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===Example code===
We can use the following code in [[
<!--
% this code is released to Public Domain
% (c) 2007 Muthiah Annamalai
% Author: Muthiah Annamalai
%
% This code was written based on Prof. Danner's resource on PWE:
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-->
<syntaxhighlight lang="matlab">
%
% solve the DBR photonic band structure for a simple
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% we assume an infinite stack of 1D alternating eps_r|air layers
% y-polarized, z-directed plane wave incident on the stack
% periodic in the z-direction;
%
% parameters
d = 8; % air gap
a = 10; % total periodicity
d_over_a = d / a;
eps_r = 12.2500; % dielectric constant, like GaAs,
% max F.S coefs for representing E field, and Eps(r), are
Mmax = 50;
% Q matrix is non-symmetric in this case, Qij != Qji
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% here n runs from -Mmax to + Mmax,
freqs = [];
for Kz = - pi / a:pi / (10 * a): + pi / a
Q = zeros(2 * Mmax + 1);
for x = 1:2 * Mmax + 1
for y = 1:2 * Mmax + 1
X = x - Mmax;
Y = y - Mmax;
kn = (1 - 1 / eps_r) * d_over_a .* sinc((X - Y) .* d_over_a) + ((X - Y) == 0) * 1 / eps_r;
Q(x, y) = (2 * pi * (Y - 1) / a + Kz) .^ 2 * kn; % -Mmax<=(Y-1)<=Mmax
end
end
fprintf('Kz = %g\n', Kz)
omega_c = eig(Q);
omega_c = sort(sqrt(omega_c)); % important step.
freqs = [freqs; omega_c.'];
end
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figure()
hold on
idx = 1;
for idx = 1:length(- pi / a:pi / (10 * a): + pi / a)
plot(- pi / a:pi / (10 * a): + pi / a, freqs(:, idx), '.-')
end
hold off
xlabel('Kz')
ylabel('omega/c')
title(sprintf('PBG of 1D DBR with d/a=%g, Epsr=%g', d / a, eps_r))
</syntaxhighlight>
==Advantages==
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