Lecture notes

9-7-10

Intro

Lecture 1

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Photonics overview

Optics overview

Ray optics

9-9-10

Intro

Lecture 2

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Review

Matrix optics

9-14-10

Review

Wave equations

9-16-10

Review

New material

Interference

9-21-10

Prof’s advice

Review

New material

Waves, ETALON

Polychromatic waves

Beam optics

9-23-10

Came in a couple minutes late…things written on the board…see his slides…I think this is a calculation of Etalon properties.

   π1
1---0.9992??

        π        π
F = 1--(1--δ)2 = 2δ

Imax   ---1---         --I0--    2
  I0  = (1- r)2 = 250k = (2δ)2 ∝ F

δ = 1 - r, ? < 1

This is something like a filter. (Etalons and cavities). It increases intensity inside the cavity by a lot…constructive interference I think

Now polychromatic waves looking at same cavity phenomena

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Transmission of Gaussian beams (optical components)

9-28-10

Homework 3 problem 4 notes

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9-30-10

Came in ~30 min late…

τ  =  ----1----
      2πνFW HM
   =  -1-F--
      2π Δν
   ≈  1-dF
      π c

Spherical mirror resonators

10-5-10

10-7-10

Reflection

10-12-10

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10-14-10

10-19-10

10-26-10

10-28-10

11-4-10

11-9-10

11-16-10

11-23-10

11-30-10

12-7-10

12-9-10

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Ray and matrix optics (chapter 1)

Intro

Postulates of ray optics

Propagation in a homogeneous medium

In this the path of minimum time is also the path of minimum distance (the latter of which is Hero’s principle), since c is constant.

Reflection from a mirror

Law of reflection:

Reflection and refraction at the boundary between two media

Simple optical components

Mirrors

Planar boundaries

Spherical boundaries and lenses

Light guides

Graded-index (GRIN) optics

Matrix optics

Matrices of simple optical components

Very cool fact from homework solutions (and that he mentioned in class)

Wave optics (chapter 2)

Introduction

Postulates of wave optics

Monochromatic waves

Solutions to Hemholtz equation

Simple optical components

Interference

Polychromatic and pulsed light

Pulsed plane wave

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Beam optics (chapter 3)

The Gaussian beam

Transmission through optical components

Transmission through an arbitrary optical system

Hermite-Gaussian beams

Resonator optics (chapter 10)

Math notes

Intro

From lecture slides

Planar-mirror resonators

How things change when there are losses

Spherical-mirror resonators

Gaussian modes

Two- and three-dimensional resonators

Microresonators

Electromagnetic optics (chapter 5)

Electromagnetic theory of light

_______________________________________________________________________________________________________ Boundary conditions between two dielectrics

In general

No free charges/currents

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_______________________________________________________________________________________________________ Fundamental theorems of vector calculus

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Electromagnetic waves in dielectric media

Linear, nondispersive, homogeneous, isotropic media

Relaxing these conditions (only listed are the changes from the previous state)…

Inhomogeneous media (e.g., GRIN materials)

Anisotropic media (but homogeneous!)

Dispersive media

Nonlinear media

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Derivation of particular equations from Maxwell’s equations

Maxwell’s equations in matter (general):

 ∇ ⋅D   =  ρf
∇ × E   =  - ∂B-
             ∂t
 ∇ ⋅B   =  0
∇ × H   =  J  + ∂D-
            f   ∂t

Assuming no currents or charges (source-free):

 ∇ ⋅D  =   0
∇ × E  =   - ∂B
             ∂t
 ∇ ⋅B  =   0
∇ × H  =   ∂D-
           ∂t
This becomes (source-free):
   ∇ ⋅(ϵ0E +P )  =  0
                      ∂(μ0H-+-μ0M-)
         ∇ × E   =  -      ∂t
∇ ⋅(μ0H + μ0M )  =  0
                    ∂(ϵ0E +P )
         ∇ × H   =  ----∂t----
Starting with the second equation, we have (source-free all the way through):
                         ∂(μ0H  + μ0M )
            ∇ × E   =  - -----∂t------
                           (∂ (- μ H - μ M ))
   -→  ∇ × (∇ ×E )  =  ∇ ×  -----0-----0---
                                   ∂t
- → ∇ (∇ ⋅E )- ∇2E   =  - μ0 ∂-(∇ × H) - μ0 ∂-(∇ × M )
                           ∂t            ∂t
Our grand starting point for the electric field (assuming all is similar for the magnetic field) is (source-free):
|-------------------------------------------|
|                 ∂2              ∂         |
|∇ × (∇ ×E ) = - μ0∂t2 (ϵ0E + P )- μ0∂t (∇ × M )
---------------------------------------------

Dirk said that the permeability is typically constant throughout the material, so I’m pretty sure that implies ∇× M = 0:

                 ∂2-
∇ × (∇ × E) = - μ0∂t2 (ϵ0E +P )

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Monochromatic electromagnetic waves

Elementary electromagnetic waves

The transverse electromagnetic (TEM) plane wave

The spherical wave

Paraxial rays (points near the z-axis)

The Gaussian beam

Optics of conductive media

Polarization optics (chapter 6)

Intro

Reflection and refraction

TE Fresnel equations
  ′
E--= -----2ncoμsi---- = t⊥ = ts
E    n cosi + μ′n ′cosr

 ′′          μ- ′
E--= n-cos-i--μμ′n-cosr = r⊥ = rs
E    n cos i+ μ′n ′cosr

TM Fresnel equations
E ′       2nn′cosi
E--= nn′cosr+--μ′n′2cosi = t∥ = tp
               μ

E′′  μμ′n′2cosi- nn′cosr
E--= -μ′n′2cosi+-nn′cosr = r∥ = rp
     μ

Photonic-crystal optics (chapter 7)

Intro

From lecture slides

One-dimensional photonic crystals

Two- and three-dimensional photonic crystals

Photon optics (chapter 12)

Intro

From lecture slides

The photon

Photon streams

Photons and atoms (chapter 13)

Intro

Energy levels

Occupation of energy levels

Interactions of photons with atoms

Spontaneous emission

Absorption

Stimulated emission

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Spontaneous emission into all modes

Induced (stimulated) transitions: absorption and stimulated emission

Homogeneous line broadening

This is when all of the atoms of a medium are taken to be identical and to have identical lineshape functions.

Lifetime broadening

Collision broadening

Inhomogeneous line broadening

Thermal light

Laser amplifiers (chapter 14)

Tip

Intro

Theory of laser amplification

Amplifier pumping

Pumping schemes

Four-level system

Three-level system

Amplifier nonlinearity

Saturated gain in inhomogeneously broadened media

Doppler-broadened medium

Lasers (chapter 15)

Intro

Theory of laser oscillation

Characteristics of the laser output

Power

Spectral distribution

Homogeneously broadened medium

Inhomogeneously broadened medium

Spectral hole burning in a Doppler-broadened medium

Spatial distribution and polarization

Mode selection

Common lasers (skipping details)

Solid-state lasers

Examples are ruby, alexandrite, Nd3+:YAG, Nd3+:glass, Er3+:silica fiber, Nd3+:YVO4, Yb3+:YAG, Ti3+:sapphire, fiber lasers, Raman fiber lasers, random lasers (scattering itself provides feedback)

Gas lasers

Examples are He-Ne, Ar+, Kr+ (atomic and ionic lasers), CO2, methanol, water (molecular gas lasers), excimer (“excited dimer”) lasers, chemical lasers such as HF

Other lasers

Organic dye lasers, solid-state dye lasers, extreme UV and x-ray lasers, free-electron lasers

Pulsed lasers

Why pulse lasers? Doing it greatly increases optical power (total energy is the same of course, it’s just stored in the “off time”).

Methods of pulsing lasers

Obviously we should do this internally, not externally, to not waste energy.

Gain switching (periodically increasing gain, constant loss)

Turn the laser pump on and off. These is easy to do using electrical pulses.

Q-switching (constant gain, periodically decreasing loss)

Reduce the loss via a modulated absorber inside the resonator. Energy is stored in the atoms.

Cavity dumping (constant gain, periodically increasing loss)

Increase the loss via altering the mirror transmittance. Energy is stored in the photons. Like periodically dumping a bucket of water that’s constantly being filled.

Mode locking

Couple together the modes of a laser and lock their phases to each other. Like Fourier components.