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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
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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
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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