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 2022-5-23

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https://ww2.mathworks.cn/matlabcentral/answers/1725225-what-command-s-can-i-use-to-multiply-matrices-m_g-and-m_a-via-transfer-matrix-method-n-times-given-n

评论： Jan 2022-5-26

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)];

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Craig Egan Allistair Tan 2022-5-26

I plan to define M_A and M_G as 2x2 matrices that represent the characteristic matrix of AlAs and GaAs, respectively, multiply them N times for each AlAs/GaAs pair, applying the Transfer Matrix Method, and then from the resulting 2x2 matrix, obtain the reflectivity of the overall DBR structure.

Jan 2022-5-26

@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.

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