Advanced Classical Optics
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Advanced Classical Optics

Notes and problems from UofT PHY485H1F 2012

About the Book

This book is based on my lecture notes for the Fall 2012, University of Toronto Advanced Classical Optics course (PHY485H1F), taught by Prof. Joseph H. Thywissen.

About the Author

Peeter Joot
Peeter Joot

Peeter Joot is a math and physics enthusiast with a love of geometric algebra.

Peeter's education includes a B.A.Sc from UofT (1997 Engineering Science - computer engineering), 2019 UofT M.Eng (ECE electromagnetics), a lot of self-study, and non-degree study of most of the interesting 4th year UofT undergrad physics courses.

Peeter's day job is software development. He has over 20 years of experience with low level systems programing, operating system and hardware abstraction and exploitation, concurrency, and large scale refactoring. Peeter works for LzLabs and now has fun with PL/I, COBOL, JCL, VSAM, CICS and other legacy subsystems sure to scare away most developers of his generation.

Table of 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

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