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…