Computational Physics: Four Wave Mixing Signal Amplification

In summary: Overall, it is important to be careful and thorough when working with non-linear processes like Four Wave Mixing, as small errors in units or equations can have a significant impact on the results. In summary, when working with non-linear processes such as Four Wave Mixing, it is important to use consistent units, double check equations and constants, and validate your code with analytical solutions or experimental data.
  • #1
eahaidar
71
1
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');
 
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  • #2

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.
 

FAQ: Computational Physics: Four Wave Mixing Signal Amplification

1. What is Computational Physics?

Computational Physics is a branch of physics that uses computer simulations and mathematical models to study physical systems that are too complex to be studied analytically. It involves using advanced algorithms and programming techniques to solve complex physical problems.

2. What is Four Wave Mixing Signal Amplification?

Four Wave Mixing (FWM) is a nonlinear optical process in which the interaction of multiple laser beams results in the generation of a new beam at a different frequency. FWM signal amplification is a technique that uses FWM to amplify a weak optical signal by mixing it with strong laser beams.

3. How does Computational Physics help in understanding Four Wave Mixing Signal Amplification?

Computational Physics allows us to simulate the complex interactions between multiple laser beams and understand the underlying physics of FWM signal amplification. By using computer simulations, we can study a wide range of parameters and optimize the conditions for maximum signal amplification.

4. What are the applications of Computational Physics in Four Wave Mixing Signal Amplification?

Computational Physics has a wide range of applications in the study of FWM signal amplification. It can be used to design and optimize optical devices such as optical amplifiers and frequency converters used in telecommunications. It is also used in quantum information processing and quantum computing.

5. What are the challenges in using Computational Physics for studying Four Wave Mixing Signal Amplification?

One of the main challenges in using Computational Physics for studying FWM signal amplification is the complexity of the mathematical models and algorithms involved. It requires a deep understanding of both physics and computer science. Another challenge is the computational power required to simulate large-scale systems, which may limit the scope of the study.

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