## The course

This page describes the notes (382 pages, 6″x9″) from the fall 2012 session of the University of Toronto Advanced Classical Optics course (PHY485H1F), taught by Prof. Joseph H. Thywissen, which I took as a non-degree student.

These notes are available in three forms:

- On amazon (kindle-direct-publishing) for $11 USD,
- As a free PDF,
- As latex sources (, makefiles, figures, …) to build/modify yourself.

The official course description at the time was:

This course builds on a student’s knowledge of basic electromagnetic theory by focusing attention on light including elementary aspects of the propagation of optical beams and their interaction with matter. We examine light polarization, coherence, interference and diffraction as we move towards a description of lasers within a semiclassical picture in which the fields are treated classically and matter is treated quantum mechanically. In between we discuss Gaussian beam modes and their relation to optical resonators as well as fibre and slab waveguides

Mathematica notebooks associated with the class are also available.

## Contributing.

Should you wish to actively contribute typo fixes (or additions, editing, …) to these notes, you can do so by contacting me, or by forking your own copy of the associated git repositories and building the book pdf from source, and submitting a subsequent merge request.

git clone git@github.com:peeterjoot/latex-notes-compilations.git peeterjoot cd peeterjoot submods="figures/phy485-optics phy485-optics mathematica latex" for i in $submods ; do git submodule update --init $i (cd $i && git checkout master) done export PATH=`pwd`/latex/bin:$PATH cd phy485-optics make

I reserve the right to impose dictatorial control over any editing and content decisions, and may not accept merge requests as-is, or at all. That said, I’ll probably not refuse reasonable suggestions or merge requests.

## Contents:

- Copyright
- Document Version
- Dedication
- Preface
- Contents
- List of Figures
- Course Notes
- 1 Matrix methods in Geometric Optics
- 1.1 Missing content
- 1.2 Matrix methods
- 1.2.1 Free propagation
- 1.2.2 Refraction off of a flat lens
- 1.2.3 Refraction of a curved surface
- 1.2.4 ABCD matrix for a lens
- 1.2.5 Properties of the transfer matrix
- 1.3 Problems
- 2 Geometric optics: Rays and and optics with graded index
- 2.1 Reading
- 2.2 Eikonal equation. Where are the rays in Maxwell’s equations?
- 2.3 Poynting vector
- 2.4 Ray equation
- 2.5 GRIN (Graded Refractive INdex) optics
- 2.6 Trap a ray
- 2.7 Gradium Lens
- 2.7.1 Phase delay in GRIN lens?
- 2.8 Ray equation and action minimization
- 2.9 Problems
- 3 Diffraction
- 3.1 Context
- 3.2 Diffraction
- 3.3 A calculated example: pinhole
- 3.4 Fresnel and Fraunhofer diffraction (non-pinhole apertures)
- 3.5 Fresnel diffraction from an edge
- 3.6 Problems
- 4 Coherence
- 4.1 Interference
- 4.2 Zoology of interferometers
- 4.3 Lloyd’s interferometer
- 4.4 Types of coherence
- 4.4.1 Longitudinal coherence
- 4.4.2 Transverse coherence
- 4.5 More general mutual coherence
- 4.6 Temporal Coherence (cont.)
- 4.7 Spatial coherence
- 4.8 Spatial Coherence (cont.)
- 4.9 What’s so special about this pathlength difference?
- 4.10 Continuum spatial distribution
- 4.11 Full derivation of the Van Cittert-Zernike theorem
- 4.12 Problems
- 5 Multiple interference
- 5.1 Multiple interference
- 5.2 Fabry-Perot interferometry
- 5.3 Fabry-Perot Etalon review
- 5.4 Cavity (or Etalon) \(Fabry-Perot\) as an oscillator
- 5.5 Diffraction grating interferometry
- 5.6 Problems
- 6 Lasers and Gaussian beams
- 6.1 Lasers
- 6.2 Laser pump rates
- 6.3 Gaussian modes
- 6.4 Non-dimensionalized comparison of QM and spatial light equations
- 6.5 Solving the homogeneous paraxial wave equation
- 6.6 Guoy phase shifts and higher order Gaussian modes
- 6.7 Spectral line width (coherence time) of laser
- 6.8 Number of photons per free space mode
- 6.9 Problems
- Course prep
- 7 Derivation of Fresnel equations for mixed polarization
- 7.1 Motivation
- 7.2 Setup
- 7.3 Solving for the Fresnel equations
- 8 Some worked problems from “Modern Optics”, the vectoral nature of light
- Appendixes
- A Mathematica notebooks
- B Cosine Transforms
- B.1 Motivation
- C Possible content for formula sheet (up to midterm)
- C.1 Rules
- C.2 Geometric optics
- C.3 Misc trig
- C.4 Eikonal
- C.5 Wave relations
- C.6 Electrodynamics
- C.7 Misc calculus results
- C.8 Diffraction
- C.9 Coherence
- C.9.1 Temporal coherence
- C.9.2 Spatial coherence
- C.10 Multiple interference
- C.10.1 Fabry-Perot
- C.10.2 Diffraction grating interferometry
- C.11 Lasers
- C.12 Gaussian beams
- C.13 Fourier transforms
- D Planck blackbody summation
- D.1 Motivation
- D.2 Guts
- E Vector identities
- E.1 Curl of curl
- F Fowles optics typos
- G Typos in the course text
- Bibliography