Distributed Bragg Reflector: Photonic Stopband Simulator

Stack Design

High index n_H 2.35

Low index n_L 1.45

Layer pairs N 6

Incidence angle θ₀ 0°

Live Result

R at λ₀

--%

T at λ₀

--%

Stopband

-- nm

d_H = -- nm, d_L = -- nm, λ₀ = 550 nm

How it works

A Distributed Bragg Reflector (DBR) stacks two transparent materials of alternating refractive index n_H and n_L, each cut to a quarter of the design wavelength:

d_H = λ₀ / (4·n_H)
d_L = λ₀ / (4·n_L)   (λ₀ = 550 nm)

Reflectance is computed with the transfer-matrix (characteristic matrix) method, not an approximation. Each layer j contributes:

δ_j = (2π/λ)·n_j·d_j·cosθ_j
M_j = [ cosδ_j        i·sinδ_j/η_j ]
      [ i·η_j·sinδ_j  cosδ_j       ]
η_j = n_j·cosθ_j  (Snell: n₀sinθ₀ = n_j sinθ_j)

The per-layer matrices multiply into one total matrix M = M₁M₂…M_2N, which is combined with the incident-medium and substrate admittances (η₀, η_sub) to give the complex amplitude reflection r and the reflectance R = |r|².

n_H, n_L — the two material indices; a bigger contrast (n_H − n_L) widens the stopband and boosts peak reflectance per pair.
N — number of HL periods; more pairs push peak R toward 100% exponentially.
θ₀ — incidence angle; tilting the stack blue-shifts the stopband and splits it for the two polarizations (this model uses s-polarization).

This exact math designs the mirrors inside laser cavities, dielectric mirrors, and anti-reflection or high-reflection coatings on real optics.

Reflectance R(λ)

High index (n_H) Low index (n_L) Photon

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