I need help in solving a matrix (Tensors)
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E0 = 5; % Permivittity at infinite frequency
W_P = 13.4e15; % Plasma Frequency
Gamma = 0.7e14; % collison Frequency
c = 3e8; % Speed of light in vacuum
e0 = 8.85e-12; % Permivittity in free space
lambda=1350e-9:10e-9:1750e-9;
f=c./lambda;
w=2*pi*f;
e11 = E0-(W_P^2./(w.^2-(1i*Gamma.*w)));
e22=16.2;
e33=11.9;
h1= 8; %Silver
h2= 25; %Silica
h3=19; %Germanium
e_TM=(e11.*e22.*e33)./((e22.*e33.*h1)+(e11.*e33.*h2)+(e11.*e22.*h3))./(h1+h2+h3);
e_TE=((e11.*h1)+(e22.*h2)+(e33.*h3))./(h1+h2+h3);
figure
plot(lambda,real(e_TM),'b',lambda,imag(e_TM),'g')
xlabel('Wavelength')
ylabel('permivittity (TM Mode)')
legend('Real','Imag')
figure
plot(lambda,real(e_TE),'b',lambda,imag(e_TE),'g')
xlabel('Wavelength')
ylabel('permivittity (TE Mode)')
legend('Real','Imag')
Here, I need to caluculate
figure
plot(lambda,real(e_eff),'b',lambda,imag(e_eff),'g')
legend('real','Im','Location','southeast');
xlabel('Wavelength (nm)');
ylabel('Effective Permittivity');
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Accepted Answer
Morgan
on 7 Feb 2024
Edited: Morgan
on 7 Feb 2024
If I'm understanding your question correctly, you're trying to calculatte an effective medium tensor of the form:
where
Usually , , and are fill fractions for each composite material and have values in the range of 0 to 1, but I could just be unfamiliar with the exact effective medium model you're using. I've also never encountered a material with only one dispersive (varies with frequency) tensor element. Usually each tensor element is dispersive.
Assuming this is the case, however, the code you're looking for is:
e_eff = zeros(3,3,length(w));
e_eff(1,1,:) = e0*e_TE(:);
e_eff(2,2,:) = e0*e_TE(:);
e_eff(3,3,:) = e0*e_TM(:);
This creates a permittivity tensor that follows the effective medium model at each frequency w you've provided.
Also, I noticed you wanted to plot the effective tensor with:
figure
plot(lambda,real(e_eff),'b',lambda,imag(e_eff),'g')
legend('real','Im','Location','southeast');
xlabel('Wavelength (nm)');
ylabel('Effective Permittivity');
MATLAB will error out saying "Data cannot have more than 2 dimensions" since you're attempting to plot 9 tensor elements per wavelength. If you could clarify what exactly you're trying to plot, I might be able to assist further.
4 Comments
Morgan
on 7 Feb 2024
If you're trying to plot the effective permittivity tensor, this does not make sense. I recommend plot each unique element of the tensor ( and ) separately like the code you had previously:
% PLOT EFFECTIVE PERMITTIVITY (TE MODE)
figure
plot(lambda,real(e_TE),'b',lambda,imag(e_TE),'g')
xlabel('Wavelength')
ylabel('permivittity (TE Mode)')
legend('Real','Imag')
% PLOT EFFECTIVE PERMITTIVITY (TM MODE)
figure
plot(lambda,real(e_TM),'b',lambda,imag(e_TM),'g')
xlabel('Wavelength')
ylabel('permivittity (TM Mode)')
legend('Real','Imag')
By chance, if you're referring to plotting an Index Ellipsoid this will be slightly more complicated and doesn't show refractive index as a function of wavelength unless you animate the plot.
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