Computational Physics: Four Wave Mixing Signal Amplification

[eahaidar]

I made this code for a non linear process called Four Wave Mixing in which. Two pulses will enter a fiber to get a new wave called idler and try to amplify the signal but I think it's not working well because of the units so I called them in the figure arbitrary units until the problem is fixed any thoughts how? Here is my code thank you

clear all;

T = 500e-12; % Time window (period)
nt = 2^14; % Number of points
dt = T/nt; % Time resolution
% Make w and t windows
t = ((1:nt)-(nt+1)/2)*dt;
t = fftshift(t);

% Create frequency window, then shift it

w = 2*pi*([-nt/2:nt/2-1])/T;
w = fftshift(w);
%Pump pulse probe
P0 = 100;
FWHM = 1e-12;
c = FWHM/(2*sqrt(2*log(2)));
u0 = sqrt(P0)*exp(-0.5*(t/c).^2);
%Signal pulse probe
Ps = 1;
Ts = 5e-12;
detun = 6.05e12;

Pf = Ps*3.042e4;
detun = detun*2*pi;
fbw = 0.44/Ts;
FWHM_omega = 2*pi*fbw;
c = FWHM_omega/(2*sqrt(2*log(2)));
uw = sqrt(2*Pf)*exp(-0.25*((w-detun)/c).^2);
u1 = (ifft(uw));

u = fftshift(u0+u1);

figure
subplot(1,2,1)
plot(w/(1e12)/(2*pi),abs(fft(u)).^2)
xlabel('Frequency (THz)')
ylabel('Arb. Units')
xlim([-10 10])
ut = ifft(uw);
subplot(1,2,2)
plot(t/(1e-12),fftshift(abs(u).^2))
xlabel('Time(ps)')
ylabel('Power (W)')
xlim([-6 6])

%split step method
beta2=0;
beta3=0; alpha=0;
h=0.001;%h = L/step_num; % step size in z
D=(1i.*beta2.*0.5.*w.^2)-((1./6).*1i.*beta3.*w.^3); % dispersion operator
step_num = 1000; % No. of z steps

gamma=1;
temp2=fft(u);
temp3=temp2.*exp(u.*h.*0.5);
temp4=ifft(temp3);
%%%%%%%%%

for m=1:step_num
Nonlinear=exp(1i.*h*gamma.*u.^2).*temp4;
temp5=fft(Nonlinear);
temp6=temp5.*exp(D.*h./2);
temp4=ifft(temp6);
end
temp8=fft(temp4);
temp9=temp8.*exp(-1.*(h./2).*D);
temp10=ifft(temp9);
% final pulse
tempo=fftshift(fft(temp10)).*(nt*dt)/sqrt(2*pi); %Final spectrum

%----Plot output pulse shape and spectrum
figure;
subplot(2,1,1);
plot(t/(1e-12), abs(temp10).^2,'-k'); hold on;
axis([-20 20 0 inf]);
xlabel(' Time');
ylabel(' Power');
title(' Output Pulse Shape and Spectrum');
subplot(2,1,2);
plot(w/(1e12)/(2*pi), abs(tempo).^2, '-k');
hold on;
axis([-10 10 0 inf]);
xlabel('Normalized Frequency');
ylabel('Spectral Power');

 

[AndyW]

First, it is important to specify what units you are using in your code. Are you using SI units (meters, seconds, etc.) or some other unit system? It is crucial to use consistent units throughout your code to avoid errors and confusion.

Secondly, it is important to double check the equations and constants you are using in your code. For example, in the line where you define FWHM_omega, you are using the value of fbw (full width at half maximum) in seconds, but then you are dividing it by T (which is in seconds) again. This may lead to incorrect results in your code.

Additionally, it is important to carefully check the units of the variables you are using in your equations. For example, in the Nonlinear equation, you are using u (which has units of amplitude) in the exponent, but also multiplying it by h (which has units of distance). This may also lead to incorrect results.

One way to troubleshoot these issues is to check the units of each variable and equation, and make sure they are consistent and make sense. You may also consider using a unit conversion tool to help you convert between different units.

Finally, it is always helpful to double check your code with analytical solutions or with experimental data to make sure it is giving the expected results. This can help identify any issues with the code and guide you in finding the correct solution.