1

Introduction to Optical Electronics

Quantum (Photon) Optics (Ch 12)

Resonators (Ch 10)

Electromagnetic Optics (Ch 5)

Wave Optics (Ch 2 & 3)

Ray Optics (Ch 1)

Photons & Atoms (Ch 13)

Laser Amplifiers (Ch 14)

Lasers (Ch 15) Photons in Semiconductors (Ch 16)

Semiconductor Photon Detectors (Ch 18)

Semiconductor Photon Sources (Ch 17)

Optics Physics Optoelectronics

2

Optics

Ray Optics (Geometrical Optics)

Wave Optics (Gaussian Beam)

E&M Optics (Geometrical Optics)

Quantum Optics (Photon Optics)

1 1 2 2

Snell's Law

sin sinn n 21

1n 2n

• Focus on location & direction of light rays• Limit of Wave Optics where 0

• Scalar wave theory (Single scalar wavefunction describes light)

• Two mutually coupled vector waves (E & M)

• Describes certain optical phenomena that arecharacteristically quantum mechanical

2 20

0 2( ) exp exp ( )

( ) ( ) 2 ( )

WU A jkz jk j z

W z W z R z

r

2z0 z0 2z0z0

W0

W0

z

x

E-field of Gaussian Beam

2

1 h

h

h

Stimulated Emission

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Chronological Development of Optics

• Euclid (300 BC)• Hero of Alexandria (150 BC – 250 AD ?)• Alhazen (1000 AD)• Franciscan Roger Bacon (1215 – 1294)• Johannes Kepler (1571 – 1630)• Willebrord Snell (1591 – 1626)• Rene Descartes (1596 – 1650)• Pierre de Fermat (1601 – 1665)

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Simple OpticsSpherical Mirror

• Rays parallel to and close to axis (paraxial) act like a paraboloid mirror

• Parallel rays further from axis focus to caustic (green line)

• The caustic is the surface perpendicular to all reflected parallel rays

R R2

Paraboloid

Spherical

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Refraction & Total Internal ReflectionSnell’s law of refraction: 1 1 2 2sin sinn n

2 1n n

2n

1 2n n

12

1 2 2

1 2 1

and / 2

sin sin /c

n n

n n

12

11

1 2n n

c

For Total Internal Reflection:

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Concave & Convex Mirrors

z1 -R z2 02

R

P1 P2

2

C

A

F

1

y

Sign Convention for Mirrors

RNegative for Concave

Positive for Convex

zNegative on Right

Positive on Left

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Concave & Convex Mirrors(Paraxial Approximation)

z1 -R z2 0

2

R

z1 0 z2 R

2

R

1 2

Imaging Equation

1 1 2 1

z z R f

2 2

1 1

Magnification

My z

y z

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Spherical Boundaries Refraction

1 2 2 1

1 2

n n n n

z z R

1 2

1n 2n

y

R

P1 C P2

i

2

r

V

12

1z 2z

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Sign Conventions for Lensesfor light moving Left to Right

z1, f1 + left of Vertex

z2, f2 + right of Vertex

R + if C is right of Vertex

y1, y2 + above optical axis

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Spherical Boundaries Refraction

1n 2n

y

O

1 1 1( , )P y z

2 2 2( , )P y z

z z

1 2 2 1

1 2

22 1

1

n n n n

z z R

zy y

z

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Thin Lenses

1P 2P

1 2

1z 2z

y

O

1 1 1( , )P y z

2 2 2( , )P y z

F

1z 2zO

f

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Positive Lenses(Thicker Center)

Negative Lenses(Thinner Center)

Lenses

Bi-convex• R1 > 0• R2 < 0

Planar Convex• R1 = ∞• R2 < 0

Meniscus Convex• R1 > 0• R2 > 0• R2 > R1

Bi-concave• R1 < 0• R2 > 0

Planar Concave• R1 = ∞• R2 > 0

Meniscus Concave• R1 > 0• R2 > 0• R1>R2

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Ray Transfer Matrix (ABCD Matrix)

A method for mapping rays through a series of optical elements. Assumes:– Paraxial approximation (slope = rise/run = tan )

– Linear relation between exit (y2, 2) and entrance (y1, 1) coordinates

2 1

2 1

A B

C D

y y

where A, B, C and D are real.1

2

y1

y2

Input Plane Output Plane

Optic Axis

z1 z2

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ABCD MatrixExample: Free Space

2 1

2 1

1

0 1

y yd

1

2

y1

y2

Input Plane Output Plane

Optic Axisd

2 1 1

2 1

y y d

1

0 1

d

M

z1 z2

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ABCD MatrixExample: Refraction across planar boundary

2 11

2 12

1 0

0

y yn

n

2 1

2 2 1 1

12 1

2

sin sin ,

y y

n n

n

n

1

2

1 0

0n

n

M

1

2

y1= y2

Optic Axisz1,2

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ABCD MatrixExample: Thin Lens

2 1

2 1

1 0

11

y y

f

2 1

2 1

y y

y

f

1 0

11

f

M

1

2

Input Plane Output Plane

Optic Axisz1

z2

y1 y2

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Concave Mirrors

1 01 0

12 11fR

M

2

R

-R

2

R

-R

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Simple Optical Components

1 2 1

2 2

1 0n n nn R n

M

1

0 1

d

M

1

1 0

1f

M

1 0

0 1

M

1

2

1 0

0 nn

M

2

1 0

1R

M

Free-Space Propagation

Refraction at a Planar Boundary

Refraction as a Spherical Boundary

Transmission Through a Thin Lens

Refraction from a Planar Mirror

Refraction from a Spherical Mirror

convex, R>0; concave, R<0

convex, f>0; concave, f<0

convex, R>0; concave, R<0

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Optical Cavities

d

R1R2

M1 M2

Unit Cell

…1

1

22

2

2

Rf

Rf

1 1 2 2

2 2

1 2 1 1 2 2

1 1

1 11 1

1 1

1 11 1 1

d d

d d

f f f f

d dd d

f f

d d d d

f f f f f f

M

d d d

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Explain these lens systems

1M

2M

3M

4M

1. Parallel rays entering the system all exit at the same y2

2. Rays entering the system at the same point y1, all exit at y2.

3. Parallel rays enter system, emerging rays are also parallel

4. Rays emit from a single point, emerge parallel

1

2y

1y2y

12

1y 2

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Introduction to Optical Electronics

Quantum (Photon) Optics (Ch 12)

Resonators (Ch 10)

Electromagnetic Optics (Ch 5)

Wave Optics (Ch 2 & 3)

Ray Optics (Ch 1)

Photons & Atoms (Ch 13)

Laser Amplifiers (Ch 14)

Lasers (Ch 15) Photons in Semiconductors (Ch 16)

Semiconductor Photon Detectors (Ch 18)

Semiconductor Photon Sources (Ch 17)

Optics Physics Optoelectronics

22

Chronological Development of Optics (part 2)

• Robert Hooke (1635 – 1703)• Isaac Newton (1642 – 1727)• Christian Huygens (1629 – 1695)• Thomas Young (1772 – 1829)• Augustin Fresnel (1788 – 1827)

• Speed of Light– Christenson Romer (1644 – 1710)– Armand Fizeau (1819 – 1896)– Jean Bernard Foucault (1819 – 1868)

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Wavefunction (monochromatic) Wave Equation

Complex Wavefunction Wave Equation

Complex Amplitude Helmholtz Equation

Paraxial Wave* Paraxial Helmholtz Equation

Wave Optics

( ) ( ) j k zU A er r

22

2 2

10

uu

c t

( , ) ( ) cos[2 ( )]u t a t r r r

( ) 2( , ) ( ) j j tU t a e e rr r2

22 2

10

UU

c t

( )( ) ( ) jU a e rr r 2 2 ( ) 0k U r

2T 2 0

AA j k

z

*A(r) varies slowly with respect to

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Elementary Waves

2 2

2

(Fresnel Approx to a spherical wave)

Spherical Wave ( )

Paraboloidal Wave( )

Plane Waves ( )

jkr

x yjkj k z z

j

AU e

r

AU e e

z

U Ae

k r

r

r

r

Spherical Paraboloidal Plane