Photonic Crystal Bandgap

Band structure and stop bands in a 1D dielectric multilayer photonic crystal
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Relative bandgap width Δω/ω₀

Photonic Bandgap

A periodic dielectric stack creates a photonic band structure analogous to electrons in crystals. At certain frequencies, Bragg reflections from all layers add constructively — creating a photonic bandgap where light cannot propagate.

Bragg condition: 2(n₁d₁ + n₂d₂) = mλ
Gap width: Δω/ω₀ = (4/π)arcsin|(n₁−n₂)/(n₁+n₂)|

Quarter-wave stack (n₁d₁ = n₂d₂ = λ/4) maximizes the bandgap. Omnidirectional reflection arises when the bandgap exists for all angles and polarizations.

Applications: laser mirrors, VCSEL cavities, optical fiber coatings, structural color in butterfly wings (no pigment — just photonic crystals).