Optics & Photonics

From rays to photons, and the engineering in between

About this course

Optics built up in layers — rays, polarisation, interference and coherence, Fourier optics, Gaussian beams and lasers.

What you will be able to do

  • Apply Fermat's principle and ray matrices to optical systems
  • Describe polarisation algebraically and explain birefringence and Brewster's angle
  • Analyse interference and interferometers in terms of coherence
  • Use Fourier optics to explain imaging and the resolution limit
  • Describe Gaussian beams, laser threshold, and where classical optics stops

What this course covers

  • Jones Vector: polarization as a complex 2D vector
  • The three-polarizer experiment as a motivating test
  • Polarizer as a projection matrix; Malus's law as a consequence
  • Wave plates as unitary matrices; two kinds of devices
  • Three-polarizer calculation and the N-polarizer limit
  • Non-commutativity of optical elements
  • Limits of Jones calculus: unpolarized light cannot be a Jones vector
  • The Gaussian beam: shape and Rayleigh range
  • Radius/diameter and unit-tracking cautions
  • The waist–divergence lock (beam spread prohibition)
  • The beam-spread prohibition and the optimal beam
  • Ray-transfer matrices and the round-trip stability criterion
  • Named cavities, the marginal boundary, and the G-parameter limit
  • The hair: sensitivity at the stability boundary and beam–ray equivalence
  • Limits of the ideal model and the M² factor
  • Four pictures of light and course framing
  • Fermat's principle and optical path length
  • Deriving Snell's law from Fermat's principle
  • Stationary vs. least time — the correct statement of Fermat's principle
  • Limits of ray optics — the pinhole camera argument
  • Reflection law derived from Fermat's principle
  • Stationarity as a unifying principle across physics
  • Key vocabulary: aperture function, spatial frequency, three planes
  • Fraunhofer diffraction as exact Fourier transform
  • Lens maps angle to position: transform becomes a physical plane
  • Role of phase: fields versus intensities in the focal plane
  • Spatial filtering: low-pass and high-pass masks
  • Focal-plane filtering is not spatial averaging
  • Lens rim as inherent low-pass filter and resolution limit
  • Coherence as a source property
  • Complex degree of coherence and visibility
  • Coherence length and the rule-of-thumb critique
  • Shape, not width, determines visibility
  • Phase of γ and fringe inversion at revival
  • Spatial coherence as the same Fourier sum
  • Worked specification and capstone lessons
  • Birefringence and the index ellipsoid
  • Cut angle and its effect on birefringence
  • The waveplate thickness equation
  • The ladder of equivalent thicknesses
  • Retardance versus rotation: waveplates and optical activity
  • The cost of the ladder: drift, temperature, and cutting tolerance
  • Phase versus length: the central result
  • Snell's law as a given foundation
  • Refraction equation's solution set and when it is empty
  • Enumeration of the critical edge across seven interfaces
  • The critical angle and the grazing refracted ray
  • Solid-angle fraction of directions that escape
  • Step-index optical fibre and numerical aperture
  • Modal delay spread: the price of a wider acceptance cone
  • Evanescent field and the meaning of 'total'
  • Spatial frequency and numerical aperture defined
  • The cutoff as an exact zero, not a soft roll-off
  • Abbe distance versus Rayleigh criterion: two different kinds of number
  • Structured illumination: doubling the effective cutoff by adding a known pattern
  • Localization precision versus resolution: the single-point prior
  • Comparison of super-resolution methods: what each adds and what it costs
  • The diffraction limit reframed: a limit on one measurement, not on knowledge
  • Laser threshold as exact round-trip equality
  • Loss budget and output-coupler dominance
  • Bracketing irrational numbers instead of rounding
  • Threshold gain coefficient and inversion density
  • Gain saturation and the gain clamp above threshold
  • Single-mode oscillation from the gain clamp
  • Limits of the steady-state model and falsification
  • Interferometer as a length-to-count converter
  • Fringe count formula and exact linearity
  • Michelson vs. Mach-Zehnder: crossings and sensitivity
  • Two-port energy conservation and optical switching
  • Sagnac interferometer and reciprocal cancellation
  • Michelson common-mode rejection vs. Sagnac exact rejection
  • Strain sensitivity on a long arm and Sagnac rotation limit
  • Worked specification: arm-matching bound
  • Classical optics' divisibility assumption and its failure
  • Poisson counting law and its terms
  • Variance equals mean: the central identity
  • The shot-noise floor: brightness vs. noise trade-off
  • Verdict cost: discriminating two sources
  • The four frontiers and which assumptions they expire
  • Interferometer fringe cost and closing synthesis
  • Fabry-Perot cavity: infinite beam family
  • Airy function from geometric series
  • Free spectral range and finesse
  • Cost of high finesse: settling time and throughput
  • Airy function vs. two-beam fringe: a provable distinction
  • Thin-film coating as the same series
  • Worked case: loss and flatness degrade finesse
  • S and P polarization vocabulary and Fresnel coefficient definitions
  • The one structural asymmetry between the two Fresnel coefficients
  • Exact zero versus very small: why the distinction is the whole lecture
  • Brewster's angle as an exact root of the P numerator
  • Degree of polarization and its unique maximum at Brewster's angle
  • Whose angle it is: dependence on index ratio, not wavelength or brightness
  • Complex index, pseudo-Brewster minimum, and where the exact result stops
  • Applications: Brewster windows and ellipsometry
  • Core vocabulary: object, image, focal length, magnification, real vs. virtual
  • The thin-lens equation and focal length
  • Two sign conventions: Real-is-Positive (R) vs. Cartesian (C)
  • Real vs. virtual images: convention-independent definition
  • What survives a change of convention: the invariance ledger
  • Worked case: classifying an image from a given result
  • Ray as a two-number vector; the paraxial approximation
  • The two-matrix catalog of first-order optics
  • Non-commutativity and the commutator as a computable number
  • Instrument as an ordered matrix product: enumeration of distinct instruments
  • Afocal systems: the telescope and beam expander from one parts list
  • Spherical aberration and coma: where the paraxial tool fails
  • Chromatic aberration and the achromatic doublet

Syllabus

  1. Rays and Imaging

    1. L1 · Fermat's Principle, and Where Rays Come From
    2. L2 · Total Internal Reflection, and How Light Gets Trapped in Glass
    3. L3 · Lenses and Mirrors, and the Image That Is Not There
    4. L4 · Ray Matrices, and Why Real Lenses Disappoint

  2. Polarisation

    1. L5 · Polarization, and the Algebra of a Two-Vector
    2. L6 · Birefringence, and Cutting a Crystal to Order
    3. L7 · Brewster and Fresnel, and the Angle That Kills a Reflection

  3. Coherence and Interference

    1. L8 · Coherence, and What a Source Can Promise
    2. L9 · Interferometers, and Measuring a Fraction of a Wavelength
    3. L10 · Fabry-Perot, and What Many Beams Do That Two Cannot

  4. Fourier Optics and Resolution

    1. L11 · Fourier Optics, and the Lens as a Transform
    2. L12 · Resolution, and Beating a Limit That Was Called Fundamental

  5. Beams, Lasers and Photons

    1. L13 · Gaussian Beams, and the Shape a Laser Actually Has
    2. L14 · Lasers, and Why Threshold Is a Real Number
    3. L15 · Photons, Detection, and Where Classical Optics Stops