Photonic Crystal Bragg Stack

Bragg Stack Design

Design wavelength λ₀ 550 nm

Layer pairs N 8

High index n_H (vs n_L=1.45) 2.40

Probe Light

Probe wavelength λ 550 nm

Reflectance R(λ)

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Transmittance T(λ)

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Gap center

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Gap width

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Reflectance Spectrum

How it works

A 1D photonic crystal is a stack of alternating dielectric layers with indices n_H and n_L, each a quarter-wave thick at a chosen design wavelength λ₀: d = λ₀ / (4n). Interference between the many partial reflections at each interface builds a photonic band gap — a wavelength range that cannot propagate through the stack at all, exactly the mechanism behind dielectric mirrors, DBR laser facets and anti-reflection coatings.

The field is computed exactly with the standard optical transfer-matrix method. Each layer j contributes a 2×2 characteristic matrix relating the field (E, H) at its front and back faces:

M_j = [ cos δ_j        i sin δ_j / η_j ]
      [ i η_j sin δ_j   cos δ_j        ]
δ_j = 2π n_j d_j / λ     η_j = n_j (TE, normal incidence)

Multiplying all layer matrices together and combining with the substrate admittance gives the complex reflection coefficient r, so R = |r|², T = 1 − R (lossless stack, energy is conserved). The same matrices, applied interface by interface, give the exact field amplitude everywhere — that field is what the moving curve through the stack shows: a standing wave that propagates outside the gap and decays evanescently into the stack when λ sits inside the gap.

λ₀ sets where the layers are quarter-wave and shifts the gap.
N (layer pairs) — more pairs make the gap deeper and its edges sharper.
n_H — a bigger index contrast with n_L widens the gap.
λ — the probe wavelength; sweep it through the gap to watch the field switch from a propagating wave to an exponentially localized one.

High index layer (n_H) Low index layer (n_L = 1.45) EM field amplitude

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