# Plot the normal-incidence reflectance of this bragg reflector from 300 nm to 800 nm, just like lecture, using the thicknesses found in (a), for 2, 4, and 8 periods.

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OMEIR HUSSAIN on 30 Apr 2024
Commented: Jacob Mathew on 22 May 2024 at 9:27
an example of a Bragg reflector made out of ZnS and MgF2 films. Assume that you want to make a Bragg reflector centered about a free space wavelength of 600 nm. (a) (1 pt) What thicknesses of ZnS and MgF2 do you need to use (I have calcualted these.? (b) (3 pts) Plot the normal-incidence reflectance of this reflector from 300 nm to 800 nm, just like lecture, using the thicknesses found in (a), for 2, 4, and 8 periods. For both (a) and (b), you can use the same refractive indices as given in lecture, and you can ignore dispersion.
Code
clc;
clear all;
close all;
% Wavelength range from 300 nm to 800 nm
wavelengths = linspace(300, 800, 500) * 1e-9; % Convert to meters
% Thicknesses of ZnS and MgF2 layers
d_zns = 68.18e-9; % meters
d_mgf2 = 108.70e-9; % meters
% Number of periods
periods = [2, 4, 8];
% Plot reflectance for different numbers of periods
figure;
hold on;
for n = periods
reflectance = bragg_reflectance(wavelengths, d_zns, d_mgf2, n);
plot(wavelengths * 1e9, reflectance, 'DisplayName', sprintf('%d periods', n));
end
xlabel('Wavelength (nm)');
ylabel('Reflectance');
title('Normal-Incidence Reflectance of Bragg Reflector');
legend('show');
grid on;
% Function definition at the end of the script
function reflectance = bragg_reflectance(wavelengths, d_zns, d_mgf2, n_periods)
% Constants
n_air = 1.0; % Refractive index of air
n_zns = 2.2; % Refractive index of ZnS
n_mgf2 = 1.38; % Refractive index of MgF2
k = 2 * pi ./ wavelengths; % Wavevector
% Initialize reflectance array
reflectance = zeros(size(wavelengths));
for i = 1:length(wavelengths)
% Transfer matrix for ZnS layer
M_zns = [cos(k(i) * n_zns * d_zns), -1i * sin(k(i) * n_zns * d_zns) / n_zns;
-1i * n_zns * sin(k(i) * n_zns * d_zns), cos(k(i) * n_zns * d_zns)];
% Transfer matrix for MgF2 layer
M_mgf2 = [cos(k(i) * n_mgf2 * d_mgf2), -1i * sin(k(i) * n_mgf2 * d_mgf2) / n_mgf2;
-1i * n_mgf2 * sin(k(i) * n_mgf2 * d_mgf2), cos(k(i) * n_mgf2 * d_mgf2)];
% Transfer matrix for entire stack
M_stack = M_mgf2 * M_zns;
for j = 2:n_periods
M_stack = M_stack * (M_mgf2 * M_zns);
end
% Fresnel coefficients
r = (M_stack(1, 1) + M_stack(1, 2) * n_air) / (M_stack(2, 1) + M_stack(2, 2) * n_air);
% Reflectance
reflectance(i) = abs(r)^2;
end
end
I am not able to get the correct output
Jacob Mathew on 22 May 2024 at 9:27
After going through your query, I understand that you are not getting the expected plot. However, it is difficult to diagnose why without a reference to what is the expected graph.
The code that you provided runs and plots all 3 periods without error. The reason why they might not be visible is the scale of the plots varying largely. If you plot them individually, you can distinctly see them:

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