ECEn 662R                                        Physical Optics                                       Winter 2007





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