Generation, propagation, manipulation, and detection of light at interfaces and in linearly-responding media — the applied-optics wing of classical and quantum electrodynamics. Fresnel equations (Fresnel 1823) — for a plane wave incident…
photonics
Fresnel at normal incidence: r = (n₁−n₂)/(n₁+n₂)
Fresnel equations (Fresnel 1823) for a plane wave at a planar interface between two non-magnetic, non-absorbing dielectrics of real…
Snell's law & total internal reflection: sin θ_c = n₂/n₁
Snell's law n₁ sin θ_i = n₂ sin θ_t follows from continuity of the tangential wave vector at a planar dielectric interface. For n₁ > n₂…
Lorentz oscillator ε(ω) = 1 + ω_p²/(ω₀²−ω²−iγω)
Lorentz oscillator model — bound electrons treated as damped harmonic oscillators with natural frequency ω₀, damping γ, and plasma…
R + T ≡ 1 and air→glass pin R=1/25, T=24/25 (exact)
Closed-form identity and pinned rational evaluation of the normal-incidence Fresnel equations. Energy conservation: R + T = r² + (1 − r²)…
Glass-air TIR: sin²θ_c = 4/9 (exact)
Closed-form evaluation of the critical-angle formula at the canonical glass–air interface. sin θ_c = n₂/n₁; substituting n₁ = 3/2, n₂ = 1…
ε(ω₀) = 1 + i·ω_p²/(γ·ω₀): Re=1, Im=ω_p²/(γω₀) (exact)
Closed-form symbolic evaluation of the Lorentz dielectric function at resonance. Substituting ω = ω₀ kills the ω₀² − ω² numerator in the…
Total-internal-reflection critical angle: sin(theta_c) = n_2/n_1; sqrt-2 instance
Total-internal-reflection critical-angle framework (Snell 1621; Newton 1704 Opticks). Setup: light propagating from a denser medium n_1 to…
Fabry-Perot cavity finesse F = pi sqrt(R)/(1 - R); rational canonical form
Fabry-Perot cavity-finesse framework (Fabry-Perot 1899 Annales de Chimie et de Physique). Setup: a Fabry-Perot interferometer is two…
Coherent state |alpha> = e^{-|alpha|^2/2} sum alpha^n/sqrt(n!) |n>; permutation/factorial
Coherent-state framework (Schroedinger 1926 Naturwissenschaften 14, 664; Glauber 1963 Phys Rev 130, 2529). Setup: the coherent state…
Theorem: 2 sin^2(pi/4) - 1 = 0 (TIR sqrt-2-medium 45-degree critical angle)
Theorem (TIR-pi-over-4 canonical): for n_1 = sqrt(2), n_2 = 1 the critical angle theta_c satisfies sin theta_c = 1/sqrt(2), so sin^2…
Theorem: F (1 - R) - pi sqrt(R) = 0 (Fabry-Perot rational-finesse identity)
Theorem (cavity-finesse-rational canonical): F = pi sqrt(R)/(1 - R) cleared of denominator gives F(1-R) = pi sqrt(R), residual F(1-R) - pi…
Theorem: sum_{n=0}^inf alpha^{2n}/n! exp(-alpha^2) - 1 = 0 (coherent-state Poisson normalisation)
Theorem (coherent-state-Poisson-normalisation canonical): sum_{n=0}^{infty} (|alpha|^{2n}/n!) exp(-|alpha|^2) = exp(-|alpha|^2) *…
Photonic crystals (Yablonovitch 1987)
E Yablonovitch 1987 + S John 1987 photonic-bandgap; modern slow-light + photonic-crystal-fibers Russell 2003 + topological-photonics.
Frequency comb (Hall-Hansch 2005)
Hall-Hansch Nobel 2005 mode-locked-laser optical frequency comb; modern attoclock + atomic-clock-comparison; ppb-precision metrology.
Metamaterials (Pendry 1999)
Veselago 1968 negative-index theory; Pendry 1999-2000 split-ring-resonator + perfect-lens; Smith 2000 first negative-index demonstration.
Plasmonics (Stockman 2008)
Stockman 2008 review nano-plasmonics; LSPR Mie-theory; modern plasmonic-metasurfaces + nanolasers + sub-diffraction guiding.
Silicon photonics (2000s)
Soref-Lorenzo 1986 + Lipson 2010s + Vahala 2003; CMOS-compatible photonics; modern silicon-PIC + co-packaged optics datacenters.
Topological photonics (Haldane-Raghu 2008)
Haldane-Raghu 2008 photonic-quantum-Hall; Wang-Soljacic 2009 magneto-photonic-crystal demonstration; modern Floquet + non-Hermitian…
Photonic bandgap (Yablonovitch 1987)
E Yablonovitch 1987 photonic-bandgap; modern modern foundational text + photonic-crystals + topological-photonics + chiral 2024.
Optical fiber (Kao 1966)
C Kao 1966 (Nobel 2009) low-loss-fiber predict; modern modern foundational text + DWDM 100Tbps backbone + space-division multiplex.
Frequency comb (Hall-Hänsch Nobel 2005)
J Hall-T Hänsch 2005 (Nobel 2005) optical-frequency-comb; modern modern atomic-clock 10^-19 + Sisyphus precision-spectroscopy.
FDTD (Yee 1966)
K Yee 1966 finite-difference-time-domain; modern modern foundational text + meep + Lumerical + 2024 GPU-MEEP exascale.
Purcell effect (1946)
E Purcell 1946 cavity-enhanced-spontaneous-emission F=3λ³Q/(4π²V); modern modern foundational + nano-cavity Ag-coated + plasmonic-nano.
Topological photonic (Haldane-Raghu 2008)
F D M Haldane-S Raghu 2008 topological-photonic-Floquet; modern Wang 2009 first-realization gyromagnetic + Khanikaev 2013 + valley.