Transfer matrix Method for trilayer
%TMM 3 Layers
% SOURCE PARAMETERS
c = 3e8; % Speed of light in vacuum
% Operating frequencies
lmd = 800e-9;
freq = c./lmd;
omega = 2.*pi.*freq;
% Wavevector for free space
K0 = (2*pi)./lmd;
N = 1; % Number of layers excluding substrate and superstate
% Permivittity values
eps = [1,2.25,1];
% perambility values
mu = [1,1,1]; %permeability of every layer
% Refractive index
n = [sqrt((eps(1)*mu(1))),sqrt((eps(2)*mu(2))),sqrt((eps(3)*mu(3)))];
% Layer thickness
d = [600e-9,200e-9,600e-9]; %thickness of 2nd, 3rd and 4th layer in nm
% Angle of incidences
theta = 0:5:90;
thetaa = [0 0 0]; % Incident angles(in degrees)
% Wave vector
k2x = n(1,2).*(omega./c).*cosd(thetaa(1,2));
% Propagation Matrix
phi2 = k2x*d(1,2);
P2 = [exp(1i*phi2) 0; 0 exp(-1i*phi2)];
D1=zeros(2,length(theta));
% Dynamical matrix 1
D1_11 = 1;
D1_12 = 1;
D1_21 = n(1,1).*cosd(theta);
D1_22 = -n(1,1).*cosd(theta);
% D1 = [D1_11 D1_12; D1_21 D1_22]
% Dynamical matrix 2
D2_11 = 1;
D2_12 = 1;
D2_21 = n(1,2)*cosd(theta(1,2));
D2_22 = -n(1,2)*cosd(theta(1,2));
% D2 = [D2_11 D2_12; D2_21 D2_22]
% Dynamical matrix
D3_11 = 1;
D3_12 = 1;
D3_21 = n(1,3)*cosd(theta(1,3));
D3_22 = -n(1,3)*cosd(theta(1,3));
% D3 = [D3_11 D3_12; D3_21 D3_22]
for ii = 1:length(theta)
D_1 = [D1_11(1,ii) D1_12(1,ii); D1_21(1,ii) D1_22(1,ii)]
D_2 = [D2_11(1,ii) D2_12(1,ii); D2_21(1,ii) D2_22(1,ii)]
D_3 = [D3_11(1,ii) D3_12(1,ii); D3_21(1,ii) D3_22(1,ii)]
M = D_1^(-1)*D_2*P2*D_2^(-1)*D_3;
rs = M(2,1)./M(1,1)
ts = 1./M(1,1)
Rs = abs(rs.^2)
Ts = ((n(1,3).*cosd(thetaa(1,3))./(n(1,1).*cosd(theta))).*abs(ts.^2))
Frensel_s = Rs + Ts
end
% Dynamical Matrix for S – Wave
plot(theta,Rs,theta,Ts)
legend(‘R’,’T’)
%% Graph output should be like this%TMM 3 Layers
% SOURCE PARAMETERS
c = 3e8; % Speed of light in vacuum
% Operating frequencies
lmd = 800e-9;
freq = c./lmd;
omega = 2.*pi.*freq;
% Wavevector for free space
K0 = (2*pi)./lmd;
N = 1; % Number of layers excluding substrate and superstate
% Permivittity values
eps = [1,2.25,1];
% perambility values
mu = [1,1,1]; %permeability of every layer
% Refractive index
n = [sqrt((eps(1)*mu(1))),sqrt((eps(2)*mu(2))),sqrt((eps(3)*mu(3)))];
% Layer thickness
d = [600e-9,200e-9,600e-9]; %thickness of 2nd, 3rd and 4th layer in nm
% Angle of incidences
theta = 0:5:90;
thetaa = [0 0 0]; % Incident angles(in degrees)
% Wave vector
k2x = n(1,2).*(omega./c).*cosd(thetaa(1,2));
% Propagation Matrix
phi2 = k2x*d(1,2);
P2 = [exp(1i*phi2) 0; 0 exp(-1i*phi2)];
D1=zeros(2,length(theta));
% Dynamical matrix 1
D1_11 = 1;
D1_12 = 1;
D1_21 = n(1,1).*cosd(theta);
D1_22 = -n(1,1).*cosd(theta);
% D1 = [D1_11 D1_12; D1_21 D1_22]
% Dynamical matrix 2
D2_11 = 1;
D2_12 = 1;
D2_21 = n(1,2)*cosd(theta(1,2));
D2_22 = -n(1,2)*cosd(theta(1,2));
% D2 = [D2_11 D2_12; D2_21 D2_22]
% Dynamical matrix
D3_11 = 1;
D3_12 = 1;
D3_21 = n(1,3)*cosd(theta(1,3));
D3_22 = -n(1,3)*cosd(theta(1,3));
% D3 = [D3_11 D3_12; D3_21 D3_22]
for ii = 1:length(theta)
D_1 = [D1_11(1,ii) D1_12(1,ii); D1_21(1,ii) D1_22(1,ii)]
D_2 = [D2_11(1,ii) D2_12(1,ii); D2_21(1,ii) D2_22(1,ii)]
D_3 = [D3_11(1,ii) D3_12(1,ii); D3_21(1,ii) D3_22(1,ii)]
M = D_1^(-1)*D_2*P2*D_2^(-1)*D_3;
rs = M(2,1)./M(1,1)
ts = 1./M(1,1)
Rs = abs(rs.^2)
Ts = ((n(1,3).*cosd(thetaa(1,3))./(n(1,1).*cosd(theta))).*abs(ts.^2))
Frensel_s = Rs + Ts
end
% Dynamical Matrix for S – Wave
plot(theta,Rs,theta,Ts)
legend(‘R’,’T’)
%% Graph output should be like this %TMM 3 Layers
% SOURCE PARAMETERS
c = 3e8; % Speed of light in vacuum
% Operating frequencies
lmd = 800e-9;
freq = c./lmd;
omega = 2.*pi.*freq;
% Wavevector for free space
K0 = (2*pi)./lmd;
N = 1; % Number of layers excluding substrate and superstate
% Permivittity values
eps = [1,2.25,1];
% perambility values
mu = [1,1,1]; %permeability of every layer
% Refractive index
n = [sqrt((eps(1)*mu(1))),sqrt((eps(2)*mu(2))),sqrt((eps(3)*mu(3)))];
% Layer thickness
d = [600e-9,200e-9,600e-9]; %thickness of 2nd, 3rd and 4th layer in nm
% Angle of incidences
theta = 0:5:90;
thetaa = [0 0 0]; % Incident angles(in degrees)
% Wave vector
k2x = n(1,2).*(omega./c).*cosd(thetaa(1,2));
% Propagation Matrix
phi2 = k2x*d(1,2);
P2 = [exp(1i*phi2) 0; 0 exp(-1i*phi2)];
D1=zeros(2,length(theta));
% Dynamical matrix 1
D1_11 = 1;
D1_12 = 1;
D1_21 = n(1,1).*cosd(theta);
D1_22 = -n(1,1).*cosd(theta);
% D1 = [D1_11 D1_12; D1_21 D1_22]
% Dynamical matrix 2
D2_11 = 1;
D2_12 = 1;
D2_21 = n(1,2)*cosd(theta(1,2));
D2_22 = -n(1,2)*cosd(theta(1,2));
% D2 = [D2_11 D2_12; D2_21 D2_22]
% Dynamical matrix
D3_11 = 1;
D3_12 = 1;
D3_21 = n(1,3)*cosd(theta(1,3));
D3_22 = -n(1,3)*cosd(theta(1,3));
% D3 = [D3_11 D3_12; D3_21 D3_22]
for ii = 1:length(theta)
D_1 = [D1_11(1,ii) D1_12(1,ii); D1_21(1,ii) D1_22(1,ii)]
D_2 = [D2_11(1,ii) D2_12(1,ii); D2_21(1,ii) D2_22(1,ii)]
D_3 = [D3_11(1,ii) D3_12(1,ii); D3_21(1,ii) D3_22(1,ii)]
M = D_1^(-1)*D_2*P2*D_2^(-1)*D_3;
rs = M(2,1)./M(1,1)
ts = 1./M(1,1)
Rs = abs(rs.^2)
Ts = ((n(1,3).*cosd(thetaa(1,3))./(n(1,1).*cosd(theta))).*abs(ts.^2))
Frensel_s = Rs + Ts
end
% Dynamical Matrix for S – Wave
plot(theta,Rs,theta,Ts)
legend(‘R’,’T’)
%% Graph output should be like this transfer matrix method MATLAB Answers — New Questions
