# What command/s can I use to multiply matrices M_G and M_A via Transfer Matrix Method N times given N pairs?

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Craig Egan Allistair Tan on 23 May 2022
Commented: Jan on 26 May 2022
lambda_0 = 0.980; % Cavity length of DBR mirror in micron
d_G = 0.06975562993; % Thickness of GaAs layer in micron
d_A = 0.08148984639; % Thickness of AlAs layer in micron
lambda = 0.9:0.01:1.1; % Wavelength range in micron
n_G = @(lambda) sqrt(10.906+(0.97501./(lambda.^2-(0.52886)^2))-... % Index of refraction of GaAs as a function of wavelength
0.002467.*lambda.^2)
n_A = @(lambda) sqrt(7.986+(0.97501./(lambda.^2-(0.19886)^2))-... % Index of refraction of AlAs as a function of wavelength
0.0059457.*lambda.^2)
M_G = @(lambda) [cos((2*pi*d_G.*n_G(lambda))./lambda)... % Characteristic Matrix of GaAs
(-i./n_G(lambda)).*sin((2*pi*d_G.*n_G(lambda))./lambda);...
-i.*n_G(lambda).*sin((2*pi*d_G.*n_G(lambda))./lambda)...
cos((2*pi*d_G.*n_G(lambda))./lambda)];
M_A = @(lambda) [cos((2*pi*d_A.*n_A(lambda))./lambda)... % Characteristic Matrix of AlAs
(-i./n_A(lambda)).*sin((2*pi*d_A.*n_A(lambda))./lambda);...
-i.*n_A(lambda).*sin((2*pi*d_A.*n_A(lambda))./lambda)...
cos((2*pi*d_A.*n_A(lambda))./lambda)];
Jan on 26 May 2022
@Craig Egan Allistair Tan: Okay. I do neither know, what AIAs, GaAs means, nor what "N" is, nor where do you want to apply which kind of Transfer Matrix, nor what reflectivity or DBR structure is.
All I know, is that you have defined 2 anonymous functions, which reply a [2 x 2] matrix, if you use a scalar as input and that your lambda is a vector instead.
I cannot help you, because the problem is not getiing clear to me.

R2021b

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