)7";.="'>"(&5

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=&'('75(5+('0,BC

Ec

FE

v

E

AlGaAs GaAs AlGaAs

Figure 7. Use of double heterostructure to confine carriers.

D*).441:",*)+5"(&5"(<'"@.(50*.4,"*)"(&5"&5(50',(03+(305"&.?5"7*>>505)(

*)7*+5,"'>"05>0.+(*'):"."+!%&,-$.&'*,"+05.(57".,",&'<)"*)"D*;305"EC"F5+.3,5"(&5

05>0.+(*?5"*)75G"*,"&*;&50"*)"(&5""/*&"(&.)"*)"(&5""(!..$0,:"H)544I,"4.<"=057*+(,"(&.(

4*;&("(0.?54*);".(",&.44'<"5)'3;&".);45,"+.)"/5"#/#!(()'$0#&*0!(()'*&1(&"#&.".("(&5

*)(50>.+5,:"&54=*);"('"+')>*)5"(&5"4*;&("('"(&5";.*)"05;*')C"J&*,"*,"K)'<)".,"/2#$"!(

"/01$0&3&0#4

core

cladding

cladding

n2

n1n

2

refracted

!

p

p

n

longitudinal

direction

transvers

e

lateral

Figure 8. Optical confinement in double heterostructure.

J&5"@.G*@3@".);45">'0"."0.1"('"/5";3*757"*,";*?5)"/1

''"",*)[email protected] !

0L08 MEN

Page 116: PHOTONICS) LABORATORY) ) )

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.)7"E0.757A*)75@",5>.0.(5A+')<*)5J5)("&5(50',(03+(305"KLM;NOPQRB"('").J5".

<5=G";)"(&5"LM;NOPQ"4.,50B"(&5"+'J>',*(*')"'<"(&5"+4.77*)E"4.150,"*,"?.0*57

+')(*)3'3,41B".)7"(&505<'05",'"*,"(&5"05<0.+(*?5"*)75@G"H&*,"&.,"(&5"5<<5+("'<

+')(*)3'3,41"/5)7*)E"(&5"/5.J,",'"(&.("(&51"(0.?54"."+30?57">.(&".)7".05

+')(*)3.441"/5)("/.+C"('=.07"(&5"+'05G"H&5"S,5>.0.(5"+')<*)5J5)(S",(03+(305"&.,

."+5)(50"=544"<'0"+')<*)*)E"+.00*50,B".)7".)"'3(50"4.150"('">0'?*75"."4.0E5"5)'3E&

*)75@"+&.)E5"<'0"5<<5+(*?5"*)75@"E3*7*)EG

n1

n2

(a) (b) (c)

(d)(e)

Figure 9. Various lasers refractive index profiles (transverse): a) double

heterostructure, b) single quantum well, c) multiple quantum well, d) separate

confinement heterostructure, and e) GRINSCH

Page 117: PHOTONICS) LABORATORY) ) )

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=*>305"89J+K",&'H,"."0*7>5"H.<5>3*75D")'(5"(&.(".4(&'3>&"(&5".+(*<5"4.150"*(,54C"*,

)'("/'3)757"4.(50.441"/1"."05C0.+(*<5"*)75@"+&.)>5E""(&5"4*>&("*)"(&5"4.,50"&.,

5<.)5,+5)("(.*4,"'3(,*75"(&5".+(*<5"4.150"*(,54CD".)7"(&5,5"5<.)5,+5)("(.*4,

5@B50*5)+5"(&5"*)75@">3*7*)>"*)"(&5"0*7>5F"L5.0"*)"A*)7"(&.("(&5"(50A"M*)75@

>3*7*)>M""'0"M>.*)">3*7*)>M"J7*,+3,,57")5@(K".4H.1,"05C50,"('"(&5")*+$,*)"7*05+(*')E

,*)+5"*("*,".,,3A57"(&505"*,"*)75@">3*7*)>"*)"(&5"(0.),<50,5"7*05+(*')F

metal contact

active layer

P

N

N N

n

oxide

(a)

P

N

(b)

P

N

(c)

Figure 10. Index guided laser structures: a) buried heterostructure, b) buried-

crescent, and c) ridge-waveguide.

G"'*!"-'(!#$#&4.,50E"&'H5<50E"*,",4*>&(41"7*CC505)(F";&5"4.(50.4">3*7*)>"*,",(*44

+.3,57"/1".)"*)75@"+&.)>5E"/3("(&5"*)75@"+&.)>5"*,)N("735"('"."+&.)>5"*)

Page 118: PHOTONICS) LABORATORY) ) )

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%30541"=.*)E=3*7*)=",(03+(305,".05".?'*757"*)"G0.+(*+5"/5+.3,5"(&51"3,3.441"&.?5

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=.*)E=3*7*)=;

ion implant

(non-conductive)

Figure 11. Proton-implanted gain guiding laser diode.

!"#$%&%'($)'*+&,(+&-*'./('0"(1&2!.3)"!$'(+&-*'.

<)"(&5"<)(0'73+(*')A"C5":5)(*')57"(&.("4.,50"05K3*05"(C'"(&*)=,L"=.*)A".)7

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Page 119: PHOTONICS) LABORATORY) ) )

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Figure 12. The Fabry-Perot cavity.

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Page 120: PHOTONICS) LABORATORY) ) )

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8 7 08 6 58 6 0

Wavelength (meters)

R1=R2=0.9

R1=R2=0.7

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Figure 13. Transmission of Fabry-Perot Cavity

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Page 121: PHOTONICS) LABORATORY) ) )

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(&5"+.A*(1"@*44"5H+*(5"<'05"B&'('),"N3,("4*P5"*(>"Q'(*+5"(&.(",'<5"B&'('),",55

<'05";.*)"(&.)"'(&50,C"/5+.3,5"'D"(&5"5)50;1C",'"(&51".05"<'05"4*P541"('

05B0'73+5>"?&5"%LM"+30A5"'D"."(1B*+.4"4.,50"*,"",&'@)"*)"E*;305"89>"?&5"(&05,&'47"*,

75D*)57"/1"5H(0.B'4.(*);"(&5"4*)5"*)"(&5"4.,*);"05;*')"/.+P"('"(&5".H*,>

Page 123: PHOTONICS) LABORATORY) ) )

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889

P (mW)

I (mA)I th

Figure 14. The power-current curve of a diode laser.

:5;("45(<,"4''=".("&'>"(&5"4.,*)?"@'75,"75A54'BC"D54'>"(&05,&'47E"(&505"*,

/0'.7/.)7",B')(.)5'3,"5@*,,*')E"F*?305"89.C"G&505"*,",'@5"(&05,&'47"+3005)(E

./'A5">&*+&"4.,*)?"/5?*),C"H,">5"0.*,5"(&5"+3005)("45A54E"(&5"+30A5"*)"F*?305"89.

@'A5,"3BE"@5.)*)?"(&505"*,"@'05"5)50?1".("5.+&">.A545)?(&C"D5+.3,5"'I"(&5

F./01J%50'("+.A*(1E"&'>5A50E"+50(.*)">.A545)?(&,".05"B05I50057"/1"(&5"+.A*(1C

H,"(&5,5"+.A*(1"@'75,",55"5)'3?&"?.*)"('"4.,5E"(&51"/5?*)"('"@34(*B41".("(&5

5;B5),5"'I"(&5")')J05,').)(">.A545)?(&,C"G&5"@'75",55*)?"(&5"&*?&5,("?.*)"K*)

(&5'01L"?5(,".@B4*I*57",'"@3+&"(&.("*("3,5,"3B".44"(&5"545+(0'),E".)7")')5"'I"(&5

'(&50"@'75,">*44"?5("."+&.)+5"('"4.,5C"M)"B0.+(*+5E"&'>5A50E"7*'75"4.,50,"+.)

'B50.(5"*)"@'05"(&.)"')5"!"#$%&'(%#)!"@'75"K05,').)("@'75".4')?"(&5

4')?*(37*).4"7*05+(*')LE".)7"'I(5)"(&5"5)50?1"*,"/'3)+*)?".0'3)7"/5(>55)"(&5@

,'"I.,("1'3"7')<("75(5+("*(C"N&5)"1'3"@5.,305"(&5",B5+(03@"'I"(&5"4.,50E"1'3

@5.,305"(&5".A50.?5".@'3)("'I"B'>50"*)"(&5"A.0*'3,"4')?*(37*).4"@'75,"'A50

(&5"@5.,305@5)("(*@5C"MI"(&5"4.,50"1'3".05"@5.,30*)?"*,"@34(*@'75E"1'3">*44

B0'/./41")'(*+5"(&.(".(",'@5"+3005)("45A54,"(&505".05"@'05"@'75,"(&.)"'(&50,C

Page 124: PHOTONICS) LABORATORY) ) )

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889

thresholdgain

0

loss

gain

0

loss

0

outp

ut

outp

ut

outp

ut

wavelength

F-P

modes

wavelength

Figure 15. Evolution of lasing: a) below threshold, all emission is spontaneous, b)

above threshold, first mode sees gain, begins to lase c) well above threshold,

higher order modes can oscillate.

Page 125: PHOTONICS) LABORATORY) ) )

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(&5"(5<=50.(305"+.05:3441"'0"(&5"4.,*);">.I545);(&">*44"+&.);5B"9&5"5::*+*5)+1"':

(&5"4.,50".4,'"75+05.,5,">*(&"(5<=50.(305B"C)"=0.+(*+5"."=&'('75(5+('0?".4');">*(&

."(&50<*,('0".)7"."(5<=50.(305"+')(0'4450".05"3,3.441"*)+43757"*)"(&5"4.,50

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.)7"H5=("+'),(.)("3,*);":557/.+H"4''=,B

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(&5"5)50;1";.="':"(&5",5<*+')73+('0?">&*+&"*,".4,'".":3)+(*')"':"(5<=50.(305B"C:

(&5";.*)"+30I5"<'I5,"5)'3;&"*(">*44"+.3,5"."7*::505)("@./01A%50'("<'75"('"/5

.<=4*:*57B"9&5"5D3.(*')":'0"(&5"+&.);5"*)"/.)7";.="5)50;1">*(&"(5<=50.(305"*,

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,5<*+')73+('0"7*'75"4.,50"/5.<,".05"3,3.441"&*;&41"7*I50;5)(B"9&.("*,"/5+.3,5

(&5"'3(=3(".=50(305"':"(&5"4.,50"*,"(*)1"+'<=.057"('"(&',5"':"'(&50?"<.+0',+'=*+

4.,50,?".)7"(&.("(*)1".=50(305"+.3,5,",3/,(.)(*.4"7*::0.+(*')B"9&5".+(*I5"4.150

(&*+H)5,,"*,"(1=*+.441"')"(&5"'0750"':".":5>"(5)(&,"':"."<*+0')?".)7"(&5">*7(&"':

(&5"4.,*);",='("E*)"(&5"4.(50.4"7*05+(*')G"<.1/5"45,,"(&.)"8O"<*+0'),B"E9&5"45);(&

':"(&5"4.,50"*,"3,3.441"."+'3=45"&3)7057"<*+0'),?"('"=3("(&*);,"*)"=50,=5+(*I5BG

9&5"7*::0.+(*')".);45"':"."/5.<"':">.I545);(&"""(&0'3;&".)".=50(305"':

>*7(&"!"*,";*I5)".==0'J*<.(541"/1

Page 126: PHOTONICS) LABORATORY) ) )

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";8<=

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*?@4*+.(*')F",*)+5"(&5"5?*,,*')".@50(305"*,"#$%&&'(!*)"(&5"7*05+(*')"@50@5)7*+34.0

('"(&5"G3)+(*')"@4.)5>"(&5"7*B50C5)+5"*,"")*'("*)"(&*,"7*05+(*')D""E1@*+.4"!$H,".05"')

(&5"'0750"'I"$JKD"L)"(&5"4.(50.4"7*05+(*')>"@.0.4454"('"(&5"G3)+(*')"@4.)5>"(&5

7*II0.+(*)C"M.@50(305M"*,")'(".,"A*75>".)7"!++""*,"+4',50"('"8JK>",(*44")'("+'44*?.(57

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E&505I'05>"(&5"/5.?"@.((50)>"A&*+&"4''N,"4*N5"."&'0*O')(.4"544*@,5"*)"(&5

,'%(!-)'&*>"4''N,"4*N5"."B50(*+.4"544*@,5"*)"(&5"-%(!-)'&*.""P*C305"8Q/!"E&5"(50?"MI.0"I*547M

?5.),"(&.("1'3".05"4''N*)C".("."4*C&("/5.?".(",'?5"7*,(.)+5"0""I0'?"(&5",'30+5>

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.)7"*)"(&5")5.0"I*547"A&5)

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#;8#=

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Figure 16. Output pattern of a diode laser (edge-emitting).

R&.("7'5,"(&5"*)(5),*(1"7*,(0*/3(*')"4''N"4*N5S"2',(",5?*+')73+('0"4.,50,

@3("'3("/5.?,"A&*+&".05".@@0'T*?.(541"4'($)2'56%3##)%,/"E&.("*,>"(&5"I*547"7"'I

(&5"4.,50"*)"(&5"(0.),B50,5"7*05+(*')"8"*,"75,+0*/57"/1

Page 127: PHOTONICS) LABORATORY) ) )

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E3)+(*')G".)7"(&5"05,("*,".")'0F.4*L*)C"+'5EE*+*5)(G",'"(&.("(&5"('(.4"5)50C1"*)"(&5

E*547"*,"')5M"N&5",J'(",*L5"*,"C*D5)"/1"&,'-":*("*,"."E3)+(*')"'E"(&5"J0'J.C.(*')

7*,(.)+5",*)+5"(&5"/5.F"7*D50C5,;M"N&505"*,".",*F*4.0"5HJ05,,*')"E'0"(&5"F'75

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F'75,":#!".)7".;".05"(&5"12$*3$4"F'75,"'E"(&5"4.,50,G".)7"."C''7"4.,50"B*44"',+*44.(5

*)"')41"')5G"E3)7.F5)(.4"F'75M"O)"(&*,"+.,5"%56G".)7"(&5"*)(5),*(1"7*,(0*/3(*')"*,

."J305"K.3,,*.)":(&5"I50F*(5"J'41)'F*.4"*,"8;G"P*C305"8#".M""N&5"47%83*9:3%$4

;7:)1"'E"(&5"4.,50".05"(&5"P./01Q%50'("F'75,"B5"7*,+3,,57"5.04*50M

Mode 0 Mode 1 Mode 2

distance across beam

Figure 17. The Hermite-Gaussian intensity distributions for the first three spatial

modes.

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R'"E.0"B5"&.D5"7*,+3,,57"')41"57C5Q5F*((*)C"P./01Q%50'("4.,50,M"P'0

+'FJ45(5)5,,G"B5"B*44"/0*5E41"F5)(*')",'F5"'E"(&5"'(&50"(1J5,"'E"4.,50,"(&.(".05

+3005)(41".D.*4./45S

Page 128: PHOTONICS) LABORATORY) ) )

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.("(&5"5)7,D";&5,5"B*00'0,".05")'("+45.>57"@.+5(,F"/3(".05"0.(&50"B*00'0",(.+K,A

.4(50).(*)C"4.150,"'@"(J'"7*@@505)("05@0.+(*>5"*)75L"B.(50*.4,D";1I*+.441"9:A8::

4.150,F"(&5,5"B*00'0,"+.)"/5"75,*C)57"@'0"&*C&"'0"4'J"05@45+(*>*(1D"M'(*+5"(&.("*)

(&*,"4.,50F"(&5"+.>*(1"*,"5L(05B541",&'0(A"(&*,"&.,"(&5"5@@5+("'@",I05.7*)C"(&5"G./01A

%50'("+.>*(1"B'75,">501"@.0".I.0("*)"@05N35)+1F",'"(&.("(&5,5"4.,50,"'I50.(5"*)".

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&.>5">501"4'J"(&05,&'47,D

substrate

mirror

stacks

active layer

Figure 18. The vertical-cavity surface emitting laser (VCSEL).

6*,(0*/3(57"G557/.+K"-.,50"?"O.(&50"(&.)"3,5"(&5"B*00'0,"('"I0'>*75

'I(*+.4"@557/.+K"/1"05@45+(*)C"4*C&("/.+K".)7"@'0(&".4')C"(&5"+.>*(1F"."C0.(*)C

,(03+(305"*,"*)+'0I'0.(57"*),*75"(&5"4.,50F"G*C305"8PD";&5"C0.(*)C"*,"B.75"/1

5(+&*)C"."I50*'7*+",(03+(305"*)('"(&5",5B*+')73+('0F"(&5)"@*44*)C"*("*)"J*(&".)'(&50

B.(50*.4D"Q,"(&5"B'75"I0'I.C.(5,".4')C"(&5"+.>*(1F"I.0("'@"*("K55I,"5LI50*5)+*)C

I50*'7*+">.0*.(*'),"*)"(&5"05@0.+(*>5"*)75LF".)7"05B5B/50"."+&.)C5"*)"*)75L

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B'75D"R'B5(*B5"(&5"C0.(*)C"*,"I3("'3(,*75"'@"(&5"+.>*(1"S'0"'3(,*75"(&5"C.*)

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Page 129: PHOTONICS) LABORATORY) ) )

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(&5"/5.D"&.,"45,,"7*<50@5)+5>"M*).441F"(&5"'=(*+.4"='C50"'E"(&5".00.1"+.)"/5"<501

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'E"='C50F"(&5"/5.D"C'347"75,(0'1"(&5"'3(=3("E.+5(>

n1

n2

n1

n2

Figure 19. Distributed feedback laser (top) and distributed Bragg reflector laser

(bottom).

lasing stripes (coherently coupled)

Figure 20. A phased laser array (evanescently coupled).

Page 130: PHOTONICS) LABORATORY) ) )

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Page 131: PHOTONICS) LABORATORY) ) )

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Page 132: PHOTONICS) LABORATORY) ) )

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Page 133: PHOTONICS) LABORATORY) ) )

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Page 134: PHOTONICS) LABORATORY) ) )

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F.B545)H(&"+.)"/5"=5.,3057D

detector

source mirrorsgrating

Figure 1. Structure of a monochromator

E&5"05,'43(*')"'C"(&5"=5.,305=5)("75<5)7,"')",5B50.4"(&*)H,D"G'0"')5

(&*)HJ"(&5"4')H50"(&5"'<(*+.4"<.(&".C(50"(&5"7*,<50,*B5"545=5)("@*)"(&*,"+.,5"(&5

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Page 136: PHOTONICS) LABORATORY) ) )

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4*C&(",'30+5D

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Figure 1. Main screen of data acquisition program.

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Page 138: PHOTONICS) LABORATORY) ) )

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136

QUANTUM WELL DEVICES

INTRODUCTION

Quantum well devices have some very interesting and useful optical

properties. Aside from the fact that you can observe and believe in actual

quantum mechanics by measuring these devices, their importance in optical

modulation, particularly at high speeds, is increasing all the time.

We will review some basic quantum mechanics principles, then discuss

some specific devices. In the laboratory, you will be measuring electro-

absorption in some quantum well optical detectors. You will see the effects of

quantized energy levels, and the existence of excitons. You will believe.

REVIEW OF QUANTUM MECHANICS

You recall that quantum mechanics deals with very small objects, such as

electrons, atoms, photons, etc. Each of these can be thought of as either a particle

or a wave, depending on which is more convenient. For example, a photon,

which is a quantum of electromagnetic wave energy oscillating at some angular

frequency !, has energy E=h!, where "=!/2# is the frequency in Hz. Similarly, a

phonon is a quantum of acoustic energy (lattice vibration at angular frequency !,

whose energy is E=h!, or E = h! , where h is h/2".

We generally want to find out what is going on with electrons- what

energies can they have in a particular system, what is their average position, etc.

These things are found by solving Schrodinger's equation, which, to remind you,

is:

!

h2

2m"

2#(x ,y , z,t) + V(x , y, z)#(x, y ,z,t) = !

h

j

$#

$t [1]

where m is the mass. In semiconductors, of course, we'd use m* , the effective

mass. This equation is separable (for problems we'll encounter here) into time-

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EE 737 Photonics Laboratory Manual Quantum Well Devices

137

dependent and time-independent parts. We'll only discuss non-time-varying

potential distributions V(x,y,z), so the two equations are then:

! 2"

!x2+

2m

h2

E # V(x)( )" = 0

!$

!t+

jE

h$ = 0

[2]

Notice that we have written these equations for a one-dimensional case.

The constant E is the energy associated with a particular !, or a particular state.

The time-independent wavefunction ! is a function only of space (in this case,

the one dimension x), and the time dependent part is ". Since the second

equation is always the same for cases we'll consider, the time-dependent solution

is always going to be

!(t) = e" j#t [3]

The solution to the time-independent Schrodinger's equation depends on

the actual system being analyzed, which is described by V(x). For example, in the

infinite potential well extending from x=0 to x=L, where V(x)=0 inside the well,

and goes to ! outside, the wavefunctions are sinusoidal, and have one hump for

!1, two humps for !2, etc. The solution to Schrodinger's equations (the

wavefunctions) are:

! n =2

Lsin

n"L

x#

$

%

& [4]

and the allowed energies (there is an infinite number of them) are given by

En =n

2!

2h

2

2mL2

(infinite potential well) [5]

where n is an integer naming the particular state, m is the mass of the electron,

and L is the width of the well. Figure 1 shows the first few solutions.

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EE 737 Photonics Laboratory Manual Quantum Well Devices

138

x=0 x=L

! !

!1

!2

!3

! !

x=0 x=L

E 1

E

E

E4

3

2

Figure 1. The infinite potential well. On the left, the first three wavefunctions are

shown. On the right, the first four allowed energy levels are shown.

The wavefunction ! has no physical meaning, of course, but the quantity

!"! represents a probability density function. So for example, the most probable

location for the electron in state E1 is in the middle of the well, because that's

where the probability density function !*! is the highest for that state.

In a finite well, Figure 2, the potential energies outside the well are not

infinite. This results in wavefunctions that are mostly confined to the well, but not

completely. Since ! is non-zero outside the well, then the probability density

function !*! is also non-zero outside the well. This implies that the electron in

one of the confined states spends some fraction of its time actually outside the

well. Another way to look at this is that the electron, which is oscillating back

and forth in the well, actually penetrates the barriers a little bit. Note that there

are a finite number of solutions in a finite well; if the energy of the state gets

higher than the edge of the well, the electron won't be confined to the well, and

will appear to be a quasi-free electron. There is a quasi-continuum of states above

the top of the well.

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139

V

x=0x=L

!1

!2

V

x=0 x=L

"

"

"

1

2

3

continuum of states

Figure 2. The finite potential well. Left: first two wavefunctions. Note that they

extend outside of the well. Right: This well contains three discrete energy levels.

HETEROJUNCTIONS

All of the above should be familiar. If it isn't, go back to your notes from

EE331 and go through that material again. Meanwhile, a question that comes up

every quarter is, "So, where do these potential wells come from? How do you

make one?" The answer is "heterojunctions".

A heterojunction is a junction between two different materials. For

example, a simple silicon pn-junction diode is a homojunction because it has

silicon on both sides, even though the side may be doped differently. But a

junction between, say, GaAs and AlGaAs is a heterojunction. Each of these

materials has a different band gap, so at the junction some discontinuities occur

in the conduction band edge and valence band edge.

We will now develop the procedure for drawing the energy band diagram

for a heterojunction (or any junction, for that matter). For example, consider a

junction between a chunk of n-type material and a chunk of some different p-

type material, as shown in Figure 3.

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EE 737 Photonics Laboratory Manual Quantum Well Devices

140

p n

Figure 3. A pn junction.

We'll need to know several material properties in order to proceed. The

work function, !, is the amount of energy needed to remove an electron from the

Fermi level to the vacuum level. In a semiconductor, however, there are usually

no states at the Fermi level, so perhaps the work function is not the most useful

number to know. In fact, the work function of a semiconductor will depend on

the doping since the location of the Fermi level depends on the doping. For

semiconductors, we use the electron affinity, ", which is the amount of energy

require to move an electron from the bottom of the conduction band to the vacuum level.

Consider a specific junction, of which we'll construct the energy band

diagram. Let the p-type material be GaAs, doped with NA = 1#1018. The electron

affinity " for GaAs is 4.07 eV, and the band gap is 1.43 eV. [1] We have to

calculate the location of the Fermi level; it is EF-EV=0.414 eV.

The n-type material we'll take to be Al.3Ga.7As, which is a material like

GaAs except that 30% of the atoms which would have been Ga have been

replaced with Al. This is a ternary material, meaning it has three different

elements in it. The electron affinity for Al.3Ga.7As is 3.74 eV, and the band gap is

1.8 eV. Let this material be doped with ND=1.5#1017cm-3, resulting in EC-

EF=0.41 eV. Figure 4 shows the individual energy band diagrams before the

materials are "joined".

Now, we are interested in the energy band diagram of the junction. To

construct an energy band diagram for anything, the following rules are applied:

1. The Fermi level is constant (flat) at equilibrium.

2. Evac is continuous.

3. Eg and " are constant in any given material.

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141

To draw the energy band diagram for the diode, we start with rule 1. The

Fermi level is flat, so start by drawing a straight line, Figure 5. Next, we

construct the energy band diagrams of each material, one on the left and one on

the right.

EF

!=4.07

vac

Eg

E

E

E

EV

C

F

!=3.74

EiEg

GaAs

=1.43=1.8

Figure 4. Energy band diagrams for GaAs and Al.3Ga.7As as described in text.

EF

!=4.07vac

Eg

E

E

E

EV

C

F

!=3.74

EiEgGaAs

=1.43

=1.8

Figure 5. Energy band diagram under construction.

Next, we invoke Rule 2: Evacis continuous. Therefore, the two Evac's must

be connected in some smooth, continuous fashion, as shown in Figure 5. Finally,

we invoke Rule 3: Eg and ! are constants of the material. Now, ! for each material

is a constant, but it is different for the two different materials. That means that EC

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142

is a constant distance from Evac on each side of the junction, but there will be a

discontinuity in EC at the junction. Similarly, Eg is a constant for each material,

and so EV will run parallel to EC in each material, but there will be a

discontinuity in EV at the junction. Figure 6 shows the completed energy band

diagram for this junction. In this particular example, the discontinuity in EV isn't

very obvious, but it's there. This procedure, which works for any junction

between any materials, is known as the electron affinity rule (EAR) or the

Anderson Model (really). Note that for different choices of materials or even

doping, the "dip" could appear in the valence band edge instead.

EF

!=4.07vac

Eg

E

E

E

EV

C

F

!=3.74

EiEgGaAs

=1.43

=1.8

Ei

AlGaAs Figure 6. Energy band diagram for this particular heterojunction.

There is a potential well in this figure These wells that form at the

junction are very narrow, and so they can actually be thin enough to be quantum

wells- the energy states in the well can be quantized (Figure 7). The number of

levels in the well depend on the well depth and width. The barrier on the right

side of the well can also be thin enough for tunneling to occur.

Figure 7. Quantum well results from heterojunction.

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143

There are other ways to make quantum wells, however, the most common

being the double heterostructure. In the double heterostructure, the narrow-gap

material is sandwiched between two layers of wide-gap material. In Figure 8, an

idealized sketch of the energy band diagram is shown. Note that at each junction,

there will be some band bending and these discontinuities in the conduction and

valence band edges, but we're leaving those out to show the big picture.

Nevertheless, you can see that if the layer of narrow-gap material is thin enough,

the depression in the conduction band edge could be narrow enough to be a

quantum well, usually less than about 100Å. Again, the narrower the well, the

fewer the number of confined states.

GaAsAlGaAs AlGaAs

Ec

Ev

E

distance Figure 8. Idealized energy band diagram of a double heterostructure.

Some devices are made with multiple quantum wells. Successive layers

are laid down by molecular beam epitaxy or metal-organic chemical vapor

deposition. These layers must be carefully controlled for composition and

thickness. Also note that any imperfection at the interfaces are likely to provide

recombination paths, hence leakage currents can be a problem.

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144

E D(E)

x

Energy Band Diagram Density of States

continuum

continuum

forbidden

xD(E)

n=1n=2n=3

n=1n=2n=3

xy

Physical Device

y

E

D(E)

E

D(E) Figure 9. Comparison of various structures and bulk material. From top to

bottom: 3-D (bulk), 2-D (quantum well), 1-D (quantum wire) and 0-D (quantum box).

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145

QUANTUM STRUCTURES

Let's compare quantum structures to bulk material. For example, a double

heterojunction material in which the potential well is wider than 100Å behaves

essentially like bulk material. Figure 9 shows some key differences between bulk

and quantum structures. Notice that if we confine the electron in one direction,

leaving it essentially two dimensions in which to travel, the density of states is a

step like structure. Also notice that there are no energy states at the bottom of the

well- the first state is always somewhere above the bottom of the conduction

band (for electrons) and somewhere below the top of the valence band (for

holes). When you get to this first energy, you suddenly add a whole plane of

states. That's why the density of states function looks the way it does.

One can also confine the electron in two dimensions, leaving it free to

travel in only one direction, resulting in quantum wires. One may even speak of

quantum boxes, which have confinement in all three directions. We'll restrict

ourselves to 2-dimensional quantum wells here, however.

EXCITONS

One of the important difference between quantum wells and bulk material

is the effect of excitons. An exciton is a sort of non-intuitive thing- the standard

line is that an exciton is an electron and a hole orbiting around each other. This is

a little hard to picture, so look at Figure 10. In the energy band diagram, we say

the electron is oppositely charged form the hole, so on the average, they'll be

slightly attracted to each and tend to stay in more or less the same physical area.

A look at the crystal picture shows that the electron and the hole are both

moving around, at some average distance from each other (about 140Å in bulk).

At these distances, there can be many atoms between them, effectively screening

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146

the charge. This means that excitons are extremely loosely bound, and it takes

very little energy (about 4.2meV) to separate the electron from the hole. In fact,

at room, temperature, you'll never observe the effects of excitons in bulk

materials.

EC

EV ++

Figure 10. Exciton in bulk material.

In a quantum well, however, the electron and the hole are artificially

confined by the well itself, so they have to stay closer to each other; remember

that a quantum well is less than 100Å wide. This is smaller than the bulk exciton

radius. Figure 11 shows the wavefunctions for an electron and a hole in the

quantum well.

The exciton has an interesting effect on the absorption of this material.

Normally, you'd expect to see no absorption at energies smaller than Eg+E1+E2.

The binding energy B of the exciton, however, reduces the actual energy needed

to move the electron from the valence band to the conduction band, which

creates this exciton. This results in an absorption peak associated with the

exciton, which appears at a photon energy

Eabsorbed= Eg+E1+E2.-B [6]

which can be seen on the right hand side of the figure.

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147

Eg

E1

E2

ideal

exciton

absorp

tion

Photon energy Figure 11. Wavefunctions of electron and hole confined to quantum well.

But even that's not the whole story. After all, there could be more than one

level in the wells, meaning there could be more than one exciton. That results in

an absorption spectrum that looks like Figure 12a. Furthermore, there are really

two different types of holes in the valence band, heavy holes and light holes.

Since effective mass depends on the curvature of the E-k diagram, there are two

lines on the E-k curve for the valence band. In bulk material these two are

degenerate at the top of the valence band, but the quantum well structure

destroys the degeneracy of the heavy hole and light hole bands, so it is possible

to sometimes observe double peaks, Figure 12 b.

ELECTRICALLY CONTROLLABLE OPTICAL EFFECTS IN

SEMICONDUCTORS

There are several electro-optical effects that can be exploited in

semiconductors, which fall into three general categories: electroabsorption,

electrorefraction, and the electro-optical effect. These are actually all the same

thing, and we'll show why.

Electroabsorption is the change in absorption under the influence of an

electric field. Electrorefraction is the change in refractive index with applied

field. The absorption coefficient ! of a material (at a particular wavelength) is

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148

abso

prt

ion

n=1

n=2n=3

photon energy

ab

sop

rtio

n

photon energy

lhhh

E

kBulk Quantum

Well

(a) (b) Figure 12. a) multiple excitons; b) heavy and light holes

actually interrelated with the refractive index no., by what are known as the

Kramers-Kronig relations. The complex index of refraction is given by:

˜ n = no + i!c

2"# [7]

where ̃ n is the complex index of refraction, c is the speed of light in vacuum, and

! is the frequency of the light. The point is, if something causes a change in " ,

there will also be a change in no; they are not independent. Therefore

electroabsorption and electrorefraction are different manifestations of the same

thing. You can change absorption to turn a beam on and off (amplitude

modulation), for example, or use the same material and the same effect to phase

modulate a beam by exploiting the change in refractive index. Electrorefraction

can be used for beam steering and guiding as well.

One way to change the refractive index in semiconductor is to inject

current. The presence of the carriers themselves changes the refractive index

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149

slightly[2, 3], an effect which is exploited a great deal in confining the beam in

lasers diodes to the active layer, where optical gain is present.

Many materials, not just semiconductors, exhibit the electro-optic effect,

meaning that the refractive index changes with applied electric field. The electro-

optic effect in this sense refers to a change in refractive index resulting from the

crystal structure shifting slightly under field. The idea is that in a particular

crystal, the atoms are arrange in such a way that they have some dipole

moments. When a field is applied, depending on the direction of the field, the

dipoles move a little, and since this changes the crystal structure, it changes the

refractive index. The refractive index is then written as a power series in the

applied field:

n(E) = no !

1

2rn

3E !

1

2sn

3E

2

[8]

where no is the refractive index with no field applied, r is called the linear electro-

optic coefficient, and s is called the non-linear electro-optic coefficient.

Sometimes the linear E-O effect is called the Pockels effect, and the nonlinear

effect is called the Kerr effect.

no field

Ec

Ev

Ev

Ec

!

field applied

E=h" ! E g

E=h" < Eg

Figure 13. The Franz-Keldysh effect.

It just so happens that these effects can be quite large in quantum well

structures- larger than they are in the same materials in bulk - in fact, the

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nonlinear term is two orders of magnitude large than bulk for InGaAsP! [4] That

makes InGaAsP a good candidate for monolithically integrated phase

modulators, for example.

Another way is to change the refractive index is, of course, to change the

absorption. Examples of electroabsorption effects are the Franz-Keldysh effect,

phase-space absorption quenching (bleaching of quantum wells), and the

quantum confined Stark effect. The Franz-Keldysh effect is shown in Figure 13.

Ideally, under no field, a photon needs energy as least as great as the band gap to

be absorbed. Under a very high field, however, the bands are extremely tilted.

Under these circumstances, the wavefunction of an electron in the conduction

band may extend somewhat out into the forbidden gap. It is therefore possible

(not likely, but possible) for an electron in the valence band to go up to this state

with a slightly smaller energy than the band gap, since the hole and electron

wavefunctions overlap at the same physical location. This results in a shift of the

absorption band edge to lower energies under applied field. The Franz-Keldysh

effect, however, is relatively weak and not used much.

Another example of electrically-controllable absorption is phase-space

absorption quenching,[5] or more simply, "bleaching". Because the quantum

wells are so narrow, there is a limited number of electrons you can put into a

state in a well. Once you fill, say, the lowest state, no more absorption can occur

at energies that would normally populate this state, for example E1 in Figure

14a. When the state is empty, absorption can occur. One can fill the well by

injecting current into it, or by applying a voltage to a structure whose energy

band diagram is shown in Figure 14b. When a voltage is applied, the Fermi level

is above the lowest well state; hence it is full. When the voltage is removed

(Figure 14c), the Fermi level is below the state, and it is empty, meaning

absorption can occur.

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By far the most promising electroabsorption effect, however, is the

quantum-confined Stark effect.

E1

E2

EC

EF

VE

EC

EF

VE

Figure 14. Phase space absorption quenching.

QUANTUM CONFINED STARK EFFECT.

The Stark effect is observed in many materials, and you know that the

energy levels are quantized in a potential well, and that the number of energy

states and the energy spacings depend on the depth and the width of the well. To

find the allowed energy states, we solve Schrodinger's equation for the V(x)

shown in Figure 15a. When an electric field is applied, however, the shapes of

the wells change. Since V(x) changes, you'd expect the solutions (allowed energy

levels) to change, too, and they do. This causes the absorption edge to move,

Figure 15b.

Notice that the edge didn't just move- it also changed its shape. Recall that

the exciton peak arises because the electron and hole are artificially kept close to

each other by the potential well. Under applied field, however, the wells become

asymmetric. The electron tends to be on the right hand side of the well, on the

average, statistically speaking, and the hole tends to be on the left. They are still

in the same neighborhood,, so there is still some excitonic effect, but they are also

slightly separated. This not only reduces the binding energy B in Equation [6],

but also tends to smear out the excitonic peak.

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Another point to notice is that the second curve is labeled "10V". This is

not a lot of voltage, but it is applied across a very thin structure-yielding high

electric fields, on the order of 100kV/cm.

a)

E1

new E1

Field appliedNo field

b)

0 V

10V

exciton

big change in absorption

ab

so

rptio

n

photon energy Figure 15. QCSE: a) shifting of the energy levels under applied field, and b)

change in absorption spectrum.

COLLECTION OF PHOTO-INDUCED CARRIERS

Once the photons are absorbed, in order to detect their presence we need

to collect the carriers that are produced (for example, electrons in the conduction

band). As a bias is applied across the well, the well is distorted and the electron

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sees a slightly lower barrier (refer back to Figure 15). Not only is the barrier

lower, but it is also narrower- under no field, the barrier is essentially infinitely

thick, but under an electric field, it is possible for the electron to tunnel through

the barrier. When it tunnels, it will no longer be confined to a well, and can be

swept out of the diode and collected as current.

HOW TO IMPROVE ABSORPTION IN AN EXPERIMENT

Finally, we come to the point of the absorption itself. You recall (or can

derive) that the absorption in a material is exponential in distance:

I(x) = Ioe

!"x [9]

where I(x) is the intensity at some distance x into the material, Io is the original

intensity, and ! is the absorption coefficient, in units of inverse length. Therefore,

to maximize absorption, you want to maximize the thickness of the material.

Therein lies a problem- a quantum well is very thin. Since the wide band gap

material on either side of the well is transparent to light that the well might

absorb, the actual absorption length is very very small, Figure 16a. This can be

gotten around by going to a multiple quantum well structure, Figure 16b. Each

well is of the exact width and depth needed for the particular absorption needed,

and they are place just far enough apart that they don't interfere with each other.

(a) (b) Figure 16. Single and multiple quantum wells.

Notice that we have assumed that the light comes in perpendicular to the

quantum well layers. This is the typical configuration for photodetectors, in

which light is either shone onto the surface of the chip or sometimes brought in

through the transparent substrate.

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There is another configuration, however: the waveguide configuration,

Figure 17. It is a fortunate coincidence that the same materials that have narrow

band gaps have higher refractive indices. That means the quantum well layers

act like a dielectric waveguide (like a planar optical fiber, if you will). You can

inject light into the edge of the chip, and it will propagate along the layers and

experience a large interaction length, and hence good absorption. This

configuration is ideal for optoelectronic integrated circuits, where the light to be

absorbed (modulated or detected) is coming from another device on the same

chip, such as a laser or passive waveguide. This approach is difficult for discrete

detectors, however, because it is very difficult to couple light efficiently into

those narrow layers from an external source.

QUANTUM WELL DETECTORS

We've seen how quantum wells can be intensity or phase modulators, but

what about detectors? It turns out there are some advantages to going to a

multiple quantum well structure for photodiodes, as well.

As you know, a photodiode is a device whose output current (under

reverse bias) is proportional to the light intensity being shone on it. Figure 18

shows the current-voltage characteristic of a diode under no bias and reverse

bias. First of note that if you measure the voltage across the diode, it does change

with light but not linearly- it has a logarithmic dependence. To use a detector,

you want to operate it under reverse bias, and monitor the current. Even in the

dark, of course, there is the reverse leakage current of any diode- this is known as

the dark current. When light is incident on the detector, the current increases in a

manner linearly proportional to the light intensity.

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Figure 17. Perpendicular (top), or parallel (waveguide) configuration (bottom).

The arrows represent the incoming beam; the curve in the lower figure is the electric field strength of the guided light.

I

V

no light

light

dark current

Figure 18. I-V characteristic of a photodiode

To maximize the responsivity (the amount of current produced per watt

of incident light), you want to maximize how much light is absorbed. However,

once the electron-holes pairs are produced, you also need to collect them. In a

p.n. junction diode, one photons absorbed near the junction will produce useful

current- other e-h pairs will wander around and recombine, whereas those near

the junction will be swept across the junction and collected. Therefore, one wants

to increase the width of the junction as much as possible, so as much light as

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156

possible is absorbed there. One approach is to use a p-i-n structure, Figure 19.

The electric field across the intrinsic region sweeps the electrons and holes across

the junction for collection.

pn junctionp-i-n diode

Figure 19. Different junction styles have differing junctions widths; the pin structure produces more collectable current.

Quantum wells are another way to increase the responsivity by increasing

the probability that a particular electron will be collected. Under high field

(reverse bias), the barriers between the wells look thin near the tops, as shown in

Figure 20. Electrons excited up to states near the top of the well can tunnel

through this barrier. As they travel to the right, they are high above the well

energies, and so are not easily captured by any of the other wells. If they were

captured, they wouldn't easily escape, and eventually they'd recombine and the

information would be lost. With a quantum well structure, however, the

probability of collecting the photocurrent is increased, thus increasing the

efficiency.

Finally, one interesting use for quantum well photodetectors are for very

short wavelengths (by semiconductor standards). By intersubband detection, that

is, from one level to another in the same well, Figure 21, one can obtain detector

wavelengths previously not possible in semiconductors.

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157

No field

Field applied

Figure 20. Increased responsivity in quantum well detectors due to difficulty in

recapturing electrons.

Figure 21. Intersubband detection for high energy photons.

HOMEWORK:

1. Draw the energy band diagram for junctions between the following

materials. Use graph paper and a ruler to make sure you keep ! and Eg constant.

a) n-type Si, EC-EF=0.2 eV; !=1.39 eV for Si, Eg =1.11 eV

p-type Si, EF-EV=0.1eV

b) n-type Si, EC-EF=0.2 eV

intrinsic Si, EF=Ei

c) n-type GaAs, EC-EF=0.1 eV; !=4.07 eV, Eg =1.43 eV

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158

p-type Al0.3Ga0.7As, EF-EV=0.2eV; !=3.74 eV, Eg =1.8 eV

2. Describe in words what you think will happen when several wells are

brought close together, like maybe 10 or 20Å. Will electrons still be confined?

3. We described how the photocurrent produced by absorption of the light

is collected when the diode is under bias. Why is current collected when no bias

is applied, as shown in Figure 15 b? Hint: in a typical MQW detector, the doping

is p-i-n, where the wells are intrinsic, and are between the n and p regions. You

may wish to consult your notes from EE432 for pn junctions.

Library Problems:

Choose one of the following:

1. Find an example of a quantum well modulator that operates at 1GHz or

more in the literature. Write a page or so explaining its structure and capabilities,

and what principle it operates by (i.e. electrorefraction or electro- absorption, or

other)

2. Find an example of a quantum well detector reported inthe literature.

Write a page or so describing its fabrication, operation, capabilities, etc.

REFERENCES

1. S. Adachi, "GaAs, AlAs, AlxGa1-xAs: Material parameters for use in

research and device applications," J Appl Phys, 58, p. 62-89 (1985).

2. S. Shin and C. B. Su, "The sublinear relationship between index change

and carrier density in 1.5 and 1.3µm semiconductor lasers," IEEE Phot Tech Lett,

4, p. 534-537 (1992).

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3. J. Manning, R. Olshansky, and C. B. Su, "The Carrier-Induced Index

Change in AlGaAs and 1.3µm InGaAsP Diode Lasers," IEEE J. Quant. Elect.,

QE-19, p. 1525-1530 (1983).

4. J. E. Zucker, I. Bar-Joseph, B. I. Miller, U. Koren, and D. S. Chemla,

"Quaternary Quantum Wells for Electro-Optic Intensity and Phase Modulation at

1.3 and 1.55µm," Appl. Phys. Lett., 54, p. 10-12 (1988).

5. D. S. Chemla, I. B. Joseph, C. Klinshirn, D. A. B. Miller, J. M. Kuo, and T.

Y. Chang, "Optical reading of field-effect transistors by phase-space absoprtion

quenching in a single InGaAs quantum well conducting channel," Appl. Phys.

Lett., 50, p. 585-587 (1987).

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+3008)(41".+;3*0*)K

! "A",*)K48"+4*+N"')"(&*,".00'I"('"03)"(&8">0'K0.6

! A" /1" +4*+N*)K" ')" 8*(&80" (&8" 0*K&(" '0" 48C(

.00'I,M" 1'3" 6'G8" ." +30,'0" .4')K" (&8" H.(." >'*)(,J" (&8" 08.H'3(" *," (&8

I.G848)K(&"G.438".)H"(&8"+'008,>')H*)K"*)(8),*(1O

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EE 737 Photonics Laboratory Manual Liquid Crystals

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LIQUID CRYSTALS

INTRODUCTION

Liquid crystals find application in many areas, from thermometers to

displays and back. In this lab we will learn a bit about liquid crystals in general

and then construct a simple liquid crystal cell and use it to investigate some of

properties of liquid crystal displays.

GENERAL CONSIDERATIONS

Liquid crystals are liquids which possess some of the regularity of crystals

and a delightful interaction with light. These properties occur because liquid

crystal molecules have a long skinny molecular shape. Molecular drawings of a

few representative liquid crystal molecules are shown in Fig. 1. There the C's

represent carbon atoms, the H's represent hydrogen, the O's represent oxygen

and the N's represent nitrogen. The long skinny shape is quite evident. We note

that not all the molecules shown there have axial symmetry. The lack of

symmetry can well contribute to specific properties. The chemical names are

given along with the shapes.

The long skinny shape affects the material properties by restricting some

of the usual freedom of the molecules. In an ordinary liquid the molecules

generally have six degrees of freedom, three translational degrees and three

rotational degrees. The molecules flow back and forth (translation), roll over

each other (rotation). Intermolecular forces then keep the molecules from flying

off like a gas.

In a liquid crystal the shape of the molecules in conjunction with

intermolecular forces suppresses the rotational motion while leaving the

molecules free to translate. The intermolecular forces cause the molecules to line

up in a regular pattern. For some liquid crystals all molecules are parallel to each

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174

other, for other liquid crystals other configurations such as helical arrangement

are found. To see the effect of molecular shape and also the effect of

temperature, one might draw an analogy with a box of pencils. If one were to

shake the box long enough in the right way the pencils at the bottom would find

that they could fit better if they were parallel. Then the pencils above them

would drop in place, etc. In this way they would slowly start lining up. If we

shake too hard with too much energy they would come misoriented. If we shake

weakly they stay aligned.

H-C-C-C-C-O-C

H

H H H H

HHHC=C

C-C

C-C

H

N-C

H H

H H

C=C

C-C

H H

H H

C-C-C-C-C-C-C-C-H

H HHH H HH

H H H H H H H

Butoxybenzylidene octylanilene

H HHH H H

H H H H H H H

H-C-C-C-C-C-C-C-C-C-O-C

H H H

H H

C=C

C-C

H H

H H

C-C

C=C

C-C

H H

H H

C-C N

Octyloxy-

cyanobiphenyl

Figure 1. Typical liquid crystal molecules.

Similar things happen with liquid crystals. At high temperatures (heavy

shaking) the molecules shake enough that they loose their orientation so that the

liquid crystal acts like any other isotropic liquid. At lower temperatures the

molecules settle down and we find the delightful liquid crystal properties.

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175

Liquid crystals are divided into three main types, nematic, smectic, and

cholosteric as shown in Fig. 2. There we see a typical cube of molecules that

might be taken from a large bottle without any interaction with the container and

in the absence of any applied fields.

z

yx

Nematic

Cholesteric

A

B

C

Figure 2. Liquid crystal types.

At the upper left is a cube filled with a nematic liquid crystal. The

molecules are all parallel to each other. The ends don't necessarily line up as they

will in some other types . Mixtures of nematic liquid crystals are often used in

standard liquid crystal displays.

At the right we see three cubes of smectic liquid crystals. They have the

property that the molecules are arranged in layers as well as being all parallel. In

smectic A liquid crystals the molecules in any plane parallel to the layers are

oriented perpendicular to the planes and are located at random positions. In

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176

smectic B liquid crystals the molecules are also perpendicular to the planes but

are arranged in lines in planes parallel to the layers. In smectic C liquid crystal

the molecules are tipped with respect to the molecular planes.

At the lower left is a cube containing cholosteric liquid crystals. We see

planes parallel to the top and bottom of the cube. In any plane the molecules are

in the plane and are parallel to each other, as shown. The defining feature is that

in going from one plane to the plane above it the direction of the molecules

twists. Along any vertical line the tips of the molecules exhibit a helical

behavior. The pitch of cholosteric molecules, i.e. the vertical distance required

for a single end-to-end rotation is often of the order of magnitude of the

wavelength of light so a given cholosteric molecule will diffract light at of a

particular color. This property will often be temperature dependent so

cholosteric liquid crystals are sometimes used in thermometers.

A given liquid crystal may change from one type to another depending on

temperature. At high temperatures the liquid will be isotropic and none of the

special properties will be observed. The energy associated with intermolecular

forces is less than kT where K is Boltzmann's constant and T is the absolute

temperature. When the temperature is below a critical value nematic behavior

will be observed. For some liquid crystals lowering the temperature still further

may cause transitions to one or more smectic phases.

A very simple conceptual mechanical model showing the orientational

properties of a liquid crystal is shown in Fig. 3. There at the left we see the long

skinny liquid crystal molecules. Connecting them at each end are tiny springs

representing the intermolecular forces. When the springs are not stretched or

compressed the molecules are parallel. If some external force is applied the

relative orientation of the molecules changes and the springs are stretched

adding energy to the system as shown in the figure at the right. At equilibrium a

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177

configuration is obtained where each spring is stretched a bit and the energy

added in stretching the springs in minimized.

Figure 3. Simple mechanical model of a liquid crystal.

LIQUID CRYSTAL CELL

In useful applications liquid crystals are found in liquid crystal cells. A

simple liquid crystal cell is shown in Fig. 4. In the figure we see two parallel

glass substrates with nematic liquid crystal between them. These are glass plates

which in practice are separated by a distance of 3 to 15 microns. The surfaces of

the substrates are specially prepared to make the liquid crystal molecules at the

surface all line up in a given direction, the y direction in the figure. With no

other forces the intermolecular forces then align the rest of the molecules parallel

to those at the surface.

The inside of both glass substrates is coated with a transparent conductor,

indium-tin-oxide (ITO) to which a D.C. voltage may be applied. With no voltage

applied all the molecules are parallel to each other and to the surface in (y)

direction as shown in the drawing at the left.

When a D.C. voltage is applied to the transparent electrodes the

molecules sense the resulting D.C. electric field and develop an induced dipole

moment. That dipole moment causes them to feel a torque and to rotate to try

and align themselves with the electric field. This is resisted by the

intermolecular forces and an equilibrium configuration is attained where the

molecules are partially tipped as shown in the cross-sectional drawing at the

upper right in Fig. 4. If the applied voltage is sufficiently high all the molecules

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EE 737 Photonics Laboratory Manual Liquid Crystals

178

except those very close to the surface will all be tipped so as to be parallel to the

applied electric field as in the cross-sectional drawing at the lower right in Fig. 4.

x

y

z

substrate

ITO liquid crystal

ITOsubstrate

E

Eno field applied large field applied

small field applied

Figure 4. Typical nematic liquid crystal cell

LIQUID CRYSTAL INTERACTION WITH LIGHT

Liquid crystals can interact with light in two ways, scattering and

polarization modification. The interaction of light with liquid crystals that is

most widely used involves polarization and the change of refractive index with

molecular orientation. Since the liquid crystal molecules are long and thin they

have a larger optical dipole moment along the long axis than they do

perpendicular to it. This results in a larger refractive index for light polarized in

the long direction of the molecules than the short direction. The refractive index

also depends on the direction of propagation since the light can be polarized

only perpendicular to the propagation direction. From a different point of view,

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179

for a given direction of propagation the refractive index depends on the

orientation of the molecules with respect to the polarization. Now let's examine

some of these.

To see how the interaction of light with liquid crystals depends on the

orientation of the molecules and polarization direction for a given direction of

propagation consider Fig. 5. There we see three different cases. In each there is a

plane wave propagating in the z direction through liquid crystal molecules. In

the case at the left the molecules are oriented along the x direction and in the case

at the at the right they are oriented in the z direction. In the figure at the left light

with electric field (polarization) along the x direction will experience a large

refractive index while light polarized in the y direction will find a smaller one.

In the figure at the right light polarized in both the x and y directions will see the

same small refractive index.

xy

z

EE

xE

xyEE

y

xx

y y

x

Figure 5. Molecular refractive index, direction of propagation, and polarization of

the light.

Now consider the figure in the center where light is polarized in the x

direction. If the molecule were to start with orientation in the x direction and

slowly rotate towards the z axis the refractive index would slowly decrease until

we get to the situation in the figure at the right. Light polarized in the y

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180

direction would see the skinny dimension and small refractive index

independent of the molecular tip.

If the light is polarized other than along the x or y directions as shown in

Fig. 5 then we resolve the optical E field into components and treat the

components in the x and y directions independently. Thus to reiterate in Fig. 5 as

the molecules rotate from being parallel to the x axis to being parallel to the z axis

then the y polarization component sees a constant index and the x component

sees a decreasing index.

LIGHT INTERACTION WITH LIQUID CRYSTAL CELLS

Now let's apply what we know about refractive index variation and

polarization to our liquid crystal cell. There are various configurations we might

consider. In one simple configuration we let the light be polarized only in the x

direction. We then apply a voltage to the cell which makes the molecules rotate

in the x-z plane as in the middle case in Fig. 5. This produces a phase shifter!

Phase Shifter

To see the action of the phase shifter quantitatively we can write down a

few equations. As the molecules slowly rotate towards the z axis the refractive

index decreases causing a change in the phase of the light leaving the cell. This is

seen in the equations relating the refractive index, n, and the wavelength !, in the

liquid crystal, !", the wavelength in free space and velocities in the material, v

and in free space, c..

! =

v

f [1]

! o =

c

f [2]

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EE 737 Photonics Laboratory Manual Liquid Crystals

181

n(z) =

c

v(z) [3]

Eliminating v, and c we have

! (z) =

!o

n(z) [4]

In Eq. 1 we have written n(z) just to remind ourselves that the refractive

index depends on the angle of tip of the molecules and that the tip angle and

therefore the refractive index varies along the z axis.

Eq. 4 shows us physically why the phase of the cell in the center drawing

in Fig. 4 acts as a phase shifter. Eq. 4 says that the wavelength of the light

changes as the refractive index changes. Thus as the wavelength changes the

number of cycles of phase shift of the light that we can fit between the ends of the

cell changes, changing the phase of what comes out.

To see this in mathematical terms, this consider the expression for !, the

phase of the light leaving the cell. The incremental phase change in a distance dz

in the liquid crystal is d! =

2"

#dz and the phase change in a full cell is

!x= 2"

dz

# (z)o

L

$ [5]

where L is the cell thickness and we have put a subscript x on ! to remind

ourselves that the light is polarized in the x direction.

Eliminating " with Eq. 4 gives our most useful expression.

!x=

2"#

n(z)dz

0

L

$ [6]

We note that if the light had been polarized in the y direction there would

have been no change because the refractive index for that case remained the

same and the integral corresponding to Eq. 6 would have been

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182

!y =

2"#o

nyodzo

L

$ [7]

=

2!

" o

nyoL [8]

where nyo is the constant index for light polarized in the direction of the small

dimension of the molecules.

Intensity modulator

Now consider a cell with a different configuration of liquid crystal and

polarization. Imagine that the light is polarized at 45° to the x and y axis and

there is a polarizer (usually called an analyzer because it is transmitting output

light) which passes light polarized at 135° to the x axis and perpendicular to the

incident polarization as shown in Fig. 6. There we see the cell and analyzer and

two sets of axis drawn at the input and the output to the cell. Looking at the axes

at the cell input we see the electric field components drawn. We see that the x

and y components are nicely in phase so that they will line up to give a field in

the 45° direction as expected.

To the right of the cell we see the corresponding set of axes and the two

electric field components. There is a difference, however! The electric field

component in the x direction is lagging in phase behind that in the y direction

because the refractive index is larger and the velocity is slower.

After the light has passed through the cell the electric field component

polarized in the y direction lags in phase because it has experienced a larger

refractive index and has traveled more slowly. If we arrange things just right, by

having a voltage applied to the cell that produces just the right amount of liquid

crystal tip then the y electric field component will lag by exactly 180°. The result

is that the y field component reverses its direction and recombines with the x

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183

field component so that the combination is perpendicular to the incident light as

shown in Fig. 6. The result is that the electric field components of the exiting

light are then polarized at 135° to the x axis and pass through the analyzer.

x

y

z

E

x

y

E

analyzer

x

y

liquid

crystal cell

incoming light

polarized at 45°

Figure 6. Liquid crystal cell configured as intensity modulator

If we were to plot the light transmitted by the analyzer as a function of

voltage we would get a curve similar to that in Fig. 7. At high voltages the

output light is a minimum. That is because essentially all the liquid crystal

molecules are lined up perpendicular to the cell walls. In that case both

polarizations components experience the same refractive index and have the

same phase delay. After leaving the cell the polarization components recombine

to give the same direction as when entering it. The field is stopped by the

polarizer and the output intensity is zero. As the voltage is decreased the phase

delay between the two components increases from zero, the light becomes

elliptically polarized and a small portion is transmitted by the analyzer. This

increases until there is exactly 180° phase difference and the optical field

components combine so as to be all transmitted by the polarizer. With

continuing voltage decrease the phase difference increases and the output

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184

intensity oscillates as shown. The output intensity for zero voltage depends on

the refractive indices of the liquid crystal and the thickness of the cell.

1

0

voltage

I/I 0

Figure 7. Intensity of light transmitted by analyzer as a function of voltage applied

to the nematic liquid crystal cell.

We can now express the preceding in analytical terms. The optical electric

field entering the cell is given by

E = Eo( ˆ x + ˆ y )ej!t [9]

The field leaving the cell is

E = Eo( ˆ x ej!x + ˆ y e

j!y )ej"t [10]

The field transmitted by the polarizer Eout is that in the direction of the unit

vector

1

2( ˆ x + ˆ y )

. Thus the field of the light leaving the analyzer, Eout will be

Eout =

1

2( ˆ x ! ˆ y ) "E [11]

=

1

2( ˆ x ! ˆ y ) "Eo

ˆ x ej# x + ˆ y e

j# y( )e j$t [12]

=

Eo

2e

j!x " ej!y( )e j#t [13]

The intensity of the light leaving the analyzer is then

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185

I =1

2Z0

E2

[14]

=

Eo2

2Z0

ej! x " e

j! y( ) e" j! x " e

" j! y( ) [15]

=

Eo2

2Z0

2 ! 2cos "x ! "y( ){ }( ) [16]

=

Eo2

Z0

sin2 1

2!x " !y( )#

$ %

& ' (

[17]

Substituting in Eq. 17 for !x and !y using Eqs. 6 and 8 we have

I =Eo

2

Z0

sin2 !" o

n(x)dz0

L

# $ nyoL%

&

' (

)

* +

,

-

.

/

0

[18]

In the particular situation where the applied voltage is zero none of the

molecules are tipped and the refractive index for light polarized in the direction

is nx from the back to the front of the cell, n(z)=nxo , Eq. 18 can be further

simplified.

I = Io sin2 !

"o

nxo # nyo( )L$ % &

' ( )

[19]

where

Io=

Eo

2

Zo

[20]

The quantity Io is the maximum intensity. Eq. 19 can be used in the laboratory to

predict the results of measurements made using a parallel cell. The procedure is

to plot the output of a parallel cell and polarizer as set up in Fig. 6. The thickness

of the mylar spacer gives the thickness, L, and the refractive indices nxo and nyo

are provided along with the liquid crystal. Then the quantity

!

" o

nx0# nyo( )L

gives the number of cycles of fluctuation of the intensity. In addition the

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186

quantity

sin2 !

" o

nxo # nyo( )L$ % &

' ( )

gives the relative intensity at zero voltage. These

quantities can both be observed.

COMMERCIAL LIQUID CRYSTAL DISPLAYS

Commercial liquid crystal cells will often have a somewhat different

construction than the simple cell we have been considering. The liquid crystal

will have the twisted arrangement shown in Fig. 8. A nematic liquid crystal will

still be used with a small amount of cholosteric liquid crystal to help with the

twist. For a twist cell the treated substrates are oriented so that the liquid crystal

molecules at the cell walls are at a 45° angle rather than parallel as in the cell we

have been considering. For this case with no applied voltage the molecules

undergo a slow twist from one wall to the other as shown in Fig. 8. There is a

mirror on one side of the cell so that the light passes through the cell, is reflected

off the mirror and passes back through the cell. The polarization of the light is

rotated 45° on the first pass through the cell, and then unrotated back to its

original orientation on the return pass.

The twisted nematic cell has a intensity-voltage characteristic curve which

is more useful in many circumstances. It is shown in Fig. 9. Instead of oscillating

as in Fig. 7 it decreases monotonically from maximum to zero. This is more

useful if one wants only the one range from minimum to maximum, or if one

wants a binary output as in many liquid crystal displays. It also has the

advantage that it is easier to mass produce so that there is the desired

polarization rotation with no applied voltage.

When a voltage is applied, most of the molecules are aligned

perpendicular to the substrate. Near the ITO-coated substrate, however, there is

a thin layer whose molecules are still oriented along their original alignment. The

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EE 737 Photonics Laboratory Manual Liquid Crystals

187

liquid crystal material in these regions is birefringent, and causes a total phase

retardation between the x and y polarizations of 90° during one round trip. In

this case, the return light does not pass through the front polarizer, and the

display appears dark.

mirror twist cell polarizer

Figure 8 Twisted nematic liquid crystal cell

1

o

I/I0

voltage

Figure 9 Voltage characteristic curve of a twisted nematic cell.

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188

In practice the transparent electrode on one side is divided into separate

areas with independently controlled voltages so as to form voltage controlled

patterns. A typical pattern might be a seven segment display used to display

numbers.

HOMEWORK

1. Consider a transmissive (as opposed to reflective) nematic liquid crystal

display, such as that shown below, which is meant to be similar to that of Figure

6 in the lab manual. The voltage, when applied, produces exactly 180° of phase

lag between the x and y polarizations. There are electrodes on the front and back

glasses, and wherever they overlap it is possible to generate a field and rotate the

liquid crystals in that region. Assume the crystals are aligned vertically at both

glasses.

For each of the following display configurations, describe the appearance

you expect when a voltage is applied to some segments, and when no voltage is

applied. Do both displays work?

polarizer

electrodes LC cell

x

y

z polarizer

electrodes LC cell

2. Consider the phase shifter described in the chapter. Suppose you

wished to convey binary information on the phase of an optical wave (as in

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EE 737 Photonics Laboratory Manual Liquid Crystals

189

phase-shift keying). Also suppose the input beam is purely x polarized. Describe

how you would imprint the data onto the phase of the lightwave (shift the phase

back an forth between two states that you define). Sketch the system. How

would you detect the phase at the other end? (Hint: how do you detect the phase

of any wave? Compare it to something of known phase, such as another wave

whose phase is not being modulated. Hint 2: Interfere two beams together to find

the phase relationship.) Sketch that system too.

LIBRARY PROBLEM:

Choose one of the following:

1. Find an example of a use of liquid crystals that is not a display. Write a

page or so describing it operation and application.

2. How do they make color liquid crystal displays? (There is more than

one way, find at least one.) Describe in a page or so how these work.

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190

LIQUID CRYSTALS LABORATORY EXPERIMENT

As explained in your course notes, a liquid crystal cell operates by altering

the polarization state of the light passing though it. To acquaint yourself with a

simple polarization effect, design and construct an experiment with linear

polarizers to demonstrate Malus’ Law. If you use a white light source, you

might want to include an ultraviolet light blocking filter and an infrared-blocking

filter zZwithin your experiment. (Any ideas why?) Compare your results with

what you would expect theoretically and explain any discrepancies between the

two.

Next, you will actually make a simple liquid crystal display and

investigate some of its properties such as the contrast ratio of the display and the

effects of viewing angle.

To construct your liquid crystal display, you will sandwich the liquid

crystals between two pieces of ndium-tin-oxide (ITO) coated glass. (The ITO

coating is only on one side of the glass) ITO is a conductor that is transparent to

visible light. To obtain an optimally functioning display, it is important to begin

with the ITO glass as clean as possible. To this end, the following cleaning steps

have been developed to remove any contamination from the glass. In this

cleaning process, chemicals which are to varying degrees harmful to your skin

will be used, so USE CAUTION AT ALL TIMES. While handling the glass

plates, to protect yourself as well as the materials, you must wear gloves or

finger cots.

You will be given two 1” square pieces of ITO glass along with a special

holder which you will mount the glass in for cleaning. Make sure you know

which surface of the glass has the conductive coating on it before you put them

into the holders. You will need three 100 ml beakers in which to put the various

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EE 737 Photonics Laboratory Manual Liquid Crystal Laboratory

191

cleaning materials. Please use only enough cleaning liquid to just cover the

glass. The cleaning procedure is detailed below.

CLEANING PROCEDURE FOR ITO COATED GLASS

1.) In a 100 ml beaker, pour in the detergent Liqui-Nox. Insert the glass

holder into the detergent and put the beaker in the ultrasonic cleaner for

approximately 5 minutes.

2.) Remove the glass from the Liqui-Nox and rinse thoroughly with DI

water.

3.) Submerge glass in acetone from about 2 minutes.

4.) Blow dry the glass with nitrogen gas.

5.) Submerge glass in isopropyl alcohol to dissolve any excess acetone.

6.) Rinse thoroughly with DI and blow dry.

Once the glass substrates have been thoroughly cleaned, you must treat

the conductive surface so that the liquid crystals align in a specific direction. You

will be making a parallel cell in this experiment. That is, with no applied

voltage, the orientation of the liquid crystal molecules will be the same between

the front and back pieces of glass. To achieve this, set the glass substrate ITO

side up on a piece of tissue paper. Using your thumb and another piece of tissue

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192

paper, slowly swipe the tissue paper along the ITO surface applying a fair

amount of pressure (but not enough to break the glass). BE SURE TO SWIPE

ONLY ONCE AND ONLY IN ONE DIRECTION, KEEPING NOTE OF THE

DIRECTION. Do this to both substrates.

To contain the liquid crystal material, you will need to cut out a spacer of

0.5mil mylar as shown in Figure 1.

1"

0.75"

Figure 1 Mylar Spacer

Take the mylar cut-out and place it between the two glass plates with the

conductive side on the inside such that the directions in which you swiped the

ITO surface are parallel. Note that the glass plates should not be placed directly

on top of one another, but rather, should be offset about 1/8” horizontally and

lined up vertically (this is so that you can apply electrical contacts to the ITO

coating). This is shown in Figure 2. Use binder clips to hold the cell together.

Using a micropipet, insert a small amount (half a pipette or so) of the liquid

crystal material between the plates. Capillary action will cause the liquid to fill

the well which you have created. You now should have a functioning liquid

crystal cell.

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193

Figure 2 Position of Glass Plates

The liquid crystal cell you have built is a transmissive device. Design and

construct an experiment to measure the contrast ratio that is achievable by your

cell.

Note that a DC voltage will quickly deplate the thin electrodes. Therefore,

you should applied an AC signal that has zero volts average value (DC offset).

Keep the applied RMS voltage below 12 volts.

A commercially made liquid crystal display is also available for your use.

This display is a reflective device. Measure the contrast ratio of this display (also

applying only AC voltage) and compare this with the value obtained for your

cell. How do they compare?

Finally, you will note that depending upon the angle at which you view

the commercial display, the characters may be more or less brilliant. Design an

experiment to measure this viewing angle effect. Can you explain the origin of

this effect?

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Figure1. Spectral distribution of sunlight. Shown are AM0, AM1.5 and the radiation distribution of

a 6000 K black body.

5'4.0"+744,":3,("/7";7,*<)7;"('"./,'0/".,":3+&"'="(&7",'4.0",>7+(03:".,">',,*/47

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*)")3:70'3,";7,*<)"(0.;7'==,"('".+&*7@7"'>(*:3:">'?70"+')@70,*')A""C30(&70:'07D

;*==707)("(1>7,"'=",'4.0"+744,":.1"/7":'07".>>0'>0*.(7"='0"."<*@7)".>>4*+.(*')A""C'0

7E.:>47D",'4.0"+744,"('"/7"3,7;"='0"(&7"5>.+7"5(.(*')"C077;':":3,("/7"F0.;*.(*')G

&.0;7)7;F".<.*),("&*<&"7)70<1">.0(*+47,"*)+*;7)("=0':",>.+7".);"=0':",'4.0"=4.07

703>(*'),"H(&7,7".07">.0(*+34.041";.)<70'3,".("+70(.*)"'0/*(,I"?&*47"(&*,"*,")'("."+')+70)

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J">70=7+("H)')G;7=7+(*@7I",7:*+');3+('0"?*44"')41"./,'0/"0.;*.(*')"*="(&7"7)70<1

'="(&7">&'('),"+':>0*,*)<"(&7"*)+*;7)("0.;*.(*')"*,"<07.(70"(&.)"'0"7K3.4"('"(&7"/.);<.>

'="(&7",7:*+');3+('0"*(,74=D"*A7"&!"!LA""M'?7@70D"(&7">&1,*+,"'="(&7

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!!"#$#"%&'(')*+,"-./'0.('01"2.)3.4 5'4.0" 6744,

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Figure 2.Simple diagram of photon absorption by direct gap semiconductor wherethe photon energy is greater than the bandgap.

./,'0;(*')";0'+7,,"<7;7)<,"3;')"(&7"/.)<",(03+(307"'="(&7",7>*+')<3+('0?""@*A307"B

,&'C,"(&7"/.)<A.;"./,'0;(*')"*)".)"!DE"<*.A0.>"='0"."<*07+("/.)<A.;",7>*+')<3+('0F

,3+&".,"G.H,?""I)"(&*,"+.,7F".)"747+(0')"*,";0'>'(7<"=0'>"(&7"J.47)+7"/.)<"7<A7"('"(&7

+')<3+(*')"/.)<"7<A7"*="(&7"./,'0/7<";&'(')"7)70A1"*,"7K.+(41"7L3.4"('"(&.("'="(&7

/.)<A.;?""M'(7"(&.("*="(&7"7)70A1"'="(&7"./,'0/7<";&'(')"*,"A07.(70"(&.)"(&7"/.)<A.;F

(&7"./,'0;(*')";0'+7,,"'++30,".("<*==707)("J.437,"*)"ED,;.+7F".,",&'C)"*)"@*A307"B?""N&7

747+(0')"A7)70.(7<"*)"(&7"+')<3+(*')"/.)<"*)"(&*,"+.,7"C*44"(&7)"4',7"7)70A1"(&0'3A&

(&70>.4*O.(*')F"*?7?"&7.("A7)70.(*')F"<'C)"('"(&7"4'C7,(";',,*/47"7)70A1";',*(*')"C*(&*)

(&7"+')<3+(*')"/.)<P"*?7?"('C.0<"(&7"+')<3+(*')"/.)<">*)*>3>?""I(",&'34<"/7")'(7<

(&.("(&*,"07;07,7)(,"."07.4".)<"4.0A7"7==*+*7)+1"4',,"='0".",'4.0"+744",*)+7")'(".44"'="(&7

*)+*<7)(",'4.0"7)70A1"+.)"/7"+')J70(7<"('"747+(0*+.4"7)70A1".)<"*,"4',(".,"&7.(?""M'(7"(&.(

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:'0"&*;&70"<&'(')"7)70;*7,="(&7"<0'/./*4*(1"':"./,'0<(*')"*)+07.,7,"/7+.3,7">'07"?@

,<.+7",(.(7,".07".A.*4./47".,"(&7"+01,(.4">'>7)(3>"*)+07.,7,"B07+.44"<"C"&?DE

Figure 3. Absorption processes for indirect gap semiconductors.

F&7",*(3.(*')"*,",'>7G&.(">'07"+'><4*+.(7H":'0".)"*)H*07+("/.)H;.<

,7>*+')H3+('0=",3+&".,"5*E""I)"(&*,"+.,7=".)"*)H*07+(";.<",7>*+')H3+('0"+.)";7)70.441

./,'0/"<&'('),"(&0'3;&".("47.,("(&7"(G'"<.(&,",&'G)"*)"J*;307"$E""K,"+.)"/7",77)":'0

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,(.(7,"':"(&7"747+(0')":'0".)"./,'0<(*')"(0.),*(*')"('"(.?7"<4.+7E""F&*,"*,".++'>>'H.(7H

/1".)'(&70":3)H.>7)(.4"<.0(*+47"+.447H"(&7"<&')')="(&7"'(&70,"/7*);"':"+'30,7"(&7

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+''0H*).(7H"A*/0.(*')"G.A7,"':"(&7".('>,">.?*);"3<"(&7"+01,(.4"4.((*+7"B*E7E"4.((*+7

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Figure 4. Optical absorption coefficients of various single crystal semiconductors. [1]

C<"+'30,7"(&7",'4.0"+744"07D3*07,"(&7"+'447+(*')"'<"(&7"=&'('?7)70.(7;"+.00*70,"('

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Figure 5. Percentage of light reflected as a function of wavelength from Si with andwithout AR coatings having the refractive indices shown. [1]

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Figure 6. Geometry of a typical solar cell structure, based on the GaAs "heteroface" design.

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Figure 7. Common solar cell configurations. In cases a,b and c, the contribution from thelarge bandgap material to the photocurrent is negligible.

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Figure 8. Terminal I-V characteristics of an illuminated pn junction solar cell. Maximum powerpoint is indicated and the dark I-V is shown for comparison.

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Figure 9.Solar cell efficiency limits as a function solar cell bandgap for different solar spectra.[1]

Figure 10. Major features of a simple solar cell.

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Figure 11. Equivalent circuit of an ideal solar cell.

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Figure 12.. Effect of parasitic resistances on cell I-V characteristics for (a) Rs and (b) Rsh.

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Figure 13. Various approaches to top contact designs.

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Figure 14. Band diagrams of cell structures for enhanced carrier collection.

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+3007)(".)>"I'4(.;7",7),*);"'="(&7"'@70.(*);"+744".07">7,*0./47",*)+7"(&*,"74*<*).(7,

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*)+07.,7,E

Figure 15. DOE/NASA solar cell testing methods.

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Figure 16 Simple solar simulator.

Figure 17. Experimental configuration for measuring cell characteristics. (a) Efficiency and (b)spectral response.

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226

PART II: Introduction to several optical technologies not coveredexplicitly in the lab:

Review of OpticsPolarization

Radiometry and PhotometryUseful Optical Devices

Things Statistical(or, How to treat mesurement errors in the lab)

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y x

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y

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Figure 1. Linearly polarized light. Top: x polarization, center: y polarization; bottom:

linearly polarized light at +45°.

8)"(&9":*;309<"=9"&.>9"?0.=)"(&9"+.,9":'0"!"#!$@"A&909:'09<".(".)1"(*B9"'0

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Figure 2. Linear polarization at +135°.

I'3"<*44"&.J;"'/,;0J;B"(&.("(&*,"*,"(&;";K.+(",.=;"0;,34("<;LB"9;("*@"&.B

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x

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Figure 3. Circularly polarized light, with &=+90°.

T&<";.1"(&<":*>30<"*,"B0.;)A"&""*,"WJFGH""9:";<"?3("'30"+&.*0".("*):*)*(1".)B

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yx

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Figure 4. Elliptical polarization. In this example, !=-90°.

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Figure 5. A particular case of general elliptical polarization.

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EE 737 Photonics Laboratory Manual Radiometry and Photometry

249

RADIOMETRY AND PHOTOMETRY

INTRODUCTION

When dealing with light sources, a common question is “How bright is

it?” It turns out that “bright” can means lots of different things- high intensity,

high luminance, high radiance.... It’s important to be precise, since two sources

emitting the same number of photons may have, for example, different

intensities. To characterize a detector, one can express the incident light in a

variety of units as well, depending on the detector and the application.

Furthermore, different systems of units are sometimes used for visible

light than for invisible light. The photometric system of units is corrected for

human eye response, and therefore only applies to visible light. In this system,

since the eye is more sensitive to green light than purple light, a green source

will be “brighter” (whatever that means) than a purple source of equal energy.

The radiometric units are the same regardless of wavelength, and so apply to all

regions of the electromagnetic spectrum.

RADIOMETRIC UNITS OF EMISSION

A light source emits energy in the form of electromagnetic waves (or

photons, depending on the day of the week). The basic measurement of light

might therefore be considered to be the radiant energy Q, measured in Joules.

Qe=radiant energy (Joules) [1]

The amount of energy delivered within a certain time (or the rate of

energy delivery) would then be the radiant power, or radiant flux:

! e =

dQe

dt (Watts) [2]

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EE 737 Photonics Laboratory Manual Radiometry and Photometry

250

If the source is an extended source (for example an electroluminescent panel

such as those used in cockpits), the total optical power is perhaps not so

important as they energy emitted per unit area, the radiant fluence:

Fe =

dQe

dA (J/m2) [3]

The volumetric radiant density is the energy per unit area, symbolized by W:

We =

dQe

dV (J/m3) [4]

Even a very weak source can emit a sizable amount of energy over a

sufficiently long time, so perhaps it would be more useful to consider the rate of

energy flow than the total energy. This leads to a series of power-based units.

An extended source may emit a given amount of energy per unit area per

unit time, which would be its radiant excitance:

Me=d!

e

dA (W/m2) [5]

The most intuitive quantity is perhaps the radiant intensity, however, at

least from a perceptual point of view. From a mathematical point of view,

radiant intensity is

I

e=

d!e

d" (W/sr) [6]

where ! is a solid angle, measured in units of steradians (sr). A steradian is a unit

of solid angle, Figure 1, the same way a radian is a unit of flat angle. There are 4"

sr in a sphere:

d! = 4"sphere

# [7]

and

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EE 737 Photonics Laboratory Manual Radiometry and Photometry

251

d! =

da

r2

[8]

x

y

z

d!

r

da

Figure 1. Solid angle.

For an extended source with directional emission, the radiance may the

most useful unit:

L

e=

d2!

e

d"dA cos#=

dIe

dAcos# (W/sr-m2) [9]

PHOTOMETRIC UNITS OF EMISSION

As opposed to radiometric units, photometric units have been corrected

for the response of the human eye. The eye responds differently in daylight than

when it is night-adapted. These two curves are shown in Figure 2. The daylight

curves is the photopic response, while the night-adapted curve is the scotopic

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EE 737 Photonics Laboratory Manual Radiometry and Photometry

252

curve. When the eye is daylight-adapted, the average human vision peaks at

about 555 nm, in the yellow-green part of the visible spectrum. If we call the

photopic curve K(!), then for each radiometric unit Xe there is a corresponding

photometric unit Xv such that

Xv=K(!)Xe (monochromatic light) [10]

We have specified here that the light is monochromatic for Eq. 10 to apply.

In general the source will have some spectral spread, so one must integrate the

radiometric unit over the entire applicable spectrum:

!e= !

e(" )d"

"1

"2

# [11]

where the range !1 through !2 is limited to the visible spectrum. Energy outside

this range is not detectable by the eye an therefore does not contribute to the

photometric quantity.

The peak of the photopic curve has a value of Kmax=673 lm/W, where lm

stands for “lumens”, the photometric analog to power. The conversion factor will

be different at each visible wavelength, and it is handy to use the normalized

response curve, in which

V(! ) =

K(!)

Kmax

(photopic) [12]

and

V' (! ) =

K(! )

K 'max

(scotopic) [13]

where K’max =1725 lm/W, and occurs at 510 nm.

If luminous flux corresponds to radiant flux or power, then we should

call it

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EE 737 Photonics Laboratory Manual Radiometry and Photometry

253

!v=luminous flux (lumens) [14]

where the subscript v suggests “vision”. The analog to radiant energy is

luminous energy, measured in Talbots:

Qv=luminous energy (Talbots, or lm-s)[15]

and

!v =

dQv

dt (lumens) [16]

Similarly, the luminous energy density is given by

Wv =

dQv

dV (lm-s/m3) [17]

The photometric unit corresponding to radiant excitance is, predictably,

the luminous excitance

M

v=

d!v

dA (lm/m2 or lux) [18]

Now, the luminous intensity is given by

I

v=

d!v

d" (lm/sr or candela) [19]

The SI unit of luminous intensity is the candela (cd), and when you are

purchasing, for example, light-emitting diodes, they are typically specified in

miilicandela (mcd), since it that is the unit most relevant to our perception of the

lamps’ brightness.

Finally, the luminance corresponds to apparent brightness of an extended

source, taking into account the directionality of the source:

L

v=

dIv

da cos! (lm/m2/sr, or cd/m2) [20]

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EE 737 Photonics Laboratory Manual Radiometry and Photometry

254

Figure 2. Effect of viewing angle on radiance, intensity of a Lambertian source.

This last business of luminance (or radiance) bears some further

investigation. For example, consider a 1 cm2 flat square that emits light

uniformly over its surface and isotropically (evenly in all directions). A source

that radiates evenly in all directions (radiance or luminance = constant) is called

a Lambertian source. The intensity, however, is not a constant with viewing angle,

as may be seen from Figure 2. The intensity is the power per unit solid angle.

When the viewer (or measurement device) is directly in front of the emitting

surface, some maximum reading is obtained. As the viewer goes off axis,

however, the source plane is tilted with respect to the eye, so a cos! projection

factor must be included, which reduces the number or rays that will go through

the detection aperture. The solid angle remains the same, but the effective area

from which rays can be detected has been reduced by the projection factor. A

good example of a Lambertian source is an LED chip. It’s flat, and light is only

emitting from the top planar surface. When you look at the edge, you will detect

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EE 737 Photonics Laboratory Manual Radiometry and Photometry

255

essentially zero light, even though the photons are emitting evenly in all

directions.

The radiance is also invariant with distance from a source, whereas the

intensity is not.

UNITS OF INCIDENT LIGHT

The quantities discussed up till now have all been applied to emitting

sources. We now need to consider how to measure the amount of light landing

on an object or surface. It turns out, fortuitously, that most of the units can be

used in the same way. The total energy incident on a surface is the power

striking the surface integrated over time. The intensity of light striking, say, your

eye can be computer from the solid angle your eye subtends based on your

position relative to the source.

There is one unit that is different, however- the radiant flux crossing a unit

area. If the area in question lies on the source, this quantity is termed “radiant (or

luminous) excitance” (M), as defined earlier. If the flux being measured is

crossing a unit of area on a detecting surface, the convention is to call it

irradiance for radiometry:

E

e=

d!e

dA (W/m2) [22]

and illuminance for photometry:

E

v=

d!v

dA (lm/m2) [23]

Table 1. Radiometric Units

Quantity Symbol Units How to find

Energy Qe Joules (J) fundamental

Fluence Fe J/m2 dQe/dA

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Energy Density We J/m3 dQe/dV

Power (or radiant flux) !" Watts (W) dQe/dt

Intensity Ie W/sr d!"/d#

Excitance (emitters) Me W/m2 d!"/dA

Irradiance (detectors) Ee W/m2 d!"/dA

Radiance Le W/sr-m2 d2!"/d#dAcos$

Table 2. Photometric Units

Quantity Symbol Units How to find

Luminous energy Qv Talbot (lm-s) fundamental

Luminous energy density Wv lm-s/m3 dQv/dV

Luminous flux !% Lumens (lm) dQv/dt

Luminous intensity Iv lm/sr d!%/d#

Luminous excitance Mv lux (lm/m2) d!%/dA

Illuminance Vv lux d!%/dA

Luminance Lv lm/sr-m2 d2!%/d#dAcos$

OTHER SYSTEMS OF UNITS

The units of Watts, Joules, meters, and lumens are all part of the SI system

of units. You will occasionally encounter terms such as “stilb” and “footcandles”

from the cgs and English systems. For example, the SI unit of luminous excitance

or illuminance is the Lux (lumens/m2). In cgs units, the unit is the Phot

(lumens/cm2), and in English units the Footcandle (lm/ft2) was used. Table 3

summarizes the conversions between these systems.

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The basic unit of luminance in the SI systems is the candela/m2,

sometimes called the nit. The cgs equivalent is the stilb (candela/m2), and the

English system has the candela/ft2, no special name.

Finally, there are some units that apply only to Lambertian, diffuse

surfaces, having one lumen per unit area excitance, and these are the Apostilb

(SI), Lambert (cgs), and Footlambert (English). For more discussion of these see

the Handbook of Optics.

Table 3. Conversion factors for units of illuminance (after [1])

Footcandle Lux Phot Milliphot

1 footcandle 1 10.76 1.08E-3 1.076

1 lux 0.0929 1 100E-6 0.1

1 phot 929 10E3 1 1E3

1 milliphot 0.929 10 1E-3 1

Bibiliography

Introduction to Optics, Frank Pedrotti and Leno Pedrotti, Prentice-Hall,

1987.

Electro-optics Handbook, Ronald Waynant and Marwood Ediger, McGraw-

Hill, 1994.

HOMEWORK:

Prove Equation 7.

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REFERENCES

1. The Laser Institute of America, "American national standard for the

safe use of lasers ANSI Z136.1-1986","1986).

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USEFUL OPTICAL COMPONENTS

INTRODUCTION

When you are design a circuit, you can probably design one to do perform

a given function even with a limited vocabulary of components. If you didn’t

know that op amps existed, though, it’d be much more difficult and time

consuming. If you didn’t know transistors existed, there’d be functions you

couldn’t perform at all. The same is true in optics- there are lots of interesting

optical components out there that you may not know about. The purpose of this

section is to tell you about the existence of some of the optical components that

can make your life easier when designing an experiment. We are not trying to

imply we have all of these components at your disposal, but it is useful to know

they exist.

MIRRORS

Of course you already know about lenses and mirrors. But there are some

specialized types of both out there. Let’s start with mirrors.

The mirrors in your bathroom consists of a piece of glass with a silvered

back. If the silvering is good and the surface flat, as shown in Fgure 1a, you’ll get

a decent reflected image, with the travelling the paths shownin the top part of

Figure 1. If the back surface is curved, however, you get a fun-house mirror that

distorts your image. We can use curved mirrors intentionally to focus light,

however. Consider the spherical mirror in the bottom of Figure 1. Parallel rays

striking the surface are reflected back but not along their incoming paths. Note

that this is only true in paraxial approximation; that is, the rays are very close to

the optical axis over their entire lengths. This mirror acts just like a lens, and

even has a focal length.

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Figure 1. Top: a flat mirror. Bottom: a curved mirror focuses like a lens.

The focal length of a spherical mirror is given by

f = !

R

2 { 1}

where R is the radius of curvature of the mirror. The negative sign here reflects

the fact that the image appears on the same side of the mirror as the incoming

beam. One common use of a curved mirror is in a laser resonator cavity- the

mirrors provide focusing and optical feedback at the same time. Also, it is

sometimes necessary to use mirrors to fold an optical path back and forth to

obtain a long path on a short table. In this case, some curved mirrors are often

used to prevent the beam from expanding too much over the length of the path.

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The mirrors used in optics laboratories are front surface mirrors, meaning

that unlike your bathroom mirror, the reflecting surface is not protected by a

layer a glass. The reason for this construction is that Fresnel reflections off the

front surface of the glass would occur in addition to the expected reflection off

the metallization on the back, producing a spurious image. By putting the

reflecting surface on the front, this extra reflection is avoided. The down side of

front surface mirrors is that they are easily damaged since the metallization is

exposed, and therefore the reflecting surface should never be touched with

anything, particularly not your fingers.

You should also be aware that the effectiveness of a mirror depends on the

material it is coated with, and must be matched to the intensity of your source.

You may be surprised to learn that the standard aluminum mirror is only about

90% reflective over the visible and near-IR range, where it is most commonly

used. This can be improved with dielectric coatings (at additional cost). The

energy tolerance of the mirror before it is damaged also depends on the coating.

For mid- and far infrared light, gold mirrors are commonly used because of their

high reflectance in these wavelengths.

Other specialized mirrors in the curved mirror family are parabolic and

elliptical mirrors, used for illumination applications and concentration of light.

For example, consider a light bulb such as that you might find inside an

overhead projector. (Check out the bulb in the solar simulator or quantum well

experiment next time you are down in the lab.) It emits rays in all directions, but

the desired direction of propagation is through the optics of the projector and

onto the screen. If the bulb is placed at the focus of a parabolic reflector, then all

rays will be reflected off the parabola such that they are parallel, Figure 2.

Parabolic reflectors are also used in antennas- all rays entering the parabola are

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reflected through the focus (the incoming rays are assume parallel since the

source of the rays is assumed to be a great distance).

focus

Figure 2. Top: a parabolic reflector. Bottom; an elliptical reflector.

The elliptical reflector is useful for collecting light from a source and

focusing it at another point, as seen in the bottom of Figure 2. If the source is at

one of the foci, the rays will all converge at the other focus. Note that both the

parabolic and ellipsoidal reflector are not good for imaging, but rather for

concentration or collection of light.

Another type of reflector used in the laboratory is the retroreflector, or

corner cube. This device contains three mirrors, all mutually orthogonal. Any ray

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entering the corner cube is reflected off some or all of the surfaces, and the exit

ray will always be parallel to the incoming ray, Figure 3.

Figure 3. A retroreflector.

The utility of such a device can be understood by considering the

following engineering problem: It is desired to measure the distance to the moon

by shining a laser beam to the moon, reflecting it off a shiny object left there by

astronauts, and measuring the time it take the beam to make the round trip. Note

that implicit is the assumption that the reflected beam will return to the same

spot from which it is launched. This has actually been done, and the distance to

the moon measured to within a centimeter. It may strike you as difficult to hit the

corner cube from earth, but even the most directional laser beam spreads out to a

radius of several km by the time it gets to the moon, so aim is not as big an issue

as it first appears. Quiz question: when you look into a corner cube, what will

you see?*

Another device used to reflect a beam back parallel to its incoming path is

a roof prism, Figure 4. This works similarly to the mirror-based corner cube,

except that the optical path is no longer entirely in air, and the reflections are

Answer: your own eye. Can't be anything else.

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now total internal reflections. A solid glass trihedral retroreflector can be used to

retroreflect in three dimensions.

Figure 4. Roof Prism.

LENSES

You already know about thin lenses, which have spherical or planar

surfaces. These can be double convex (both surfaces bow out), plano-convex,

double concave, or plano concave. You have also used compound lenses- the last

time you looked through a microscope. Compound lenses are composed of

several different lenses, as in a microscope objective lens.

Although the focal length of a compound lens is often specified, this

number is not terribly useful in the lab, because it is measured with respect to an

imaginary surface corresponding to the equivalent surface in the equivalent thin

lens. For example, suppose a compound lens has a focal length of 20 mm. A ray

entering the lens parallel to the optical axis will emerge from the lens and cross

the optical axis at the focal point. If we extend the incoming ray and the outgoing

ray until they meet, that defines the principal surface from which the focal length

is measured. For a thin lens, this plane is in the center of the lens. Figure 5

illustrates these two examples. Not that for a compound lens, the location of the

principal planes (there are two, a front one and a back one) can be somewhere

inside the lens, and not necessarily in the center.

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A more useful quantity for a compound lens is its working distance,

which is the distance from the physical front of the lens to the focal point. That is

a distance you can physically measure in the lab. For a thin lens, the working

distance is essentially the same as the focal length since the lens is thin.

front

principal

plane

back

principal

plane

ff

f

working

distance

principal plane

Figure 5. Focal length, principal planes, and working distance. Top: compound

lens. Bottom: thin lens.

Cylindrical lenses are used to focus light along one direction, and leave it

unchanged along another. Such a lens might be used to create a line of light

instead of a point. Figure 6 illustrates the principle behind this type of lens.

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incoming beam

Figure 6. Cylindrical lenses focuses light along one direction only.

A lens (any lens discussed so far) operates by Snell’s law. The curved

surface causes the angle of incidence to change for the rays of a collimated beam

as one goes away from the optical axis. This changing angle of incidence also

changes the angle of refraction, so that the rays are bent according to how far

from the optical axis they lie.

An alternative way to achieve this varying bending of the rays is to

change the refractive index of the glass gradually rather than the angle of

incidence. Such a lens is called a graded index, or GRIN lens. In order to provide

enough bending, the lenses have to be reasonably "thick." Graded index lenses

are generally shaped like rods, hence the term GRIN rod, Figure 6. Usually the

grading is parabolic, that is, goes as r2 where ris the radial position. As a result,

the optical rays are continually bent. The GRIN rod in Figure 6 is cut to a length

that achieves focusing, but if it were longer, the rays would all follow sinusoidal

paths, and all the rays intersect at the nodes, or zeros of the sine function. The

length of one complete sine wave is known as the pitch of the GRIN rod.

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incoming beam

GRIN ROD

GRIN RODcollimated output

Figure 6. A graded index lens (GRIN rod). Top: focusing. Bottom: collimating.

GRIN lenses are generally quite small, and so are useful in applications

where compact size is needed, such as in coupling optical fibers to laser diodes.

They are often used in pairs, to collimate a beam for transmission across a gap,

and to collect the light and focus it onto a fiber or detector.

There is another type of lens that is pretty interesting – the Fresnel lens.

This lens, shown in Figure 7, is usually cast in acrylic and looks a little like a

regular convex lens that has been collapsed. These are often used in overhead

projectors to magnify the light coming from the light source in the base. There is

another Fresnel device called a Fresnel zone plate, which consists of a series of

transparent and opaque rings, also on a flat surface. To explain how these work,

we'd have to go into diffraction theory, which is beyond the scope of this

manual. Fresnel zone plates (not shone) act as spherical lens with multiple focal

lengths. Another key difference between Fresnel lenses and Fresnel zone plates

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in that in the zone plate, the concentric circles get closer and closer away from

the center.

Figure 7. Fresnel Lens. Top: Cross section. Bottom: top view.

OPTICAL FLATS

These are pieces of glass or other optical material, on which one or both

sides is polished to a very high degree of smoothness. They are used to measure

surface quality- the surface under test is brought very close to the polished

surface of the flat. When monochromatic light is shone through the flat, the

reflections from the flat surface interfere with the reflections from the surface

under test. For every 2! phase difference between the two surfaces results in a

fringe, so the fringes give a direct map of the contours of the surface being tested.

BEAMSPLITTERS

Beamsplitters are devices that divide an optical beam into two paths.

These can be power beamsplitters, in which some specified percentage of the

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power is deflected, while the rest continues along its original path (i.e. 50-50, 90-

10, etc.). Figure 8 shows a cube beamsplitter and how it’s used.

primary

reflection

ghost image

Figure 8. Beamsplitters Left: cube type. Right: plate beamsplitter.

The beamsplitting agent itself is a dielectric film. In the cube case, the film

is deposited onto the hypotenuse side of one of the triangular pieces, and the

pieces are cemented together. In the plate case, the film is on one of the surfaces.

In the plate case, a second, Fresnel reflection will occur at the other surface, and

antireflection coatings must be applied to avoid ghost images. In the cube case,

the Fresnel reflection goes back along the incoming path and does not create

ghosts. Because of the optical cement between the two glass pieces, however,

these cannot withstand as high of optical powers as the plate type.

There is a third type of beamsplitter- the pellicle beamsplitter. This one is

made of a stretched membrane, which is so thin that ghost images are essentially

not a problem. These are delicate, however, and can be deformed easily, ruining

them. These are also available with coatings controlling the ratio of reflected to

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transmitted power. Note that as membranes they are sensitive to acoustic

vibrations in the laboratory.

A beamsplitter can also be used as a beam combiner, as in the

interferometer of Figure 9. Two incoming rays are combined such that they travel

along the same path. In the interferometer, one beamsplitter is used to separate

the beam into two components of equal power. One beam stays unchanged, and

the other passed through some device or material that delays it. When the beams

are combined at the second beamsplitter, the phase difference acquired by the

second beam with respect to the first is measured by measuring the degree of

interference. (There is an additional fixed delay due to extra path to and from the

fixed mirrors.)

Object

under test

Figure 9. Use of beamsplitters in an interferometer.

Note that a quick and cheap way to pick a small amount of energy off a

beam, to check the signal or whatever, is to use the 4% Fresnel reflection off the

surface of a piece of glass- microscope slides are mighty handy for that. This

technique is useful for checking that a “signal” one is seeing is actually due to the

experiment, and not fluctuations in the laser source itself-, for example. The

picked off signal could also be used in a feedback loop to subtract out source

fluctuations.

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There are also polarizing beamsplitters, which send each polarization in a

different direction, as will be discussed under prisms, mext.

POLARIZERS

Polarizers are made in a variety of ways. The cheap ones are made by

stretching a polymeric plastic materials (polyvinyl alcohol, or PVA). The

stretching causes the long molecules to line up. The molecules are then dyed

with iodine, and they act as polarizers, absorbing light polarized parallel to the

molecules. The PVA is laminated between two pieces of glass or plastic for

protection. Better quality polarizers are made by embedding a grid of fine wires

in a material. Light whose electric field is polarized parallel to the wires is

transmitted

birefringent

material

Figure 10. A birefringent material can be used to separate the polarizations.

Birefringent materials are those in which the refractive index of the

material depends on the polarization of the light. When light comes into the

material, Figure 10, the refraction angle will be different for the two

polarizations, and therefore the polarizations will be separated. A classic

birefringent material is calcite.

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Separation of polarizations can also be achieved by reflection. Since

Fresnel reflection coefficient is in general different for the two polarizations, the

light after a Fresnel reflection will be partially polarized. If a number of reflecting

surfaces are stacked, then after multiple Fresnel reflections the polarization

purity of the reflected beam can be quite high. Multiple stacks are laminated

between the two pieces of glass in a polarizing beamsplitter cube, for example.

Several types of polarizing prisms are based on birefringent materials. For

example, a Wollaston prism uses birefringence to separate the two polarizations

spatially as shown in Figure 11. There is a fairly wide separation angle for this

geometry, and neither of the emerging rays propagates in the same direction as

the incoming wave, which can complicate alignment of large systems. One

normally puts a stop in front of the unwanted polarization to keep it from

propagating. On the right of Figure 11, the Rochon prism operates similarly to

the Wollaston, but has the feature that part of the beam being “kept” propagates

in the same direction as the incoming beam, the trade-off being smaller angular

separation. The output directions are controlled by proper choice of orientation

of the birefringent crystal and the angle of the interface.

The Glan-Thompson prism uses total internal reflection of one

polarization to deflect that polarization to an absorber, while the unreflected

component is allowed to progress, Figure 12.

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Figure 11. Left: Wollaston prism. Right: Rochon prism. (After [1])

absorber

Figure 12. The Glan-Thompson prism.

WAVE PLATES

In addition to linear polarizers, there are devices to create and analyze

circular and elliptical polarizations. These are the wave plates, which, in

conjunction with linear polarizers, are immensely useful in the lab.

For example, consider a quarter-wave plate. This device is birefringent, so

that the two polarizations propagate at different velocities. If the incident ray is

normal to the surface, there is no angular deviation- both polarizations continue

along the same path, but one travels faster than the other. The result is that the

two electric field components, one polarized perpendicular to the other, are out

of phase at the exit surface. If the thickness of the plate is chosen such that the

phase difference is !/4, it is called a quarter wave plate. If the incoming light has

equal field strengths in the two polarizations (i.e. is linearly polarized at 45°), the

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output will be circularly polarized. Whether the output is RCP or LCP depends

on which polarization is retarded and which is not.

45°

linear

polarizer

circularly

polarized light

quarter

wave

plate

Figure 13. Use of a linear polarizer plus a quarter-wave retarder plate to create

circularly polarized light.

Here is a typical use of a quarter-wave plate. One big problem in working

with lasers is that any back reflection off of optical components can interfere with

proper operation of the laser, depending on the strength of the reflections.

Unfortunately, reflections are unavoidable, since there will be a Fresnel reflection

off every lens and other piece of glass in the optical system. Using a quarter-

wave plate (QWP) can prevent these reflections from entering the laser cavity in

the following manner: the laser light is either already polarized, or passed

through a linear polarizer. On passing through the QWP, the light becomes, let

us say, RCP (right circularly polarized). Upon reflection, however, the returning

beam is LCP (left circularly polarized). When the LCP light passes through the

QWP, the two polarization components are retarded again by a difference of 90°.

The resultant leaving the QWP is now linearly polarized again, but at -45°,

whereas the incoming light was polarized at +45°. The polarizer in Figure 13

stops the back reflection, making an optical isolator. The QWP must be oriented

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properly, however, that is, with its optical axis at 45° to the incoming

polarization.

A half-wave plate can be used to rotate the polarization of a linearly

polarized beam to any arbitrary angle. If the HWP’s optical axis is set at some

angle ! to the incoming light’s polarization (assumed linear) then the output will

also be linearly polarized, but at an angle of 2! to the original polarization.

These wave plates discussed so far are based on optical retardation- one

(linear) polarization travels at a different velocity than the other. All

polarizations (except unpolarized light) can be broken up into linear polarized

components, and the effect of the retardation plate can be worked out.

Just as you can resolve a vector into its Cartesian components, or

equivalently into polar coordinates, so can you resolve any polarization into

either two linear polarizations, or a sum of LCP and RCP components. There are

materials (such as quartz) that are optically active- that is, they slow one of the

circularly polarized components more than the other. This also results in a

change in the output polarization state. For a more detailed discussion, take

EE833.

REFERENCES

1. R. Guenther, Modern Optics, John Wiley and Sons, New York

(1990).

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THINGS STATISTICAL

(or How To Treat Measurement Errors In The Lab)

We are considering taking measurements– analog measurements– in the

laboratory. Suppose, for example, you measure the length of your pencil using a

meter stick marked in mm. You might get the results 15 mm, 15 mm, and 15

mm. Now suppose you try to measure to within 0.1mm. In this case you might

get 15.1, 15.2, and 14.9. This is because you pushing the limits of the resolution of

the meter stick. There is some scatter to your data.

Suppose you try to locate the position of an optical image position

precisely on an optical bench. You have to judge by eye the point at which the

image is perfectly focused. Because there is a limit to how well you can do this,

you may have considerable scatter in your data. Some approach is needed to

handle these variations. In electronic measurements there will always be Johnson

noise caused by random motion of electrons in resistors. If we go to the ultimate

in precision we have to start counting electrons. If we turn up the volume on a

radio we can hear a hiss. That is noise and it will provide a limit on how small a

signal can be and still be detected. In any case, if you try to make precise

measurements your data will be random and unreproducible. This can be a

problem. We would be tempted to start pulling our hair out in response.

Average values

The solution is to consider averages! They are reproducible. There are

several averages of interest. We need to develop background on what they are

and how they will be used.

Let's consider for a moment some random data, N of 'em. Call the

quantity being measured x (for lack of imagination) and the measured values xi,

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where i= 1, 2, 3, .... N. In general, many values will be duplicated. If one plots the

values of x measured against the number of times that particular value is

measured, one might get a curve such as that shown in Figure 1. This curve is

the Gaussian distribution, sometimes called the bell curve or normal distribution,

and there is a theorem (called the Central Limit Theorem) that says that for truly

random data, if you take enough points they will describe the Gaussian curve.

0

x

Figure 1. Number of times a particular measurement occurs.

If you normalize this curve such that the area under it is 1, the curve is

then a probability density curve, P(x). It is centered around the mean, x , and

reflects the relative probability that on your next measurement you will obtain

some particular value x. The average value, or expectation value, x is given by

x

Nxi

i

N

=-

Â1

1

[1]

Now, group the like values. Let there be M different values, and let j be

the index that counts through the different ones; that is, j=1....M. Let the jth

value be repeated Nj times. Then we can rewrite our summation as

x

NN xj j

i

M

=-

Â1

1

[2]

The curve in Figure 1 would be a plot of Nj versus xj (for a large number

of data, not the example data). Next, define the probability density function P(xj):

P x

N

Nj

j( ) =[3]

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so that we have

x P xj j

j

M

==

Â1 [4]

For example, consider the following set of data:

xj Nj Pj

1.0 1 0.01

1.1 1 0.01

1.2 3 0.03

1.3 7 0.07

1.4 12 0.12

1.5 17 0.17

1.6 18 0.18

1.7 17 0.17

1.8 12 0.12

1.9 7 0.07

2.0 3 0.03

2.1 1 0.01

2.2 1 0.01

For this data, N=100 (there are 100 data points), and M=13 (there are 13

different values that occur). We see from the table that the number 1.0 occurred

only once, the number 1.1 occurred once, the number 1.2 occurred three times,

etc. The number 1.6 occurred the most often, namely 18 times.

Let's compute the average:

x x Nj j

j

= ==

Â1

100 1

13

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1

100

1 0 1 1 1 2 3 1 2 7 1 4 12 1 5 17

1 6 18 1 7 17 1 8 12 1 9 7 2 0 3 2 1 2 2

. . . . . .

. . . . . . .

+ + ¥ + ¥ + ¥ + ¥ +¥ + ¥ + ¥ + ¥ + ¥ + +

ÊËÁ

ˆ¯̃

=1.6

These data fall nicely on a bell-shaped curve, as shown in Figure 2. For

some cases, e.g., small values, the probability density curve may not be

symmetric. The Poisson distribution, for example, is skewed to the left. It was

initially checked out by Poisson to predict the number of soldiers in the Prussian

army kicked to death by mules.

1 8

1 6

1 4

1 2

1 0

8

6

4

2

Nu

mb

er

or

occu

ren

ce

s

2 .22 .01 .81 .61 .41 .21 .0

Value

Figure 2. The data from the table fall on a bell-shaped curve.

Even if the measurements are not consistent and reproducible the

averages are. We can now stop pulling our hair out.

Variance and standard deviation

Given that our measurements are random, we might like to know how

close they are. This leads to the ideas of variance and standard deviation. Let us

develop each of these. First, for each measurement xj, let's find out how far that

measurement is from the average: x xj - . Then, we'll square that difference, so

that positive and negative differences have the same effect (we're just interested

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280

in how far from the average the measurements generally are): x xj -( )2

. Then

we'll sum the squares- this results in the variance,

variance = x x Pj

j

M

j-( )=Â

2

1

[5]

where Pj is the probability of the jth value occurring.

The standard deviation, call it s, is the square root of the variance:

s = -Â( )x x Pj j2 [6]

which makes it the root mean square of the difference from average of the data.

The standard deviation is nice because it has the same units as the quantity being

measured, x.

When the number of measurements is very large, the discrete

measurements xj go to a continuous variable x. The probability density function

becomes a continuous distribution P(x), which is still normalized:

P x dx( )

-•

Ú = 1 [7]

The equation for P(x) for a Gaussian distribution then becomes

P x

x x( ) exp

( )=

- -ÊËÁ

ˆ¯̃

1

2 2

2

2s p s[8]

There are the comparable definitions.

x xP x dx=

-•

Ú ( ) [9]

and

s 2 2 2= -( ) = -

-•

Úx x x x P x dx( ) ( ) [10]

These can be easily established using two integrals from an integral table:

e dxx-

-•

Ú =2

p [11]

x e dxx2 2

2-

-•

Ú =p

[12]

and of course the appropriate substitutions.

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Looking at Eq. 8 we see that P(x) is indeed the maximum when x= x . We

also see that P(x) drops off to e-1 of its maximum value when ( )x x- = 2s . We

call the half width 2s . Thus the more scattered the measurements, the wider

the curve.

We can use the area under the curve to tell what fraction of the

measurements will satisfy certain criteria. For example

P x dx( )

-Ús

s

tells the fraction of measurements falling between minus one standard deviation

and plus one standard deviation. This turns out to be 68%. Between the two

sigma points it is 95%, and for the three sigma points 99.7% of the data will fall

between those values.

This is used by manufacturers. If for example their widget is advertised to

have 3 grams of quantity "X" then the manufacturer may decide that he wants at

least 97.7 of his widgets to contain at least 3 grams, and he designs his

manufacturing process to put three sigma more of "X" into the widgets. That

means he is providing many customers with more than their share of "X". If s is

large, he is giving away more "X" than if s is small, so he wants to improve his

manufacturing technique to make s as small as possible. If he is selling a liquid

and he wants to make sure that everyone gets he advertised amount then the

average he puts in his containers has to be greater than the advertised value by

two or three sigma in order to make sure people will get their due. The extra

added above the advertised value represents waste to the manufacturer. If he

can get instruments that are more precise and can reduce s, he saves money. The

point is that the standard deviation is an integral part of his vocabulary.

Subsidiary measurements and calculated values

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When you are making measurements in the laboratory, you often

measure several quantities, and then compute some other quantity from your

measurements. If you original data has some randomness to it, how does that

affect your final results? We will develop some equations to find the standard

deviation of calculated values.

For example, suppose you are to calculate some quantity z based on your

measurements of x and y . Then z is given by the formula z=f(x,y). We assume

that x , y, and z are random uncorrelated variables. That means that if x x- is

negative, then y y- is still just as likely to be positive as negative. Therefore we

can write:

x x y y-( ) -( ) ªÂ 0 [13]

We make a large number of set of x , y, and z . We find x , y , and z and

substitute x and y into the formula and calculate z, call it zcalc. We then ask it

zcalc is close enough to z , whatever "close enough" means.

To get a measure of "close enough:, we derive a general formula. Imagine

we take the total derivative of f(x,y).

dz

f

xdx

f

ydy= +

!

!

!

![14]

We evaluate the partial derivative using average values of x and y. We

also replace dx by x x- and similarly for dy and dz, giving

z zf

xx x

f

yy yj

x y

j

x y

j- = - + -!

!

!

!, ,

( ) ( ) [15]

We square Eq. 15 and sum over all the measurements giving

z zf

dxx x

f

dyy y

f

dx

f

dyx x y y

jx y

j

x y

j

x y x y

j j

-( ) =Ê

ËÁˆ

¯̃-( ) +

Ê

ËÁÁ

ˆ

¯˜̃ -( ) +

Ê

ËÁˆ

¯̃

Ê

ËÁÁ

ˆ

¯˜̃ -( ) -( )

ÂÂ Â

Â

22

2

2

2

2

! !

! !

, ,

, ,

[16]

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283

We notice that because the x and y measurements are uncorrelated, the

last term sums to zero. We then replace the sums of the squares in terms of the

standard deviations.

s!

s!

sfx y

x

x y

y

f

dx

f

dy2

2

2

2

2=Ê

ËÁˆ

¯̃+Ê

ËÁÁ

ˆ

¯˜̃

, ,

[17]

We substitute the measured values of sx, sy and calculate sf. If the

calculated value of z falls within z f±s then we can feel that the expression

z=f(x,y) is verified. If it is outside that range, then the formula is highly

improbable.

As an example, suppose we want to verify the formula for the focal

lengths of a lens:

1 1 1

s d f+ = [18]

We take a lens of known focal length, set the object at a particular

distance, and measure the object and image distances a large number of times.

We find the average values s and d and use them in Eq. [18] to calculate a

predicted focal length. We then calculate the standard deviations, ss and sd. We

need to find sf to compare. We find

!

!

f

s and

!

!

f

d.

f

sd

s d=

+[19]

!

!

f

s

d

s d

sd

s d=

+-

+( )2[20]

!

!

f

d

s

s d

sd

s d=

+-

+( )2[21]

We evaluate these with the average values of s and d and plug them into

the expression for sf along with the values of ss and sd.

s

!

!s

!

!sf s d

f

s

f

d2

22

22= Ê

ËÁˆ¯̃

+ ÊËÁ

ˆ¯̃

[22]

There are two general rules. If we have a sum of terms z=Ax+By, then we

add the squares of the uncertainties.

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284

s s sz x yA B2 2 2 2 2= + [23]

If we have a product, such as z=Cxy, then we add the squares of the

percentage uncertainties in x and y to get the square of the percentage

uncertainty in z.

s s sz x y

z x y

ÊË

ˆ¯

= ÊË

ˆ¯

ËÁˆ

¯̃

2 2 2

[24]

We can use the preceding procedure in a more qualitative way to get a

quick estimate of uncertainties by replacing the standard deviations by an

estimate of the maximum possible error. For example in many cases a

measurement with a meter stick cannot be off by more than a millimeter, or

perhaps a half a millimeter if one is looking closely. One would replace s

calculated as the root mean square difference by one millimeter. That will

provide a quick approximate estimate of the uncertainty before one is ready to

do the final statistical calculation.

Rejection of data

There may be cases where we have a series of random measurements,

and one datum differs considerably from the rest. We might be tempted to reject

it. If we have taken all the data in a consistent manner, we must have good

reason to throw it out. Intuition will not suffice. We can find some rationale by

using the standard variation and looking at the probability density function. Let

the measurement under question be xi, the average be x and the variance be s2.

Then the expression

exp- -( )Ê

ËÁˆ

¯̃

È

ÎÍÍ

x xi

2

2

s[25]

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285

gives the probability of the particular number occurring. If the probability of an

outrageous datum occurring is sufficiently small then one might have reason to

neglect it.

Summary

Precise data will be random and unreproducible. We must use average

values; they are reproducible. The average is the most basic quantity. The

probability density is important, and the variance, and standard deviation are all

well used quantities.

We can use the uncertainties in measured values to find the uncertainties

in calculated from measured values.

HOMEWORK:

1. Derive Equation [23].

2. Derive Equation [24].

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287

A

absorption 98, 153, 199, 239absorption coefficient 201absorption, effect of excitons 146absorption, indirect 200acoustic waves 81active layer, 107air mass zero 196American National Standards Institute 13amorphous silicon 194amplitude sensors 41anterior chamber 5antireflection coatings 203Apostilb 257atmospheric absorption 196atmospheric effects 217attenuation (fiber) 62Auger recombination 202

B

back surface field (BSF) region 203band gap 101band structure 198beam steering 90beamsplitter 269beamsplitter as beam combiner 270beamsplitter, cube 269beamsplitter, pellicle 270beamsplitters, polarizing 271BER (see bit-error-rate) 63Bessel function 32birefringence 271bit error rate 63bit error rate, measurement of 63Bragg angle 88Bragg condition 88Bragg regime of acousto-optic interactions 88Brewster angle 236Brewster windows 236bulk material 145bus lines 215Butoxybenzylidene octylanilene 174

C

cadmium telluride 194calcite 272candela 253carrier confinement 106chemical hazards (to people) 16

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chemical hazards to equipment 21cholosteric 175chopper 161, 163circularly polarized light 274cladding 27, 55cladding, 107CLEANING PROCEDURE FOR ITO COATED GLASS 191clock recovery 63collimate a beam 233combiner, beam 270Commercial liquid crystal cells 186compound lenses 264connectors (fiber) 65contact designs 215core (fiber) 27, 55cornea 4corner cube 262critical angle 27, 54current, short circuit 208current-voltage (I-V) characteristics 203cylindrical lens 266

D

dark current. 155dB 64dBm 64DBR (distributed Bragg reflector 120defect state 202degrees of freedom 173density of states function 145depletion width 206dielectric mirrors 238diffraction 117diffraction efficiency 89diffraction order. 87Diffuse reflection 234diffuse source, MPE's for 11diffusion current density 206diffusion equation 204diffusion length 202direct bandgap 198, 200direct recombination 202directional coupler 42dispersion 60distance-bandwidth product 53, 60distributed Bragg reflector 120distributed feedback laser 120divergence (of a laser diode beam) 117Doppler effect 90

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289

double-heterostructure 106dynamic range 46

E

effective mass 147efficiency loss 212Einstein coefficients 103elastomer splice 68electric dipole moment 84electric field vector 228electric flux density 228electric polarization field 84electric susceptibility 85electrical hazards (to people) 15electro-optic effect 149electro-static discharge 16electroabsorption 147, 150electron affinity 140electrorefraction 148elliptical polarization 247energy band diagram, rules for drawing 140energy bands, semiconductor 101equipment hazards 16errors, measurement 276ESD Precautions 19ESD see electro-static discharge 16excitons 145extended source viewing 5extended source viewing, MPE's for 8external reflection, defined 236eye 4Eye Damage 4eye diagram 62eye, human 252

F

Fabry-Perot cavity 110far field, 117far-field output pattern of a phased array 120Fermi level 140fill factor 209fill factor loss 212finesse, 113flats, optical 268footcandles 257Footlambert 257Fourier optics 5Fourier transform 91Franz-Keldysh effect 150

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290

free spectral range 113Fresnel reflection 269, 270Fresnel reflections 235, 261fusion splicer 67

G

gain curve 114gain guiding 110gallium arsenide 194, 200Glan-Thompson prism 272Goos-Hänchen shift 37graded index fiber 35graded index lens 266graded-index fiber 59grating 127grid lines 215GRIN (graded index) lens 266GRIN rod 266GRINSCH 108guiding of light 28

H

H2O absorption 217half-wave plate 275heavy holes 147HeNe laser 13Hermite polynomial 118Hermite-Gaussian modes 118heteroface 216heterojunction 139high voltage 15homojunction 216homojunction laser 106

I

I-V characteristics 203illuminance 255index guiding 109index of refraction 85, 229index of refraction, complex 148indium phosphide 194indium-tin-oxide 177infrared booster 210intensity modulator, liquid crystal 182interferometric sensors 42internal reflection, defined 236intersubband detection 157intersymbol interference 62intrabeam viewing 5

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291

intrabeam viewing, MPE's for 7irradiance 255ITO (indium tin oxide) 177

Jjacket (fiber) 27, 55jitter 64

KKerr effect 149Kramers-Kronig relations 148

LLabView 129, 165Lambert 257Lambertian source 254lasing threshold 114lattice vibrations 200LED (light emitting diode) 114lens (of the eye) 5lens law 232lens, compound 264lens, concave 264lens, convex 264lens, cylindrical 266lens, graded index 266lens, microescope objective 264lenses 264lifetime, minority carrier 202light emitting diode 114light holes 147linear polarization 241linearity 45link budget 64liquid crystal cell 177lnear field, 117longitudinal mode 115longitudinal modes of a laser 119loss, open circuit voltage 212loss, short circuit current 212loss,fill factor 212lumens 252luminance 254luminous energy 253luminous energy density 253luminous excitance 253luminous flux 253luminous intensity 253Lux 257

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M

Mach-Zehnder interferometer 43macrobending loss 28macrobending sensor 41magnetic field vector 228magnetic flux density 228magnetization density 228magnification M of a lens 233Malus' Law 244Malus’ Law 190materials, solar cell 194Maximum Permissible Exposure 5Maxwell's equations 227microbending 40mirror stacks 119mirror, curved 259mirror, front surface 261mirror, spherical 259mirrors 259mirrors, elliptical 261mirrors, gold 261mirrors, parabolic 261misalignment, angular (fiber) 67misalignment, lateral (fiber) 66misalignment, longitudinal (fiber) 66mode 28, 56mode coupling 39monochromator 127MPE see maximum permissible exposure 5multimode (fiber) 57multimode (laser) 115multiple quantum wells 153

N

NA see numerical aperture 56ndium-tin-oxide 190nematic 175noise 62NRZ(non-return-to-zero) 62numerical aperture 30, 56

O

Octyloxy-cyanobiphenyl 174open circuit voltage 208open circuit voltage loss 212optical activity 275optical cavity 110optical confinement. 107

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optical flats 268optical gain- 100optical path length 230optical retardation 275optical scanner 91optical switching 90

P

parasitic resistances 213Part Susceptibility Data 18particle theory of light 230pellicle beamsplitter 270permeability 228permittivity 228phase grating 86phase locking 120phase sensitive detector 163phase sensors 42phase shifter, liquid crystal 180phase-space absorption quenching 150phased laser array 120phonon 199Phot 257photodetector 195photodiode 154photometric units 256photometry 252photons 230photopic response 252photovoltage 201plane wave 229Pockels effect 149Poisson distribution 280polarization density 228polarization, circular 274polarization, elliptical 247polarization, linear 241polarizers, plastic 271polarizing beamsplitters 271polyvinyl alcohol 271population inversion 104posterior chamber 5potential well 142potential well, finite 138potential well, infinite 137power-current curve (of a laser) 114Poynting Vector 228pressure waves 81principal planes 264

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294

principal surface 264prism, Rochon 272prism, roof 263prism, Wollaston 272propagation constant b 30pumping 105PVA (polyvinyl alcohol) 271

Qquadrature. 45quantization of modes 36quantum mechanics 136quantum noise 62quantum structures 145quantum well detectors 154quarter-wave plate 273quasi-continuum 138

Rradiance 251radiant density 250radiant energy 249radiant excitance 250radiant fluence 250radiant flux 249radiant intensity 250radiant power 249radiation damage 194radiative recombination 202radiometric units 256radiometry 249Raman-Nath regime of acousto-optic interactions 87Rayleigh scattering 217real image 232receiver 60recombination processes 202reflection coefficient 113reflection.surface 203reflective device liquid crystal display 193reflector, elliptical 262refractive index 229repeatability 47resistance, lateral 214resistance, sheet 215resolution 47responsivity 156retina 5retinal damage 2retroreflector 262, 264

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295

Rochon prism 272roof prism 263

S

safety 2safety rules 14saturation current density 206Schrodinger's equation 136scotopic response 252sensitivity 46separate confinement 108seven segment display 188shear waves 81Shockley-Read-Hall (SRH) recombination 202short circuit current 208short circuit current loss 212shot noise 62signal to noise ratio 62silicon 194, 200single mode 57slab waveguide 36slit widths, monochromator 132, 162, 169slits widths, tradeoffs 128slits, monochromator 128smectic 175Snell's law 26, 54, 107, 232Snell’s law 266SNR see signal to noise ratio 62solar cell 194solar constant 196solar radiation 196solid angle 250specular reflection 234SPLICE LOSSES 65splices (fiber) 65spontaneous emission 99, 239standard deviation 280Stark effect 151step index fiber 35, 59steradians 250stilb 256stimulated emission 100, 240strain 82stress, 82sunglasses 236supermode 120surface reflection 203surface-emitting laser 119

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T

Talbots 253texturing (of solar cell surfaces) 216the Fresnel reflection 113thermal noise 62thermalization 198threshold level, choice of 61threshold, lasing 114timing jitter 64total internal reflection 26, 54, 107transient protection for laser diodes 21transimpedance amplifier 61transmissive liquid crystal display 193Triboelectric Series 19trunk lines 53tungsten filament projector lamp 218

V

V parameter 34vacuum level 140variance 280velocity, surface recombination 207Vernier micrometer 78vertical cavity laser 119virtual image 232vitreous humor 5voltage, open circuit 208

W

wave equation 228wave plates 273waveguide, laser 107wire 53Wollaston prism 272working distance 265wrist strap 20