Guided Propagation Along the Optical Fibersite.iugaza.edu.ps/mtastal/files/Pres3-fiberHO.pdf · Guided Propagation Along the Optical Fiber The Nature of Light • Quantum Theory –

Guided Propagation Along

the Optical Fiber

The Nature of Light

• Quantum Theory – Light consists of

small particles (photons)

• Wave Theory – Light travels as a

transverse electromagnetic wave

• Ray Theory – Light travels along a

straight line and obeys laws of

geometrical optics. Ray theory is valid

when the objects are much larger than

the wavelength (multimode fibers)

Refraction and reflection

Snell’s Law: n1 Sin Φ1 = n2 Sin Φ2

Critical Angle:

Sin Φc=n2/n1

the refractive index (n) of

a material is :

adimensionless number that

describes how light propagates

through that medium. It is

defined as c/v

https://www.youtube.com/watch?v=yfawFJCRDSE&t=28shttps://www.youtube.com/watch?v=dwmF9f65WWs

Classification based on Refractive index

1. Step-index Optical Fiber

2. Graded-index Optical Fiber

Step Index Fiber

Core and Cladding are glass with appropriate optical

properties while buffer is plastic for mechanical

protection

n1 n2

n1>n2

Step Index Fiber

Single Mode Step Index Fiber

Protective polymerinc coating

Buffer tube: d = 1mm

Cladding: d = 125 - 150 m

Core: d = 8 - 10 m

n

r

The cross section of a typical single-mode fiber with a tight buffertube. (d = diameter)

n1

n2

© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

Meridian Ray Representation

1

2

2

1

2

2

2

1 12 n

n

n

nn

Total Internal Reflection

Cladding

Corem ax

A

B

< c

A

B

> c

m ax

n0

n1

n2

Lost

Propagates

Maximum acceptance anglemax is that which just gives

total internal reflection at thecore-cladding interface, i.e.when = max then = c.

Rays with > max (e.g. ray

B) become refracted andpenetrate the cladding and areeventually lost.

Fiber axis


Comparison of fiber structures

Graded Index Fiber

nb

nc

O O'Ray 1

A

B'

B

AB

B' Ray 2

M

B' c/nb

c/na12

B''

na

a

b

c We can visualize a graded indexfiber by imagining a stratifiedmedium with the layers of refractiveindices na > nb > nc ... Consider two

close rays 1 and 2 launched from Oat the same time but with slightlydifferent launching angles. Ray 1just suffers total internal reflection.Ray 2 becomes refracted at B andreflected at B'.


n1

n2

21

3

nO

n1

21

3

n

n2

OO' O''

n2

(a) Multimode stepindex fiber. Ray pathsare different so thatrays arrive at differenttimes.

(b) Graded index fiber.Ray paths are differentbut so are the velocitiesalong the paths so thatall the rays arrive at thesame time.

23


Step and Graded Index Fibers

n decreases step by step from one layerto next upper layer; very thin layers.

Continuous decrease in n gives a raypath changing continuously.

TIR TIR

(a) A ray in thinly stratifed medium becomes refracted as it passes from onelayer to the next upper layer with lower n and eventually its angle satisfies TIR.(b) In a medium where n decreases continuously the path of the ray bendscontinuously.

(a) (b)


Total Internal Reflection

Fiber axis

12

34

5

Skew ray1

3

2

4

5

Fiber axis

1

2

3

Meridional ray

1, 3

2

(a) A meridionalray alwayscrosses the fiberaxis.

(b) A skew raydoes not haveto cross thefiber axis. Itzigzags aroundthe fiber axis.

Illustration of the difference between a meridional ray and a skew ray.Numbers represent reflections of the ray.

Along the fiber

Ray path projectedon to a plane normalto fiber axis

Ray path along the fiber


Skew Rays

Skew rays

Skew rays circulate around the core and

increase the dispersion

Fiber Key Parameters

Fiber Key Parameters

Major Issues in fiber-optic

Effects of Dispersion and Attenuation

1. Attenuation

• Attenuation in fiber-optic: is the gradual loss in intensity

of any kind of flux through a medium.

https://www.youtube.com/watch?v=yzHhgdRw2Gk

t0

Pi = Input light power

Emitter

Optical

InputOptical

Output

Fiber

Photodetector

Sinusoidal signal

Sinusoidal electrical signalt

t0

f1 kHz 1 MHz 1 GHz

Po / Pi

fop

0.1

0.05

f = Modulation frequency

An optical fiber link for transmitting analog signals and the effect of dispersion in thefiber on the bandwidth, fop.

Po = Output light power

Electrical signal (photocurrent)

fel

10.707

f1 kHz 1 MHz 1 GHz


Fiber Optic Link is a Low Pass Filter

for Analog Signals

Attenuation Vs Frequency

Attenuation in Fiber

Attenuation Coefficient

• Silica has lowest attenuation at 1550 nm

• Water molecules resonate and give high

attenuation around 1400 nm in standard fibers

• Attenuation happens because:

– Absorption (extrinsic and intrinsic)

– Scattering losses (Rayleigh, Raman and Brillouin…)

– Bending losses (macro and micro bending)

dB/km dB)(dB)0(

z

zPP

All Wave Fiber for DWDM

Lowest attenuation occurs at

1550 nm for Silica A

tten

uati

on

ch

ara

cte

rist

ics

Escaping wave

c

Microbending

R

Cladding

Core

Field distribution

Sharp bends change the local waveguide geometry that can lead to wavesescaping. The zigzagging ray suddenly finds itself with an incidenceangle that gives rise to either a transmitted wave, or to a greatercladding penetration; the field reaches the outside medium and some lightenergy is lost.


Bending Loss

Power loss in a curved fiber

Power in the evanescent field evaporates first

Bending-induced attenuation

Micro-bending losses

2. Dispersion

• Dispersion is the phenomenon in which the phase velocity of a

wave depends on its frequency.

• Media having this common property may be termed dispersive

media.

• Sometimes the term chromatic dispersion is used for specificity.

https://www.youtube.com/watch?v=SAEQND4NyoM

Dispersion for Digital Signals

t0

Emitter

Very short

light pulses

Input Output

Fiber

Photodetector

Digital signal

Information Information

t0

~2²

T

t

Output IntensityInput Intensity

²

An optical fiber link for transmitting digital information and the effect ofdispersion in the fiber on the output pulses.


Major Dispersions in Fiber

• Modal Dispersion: Different modes travel at different velocities, exist only in multimodal conditions

• Waveguide Dispersion: Signal in the cladding travel with a different velocity than the signal in the core, significant in single mode conditions

• Material Dispersion: Refractive index n is a function of wavelength, exists in all fibers, function of the source line width

Low order modeHigh order mode

Cladding

Core

Light pulse

t0 t

Spread,

Broadened

light pulse

IntensityIntensity

Axial

Schematic illustration of light propagation in a slab dielectric waveguide. Light pulseentering the waveguide breaks up into various modes which then propagate at differentgroup velocities down the guide. At the end of the guide, the modes combine toconstitute the output light pulse which is broader than the input light pulse.


Modal Dispersion

Polarization Mode Dispersion (PMD)

Each polarization state

has a different

velocity PMD

PM dispersion

• https://www.youtube.com/watch?v=DKCHYUxXYXo

t

Spread, ²

t0

Spectrum, ²

12o

Intensity Intensity Intensity

Cladding

CoreEmitter

Very short

light pulse

vg(

2)

vg(

1)

Input

Output

All excitation sources are inherently non-monochromatic and emit within aspectrum, ² , of wavelengths. Waves in the guide with different free spacewavelengths travel at different group velocities due to the wavelength dependenceof n1. The waves arrive at the end of the fiber at different times and hence result in

a broadened output pulse.


Material Dispersion

Material Dispersion

Zero

Dispersion

Wavelength

Modifying Chromatic Dispersion

Chromatic Dispersion = Material dispersion

+ Waveguide dispersion

• Material dispersion depends on the material properties and difficult to alter

• Waveguide dispersion can be altered by changing the fiber refractive index profile

– 1300 nm optimized

– Dispersion Shifting (to 1550 nm)

– Dispersion Flattening (from 1300 to 1550 nm)

Zero Dispersion Wavelength

0

1.2 1.3 1.4 1.5 1.61.1

-30

20

30

10

-20

-10

(m)

Dm

Dm + Dw

Dw0

Dispersion coefficient (ps km -1 nm -1)

Material dispersion coefficient (Dm) for the core material (taken asSiO2), waveguide dispersion coefficient (Dw) (a = 4.2 m) and the

total or chromatic dispersion coefficient Dch (= Dm + Dw) as a

function of free space wavelength,


Total Dispersion

For Single Mode Fibers:

For Multi Mode Fibers:

Group Velocity Dispersion

If PMD is negligible

Dispersion & Attenuation

Summary

Fiber

Production, Installation, Maintains tools

• Left to group of students (25 minutes) next

time.

• Who?

Documents

Guided Propagation Along the Optical Fibersite.iugaza.edu.ps/mtastal/files/Pres3-fiberHO.pdf · Guided Propagation Along the Optical Fiber The Nature of Light • Quantum Theory –