Learning Forum

[Arun Jana]

Hello,

I want to design one material which permitivity(as a function of frequency) as well as ch2 property (not diagonal d33,d21,d22,d15 which depends on frequency) in lumerical FDTD( iam using 2024R2)  all data i want to give in one material how i will give? and i could not able to import material  data set also.

Here i wrote in MATLAB code, which i want to design..

 

% Define Frequency range in THz

f1 = linspace(0, 10, 500)* (10^12); % in THz

w = 2 * pi * f1;

% Lorentz parameters (infrared and optical frequencies)

omegap_e = [248 274 307 628 692] * 3 * 10^10; % phonon resonant frequency for e axis

omegap_o = [152 236 265 322 363 431 586 670] * 3 * 10^10; % phonon resonant frequency for o axis

S_e = [16 1 0.16 2.55 0.34]; % oscilator strength for e-axis

S_o = [22 0.8 5.5 2.2 2.3 0.18 3.3 0.2];% oscilator strength for o-axis

Gamma_e = [21 14 25 34 49] * 3 * 10^10; % phonon damping rate for e-axis

Gamma_o = [14 12 12 11 33 12 35 47] * 3 * 10^10; % phonon damping rate for o-axis

epsilon_p_e = 4.6; % high frefency permitivity limit for e axis

epsilon_p_o = 5.0; % high frefency permitivity limit for o axis

epsilon_Le = epsilon_p_e * ones(size(w)); % Initialize epsilon_L for e axis

epsilon_Lo = epsilon_p_o * ones(size(w)); % Initialize epsilon_L for o axis

% Lorentzian contributions for e axis

for k1 = 1:length(omegap_e)

epsilon_Le = epsilon_Le + (S_e(k1) * omegap_e(k1)^2) ./ ((omegap_e(k1)^2 - w.^2) - 1i * Gamma_e(k1) * w);

end

refractive_index_e=sqrt(epsilon_Le);

n_e=refractive_index_e;

E_er=real(epsilon_Le);

E_ei=imag(epsilon_Le);

 

% Lorentzian contributions for o axis

for k2 = 1:length(omegap_o)

epsilon_Lo = epsilon_Lo + (S_o(k2) * omegap_o(k2)^2) ./ ((omegap_o(k2)^2 - w.^2) - 1i * Gamma_o(k2) * w);

end

refractive_index_o=sqrt(epsilon_Lo);

n_o=(refractive_index_o);

E_or=real(epsilon_Lo);

E_oi=imag(epsilon_Lo);

% linear microwave susceptibility

chi_e=n_e.^2-1;%% electronic contribution for e axis

chi_o=n_o.^2-1;%% electronic contribution for o axis

chi_ion_e=epsilon_Le-n_e.^2-1;% ionic contribution for e axis

chi_ion_o=(epsilon_Lo)-(n_o).^2-1;% ionic contribution for e axis

% Define constants for electronic and ionic parts

delta_333_e = 0.6*10^-12;

delta_222_e = 0.064*10^-12; 

delta_311_e =0.18*10^-12; 

delta_113_e = 0.31*10^-12; 

delta_333_ion =0.304* 10^-12;

delta_222_ion =0.0369* 10^-12; 

delta_311_ion =0.167*10^-12; 

delta_113_ion =0.41* 10^-12; 

chi_1e=3.884;

chi_3e=3.544;

% Calculate Nonlinear coefficient components

d33 = abs(delta_333_e * chi_e .* chi_3e .* chi_3e + delta_333_ion * chi_3e.* chi_3e .* chi_ion_e);

d31 = abs(delta_311_e * chi_e .* chi_1e .* chi_1e + delta_311_ion * chi_1e .* chi_1e .* chi_ion_e);

d15 = abs(delta_113_e * chi_o .* chi_1e .* chi_1e + delta_113_ion * chi_1e .* chi_1e .* chi_ion_o);

%d15 = d31+(delta_113_e * chi_o.* chi_1e.*chi_3e + delta_113_ion * chi_3e .* chi_1e.* chi_ion_o);

d22 = abs(delta_222_e * chi_o .* chi_3e .* chi_3e + delta_222_ion * chi_3e .* chi_3e .* chi_ion_o);

figure;

plot(w, d33, 'r', w, d31, 'b', w, d15, 'm', w, d22, 'k');

legend('d_{33}', 'd_{31}', 'd_{15}', 'd_{22}');

xlabel('Frequency(Hz)');

ylabel('Nonlinear Coefficient(pm/V)');

title('Nonlinear coefficient');

grid on;

% Plot w vs permitivity (real part)for e and o axis

figure;

plot(w, real(epsilon_Le), 'r', w, real(epsilon_Lo), 'b');

legend('e-axis', 'o-axis')

xlabel('Frequency (Hz)');

ylabel('Re(\epsilon)');

title('Real Permitivity');

% Plot w vs imaginary part of permitivity for e and o axis

figure;

plot(w, imag(epsilon_Le), 'r', w, imag(epsilon_Lo), 'b');

xlabel('Frequency (Hz)');

legend('e-axis', 'o-axis')

ylabel('Im(\epsilon)');

title('Imaginary permitivity');

 

please let me know .

Thank you.

[Guilin Sun]

Unfortunately right now FDTD cannot simulate non-3*3 diagonal tensor nonlinear material.

for frequency dependent nonlinear material, currently only  two

Chi3 Raman Kerr

Magnetic Electric Lorentz

can be dispersive.

For permittivity, you can simulate full 3*3 tensor with matrix tranformation: Creating anisotropic optical materials in FDTD and MODE

If you want to simulate broadband, you will need to make sure that the unitary matrix does not depend on frequency.