ECEn 662R
Physical Optics Winter
2007
COURSE SYLLABUS
1. Scalar and
Electromagnetic waves
A. Vector wave equation
1. Maxwell equations
2. Dielectric media
B. Scalar wave equation
C. Scalar monochromatic waves
1. Real representation
2. Complex representation
3. Helmholtz equation
4. Optical irradiance
5. Wavefronts
6. Elementary scalar waves
a. Plane wave
b. Spherical wave
c. Paraboloidal wave
D. Polychromatic scalar waves
1. Complex representation
for polychromatic light
2. Power spectral density
2. Quasi-monochromatic
waves
E. Monochromatic
electromagnetic (vector) waves
1. Real representation
2. Complex representation
3. Helmholtz equation
4. Energy flow for
electromagnetic fields
a. PoyntingÕs theorem
b. Poynting vector
c. Optical irradiance and
power
5. Elementary
electromagnetic waves
a. Transverse
electromagnetic (TEM) waves (E&M plane waves)
F. Relation between TEM
waves and scalar plane waves
2. Coherence
A. Qualitative overview
1. Temporal coherence
2. Spatial coherence
B. Quantitative description
1. Mutual coherence
a. Definition
b. Relation to intensity
2. Complex degree of
coherence
3. Spatial and temporal
coherence
C. Spectrum and temporal
coherence
1. Coherence time
2. Coherence length
3. Relationship between
spectral width and temporal coherence
D. Examples and rules-of-thumb
1. Apparent spatial extent
(solid angle) and spatial coherence
2. Spectrum and temporal
coherence
3. Polarization
A. Definition
B. Polarization of monochromatic
plane waves
1. Polarization ellipse
equation
2. Principle axis system
3. Complete description of
polarization state
4. Linear polarization
5. Circular polarization
C. Other polarization
representations
1. Electric field
representation
2. Ellipse representation
3. Complex number
representation
4. Ellipsometric angle
representation
5. Poincare sphere
6. Jones vector
a. Orthogonal polarization
states
b. Decomposition of
arbitrary state into sum of orthogonal states
D. Jones matrix calculus
1. Polarizers
a. Ideal & non-ideal
b. Define transmission of
an optical element represented by Jones matrix
c. Rotated polarizer
c. MalusÕs law
d. Stack of rotated
polarizers
2. Retarders (wave plates)
a. Index ellipsoid
b. Uniaxial birefringent
materials (positive & negative, c-axis)
c. Jones matrices for
general unrotated and rotated retarders
d. Half-wave retardation
plate (HWP)
e. Quarter-wave
retardation plate (QWP)
3. Examples
a. Optical isolator
b. Phase shifter,
Q-switch, CD/DVD readout
c. Form birefringence
& sub-l gratings
d. Wire grid polarizers
e. Retarders with sub-l gratings
f. Rotated arbitrary
wave plate between crossed polarizers
g. Create arbitrary
polarization state with QWP & polarizer
h. How to measure
arbitrary polarization state with QWP & polarizer
i. Wavelength
dependence of a QWP, zero and multiple order retarders
j. Babinet-Soleil
Compensator (BSC)
k. How to measure
arbitrary polarization state with BSC & fixed polarizer
l. Adiabatic
following
E. Stokes vectors
a. Definition –
monochromatic case
b. Stokes vectors for
partially polarized light
c. Stokes vectors for
special cases, fully polarized light (linear, circular, É)
d. Stokes vector
measurement
e. Relationship between
Stokes vectors & Poincare sphere
f. Partially
polarized light & Poincare sphere
g. Mueller matrices
4. Reflection and
refraction of plane waves
A. Geometry
B. Electromagnetic boundary
conditions
1. Phase terms
a. Law of reflection
b. SnellÕs law
2. Remaining terms
a. Fresnel equations
C. Reflectance and
transmittance
D. Examples
1. Normal incidence
2. Amplitude and phase
changes at arbitrary incidence
E. Total internal
reflection
1. Properties
2. Evanescent waves
3. Frustrated TIR
4. Goos-Hanchen shift
F. Brewster angle
5. Two-beam
interference
A. Mathematical description
1. Electromagnetic waves
2. Scalar waves
B. Division of wavefront
1. YoungÕs double-slit
experiment
2. Effect of coherence
3. Other configurations
a. FresnelÕs mirrors
b. LloydÕs mirror
c. FresnelÕs biprism
d. BilletÕs split lens
C. Division of amplitude
1. Dielectric slab
2. Haidinger interference
fringes
3. Fizeau fringes
4. NewtonÕs rings
5. Michelson
interferometer
6. Twyman-Green
interferometer
7. Mach-Zender
interferometer
8. Sagnac interferometer
a. Geometry
b. Measurement of
rotational speed
D. Interference of orthogonal
polarization states using an analyzer
E. Example of shearing
interferometer: Nomarski reflection interference contrast microscopy
6. Multiple beam
interference
A. Mathematical description
1. Electromagnetic waves
2. Scalar waves
B. Phasor diagrams
C. N-slit interference
D. Dielectric slab
E. Fabry-Perot
interferometer
F. Fabry-Perot
spectroscopy
G. Thin film coating on a
substrate
H. Ellipsometry
I. Single layer
antireflection coating
J. Two layer
antireflection coating
K. Stratified media
L. Bragg mirrors
7. Absorption and
dispersion
A. Dielectric materials with
absorption
1. Phenomenological
approach: absorption coefficient
2. Complex refractive
index
3. Relation between
absorption coefficient and extinction coefficient
B. Reflection at interface of
absorptive dielectric material
C. Optics of metals
D. Dispersion
1. Phenomenological
approach with examples
2. Relation between
absorption and dispersion: Kramers-Kronig relations
E. Examples
1. Absorption and
dispersion for a damped oscillator
2. Absorption and
dispersion for a medium with three resonances
3. Typical absorption and
dispersion for a medium
F. Normal and anomalous
dispersion