Optics & Photonics

The Science of Light

From the simplest reflection off a mirror to the most exotic quantum entanglement of photon pairs, optics and photonics encompass the full physics of electromagnetic radiation. This graduate-level course takes you on a journey through six major pillars of optical science, building from classical ray optics all the way to the quantum theory of light.

Classical Foundations

  • - Geometrical optics and ray tracing
  • - Wave optics, diffraction, and interference
  • - ABCD matrix formalism for optical systems
  • - Resolution limits and aberration theory

Modern Photonics

  • - Laser physics and cavity design
  • - Fiber optics and telecommunications
  • - Nonlinear frequency conversion
  • - Quantum optics and photon statistics

Why Study Optics?

Photonics is one of the most impactful areas of physics and engineering. Lasers, optical fibers, and photonic devices underpin modern telecommunications, manufacturing, medicine, and scientific instrumentation. The 2018 Nobel Prize in Physics was awarded for groundbreaking inventions in laser physics (optical tweezers and chirped-pulse amplification), and the 2005 Nobel recognized the quantum theory of optical coherence and frequency-comb techniques.

“Optics is the mother of physics. The study of light has driven the greatest revolutions in our understanding of nature, from Newton's corpuscular theory to Maxwell's electromagnetic waves to Einstein's photons and quantum electrodynamics.”

Key Equations of Optics

Throughout this course, you will derive and apply these fundamental relations:

Snell's Law

$$n_1 \sin\theta_1 = n_2 \sin\theta_2$$

Airy Diffraction Pattern

$$I(\theta) = I_0 \left[\frac{2J_1(ka\sin\theta)}{ka\sin\theta}\right]^2$$

Einstein Rate Equations

$$\frac{dN_2}{dt} = B_{12} N_1 \rho - (A_{21} + B_{21}\rho) N_2$$

Fiber V-Number

$$V = \frac{2\pi a}{\lambda}\sqrt{n_1^2 - n_2^2}$$

Second-Harmonic Generation

$$P^{(2)} = \epsilon_0 \chi^{(2)} E^2$$

Photon Correlation

$$g^{(2)}(\tau) = \frac{\langle I(t)I(t+\tau)\rangle}{\langle I\rangle^2}$$

Course Roadmap

Part I: Geometrical Optics

Fermat's principle, Snell's law, ray tracing through mirrors and lenses, ABCD matrix formalism, and Seidel aberrations. The regime where wavelength is negligible compared to feature size.

Part II: Wave Optics

Huygens-Fresnel principle, Fraunhofer and Fresnel diffraction, Airy pattern, Rayleigh resolution criterion, and thin-film interference. Light as a wave phenomenon.

Part III: Lasers

Einstein coefficients, population inversion, rate equations, cavity modes, specific laser systems (He-Ne, Nd:YAG, semiconductor), mode-locking, and Q-switching.

Part IV: Fiber Optics

Total internal reflection, step-index and graded-index fibers, numerical aperture, V-number and guided modes, chromatic dispersion, loss mechanisms, EDFA amplifiers, and WDM systems.

Part V: Nonlinear Optics

Second- and third-order susceptibilities, second-harmonic generation, parametric down-conversion, self-phase modulation, the Kerr effect, and optical solitons in fibers.

Part VI: Quantum Optics

Photon statistics (coherent, thermal, Fock states), beam splitter transformations, Hanbury Brown-Twiss experiment, Hong-Ou-Mandel effect, squeezed states, and quantum key distribution (BB84).

Prerequisites

Electrodynamics

Maxwell's equations, wave equation, plane waves, polarization, and boundary conditions.

Quantum Mechanics

Dirac notation, harmonic oscillator, creation/annihilation operators, and perturbation theory.

Mathematics

Fourier transforms, complex analysis, linear algebra, and differential equations.

Recommended Textbooks

  • -Hecht, “Optics” — Comprehensive coverage of classical optics at the advanced undergraduate level.
  • -Saleh & Teich, “Fundamentals of Photonics” — The standard graduate reference covering wave optics, lasers, fiber optics, and nonlinear optics.
  • -Siegman, “Lasers” — Authoritative treatment of laser theory, cavity design, and Gaussian beam propagation.
  • -Boyd, “Nonlinear Optics” — The definitive text on nonlinear optical processes and applications.
  • -Gerry & Knight, “Introductory Quantum Optics” — Clear presentation of photon statistics, coherence, and quantum states of light.

Historical Milestones

1621Snell discovers the law of refraction
1678Huygens proposes wave theory of light
1801Young's double-slit experiment demonstrates interference
1865Maxwell unifies electricity, magnetism, and optics
1905Einstein explains the photoelectric effect via photons
1917Einstein introduces stimulated emission (foundation of lasers)
1960Maiman demonstrates the first laser (ruby laser)
1966Kao proposes low-loss optical fibers (Nobel Prize 2009)
1984Bennett & Brassard propose BB84 quantum key distribution
1987Hong-Ou-Mandel demonstrate two-photon interference
Start Part I: Geometrical Optics →