Photonic Crystal

Physics: 1D photonic crystal: alternating layers of refractive index n₁ (thickness d₁) and n₂ (d₂). Quarter-wave condition: n₁d₁ = n₂d₂ = λ/4 maximizes the photonic bandgap. Bandgap width: Δω/ω = (4/π)·arcsin|(n₂−n₁)/(n₂+n₁)|. Transfer matrix method solves exactly. More periods N → sharper band edges, deeper stopband. Slow light: group velocity v_g = dω/dk → 0 at band edge. 2D/3D photonic crystals require bandgap for both polarizations; full 3D gap requires high index contrast. Photonic crystal fiber: hollow core guided by bandgap, not total internal reflection.