1D Photonic Crystal Band Gap

Alternating dielectric layers create photonic band gaps via Bragg interference. Quarter-wave stack condition n₁d₁ = n₂d₂ = λ/4 maximizes the gap. Transfer matrix method gives exact band structure.

Layer Parameters

Bragg wavelength λ_B
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Gap width Δω/ω₀
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Quarter-wave condition
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Transfer matrix per unit cell:
M = M₁·M₂ = [cos(δ) −i·sin(δ)/n; −i·n·sin(δ) cos(δ)]

Band gap: |tr(M)/2| > 1
At QW: gap = 4/π · arcsin((n₁-n₂)/(n₁+n₂))