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change from frequency to time domain

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abed
abed on 12 Mar 2014
%%%hello every one so here is my code in solving the NLSE(Non Linear Schrödinger Equation) using Split Step Fourier Method where I introduce a Gaussian pulse in time domain and transform it to frequency domain and use the method to observe what happens to the pulse after it enters the fiber. My next assignment is similar to this one but i need to start with the frequency domain and change it to time domain and also solve it . I know the way where i introduce a frequency Gaussian pulse but i am having a problem in the syntax any help. To know if my work is done properly the the codes should give me same results So is my code Any thoughts???%%%
L=1;%%length fiber
%---set simulation parameters
nt = 2^12; Tmax = 32; % FFT points and window size
step_num = 1000; % No. of z steps to
h = L/step_num; % step size in z
dtau = (2*Tmax)/nt; % step size in tau
%---tau and omega arrays
tau = (-nt/2:nt/2-1)*dtau; % temporal grid
w = (pi/Tmax)*[(0:nt/2-1) (-nt/2:-1)]; % frequency grid
beta2=0.25;
beta3=0;
D=(1i.*beta2.*0.5.*w.^2)-((1./6).*1i.*beta3.*w.^3); % dispersion operator
%%%%input pulse
A0=8;
A1=4;
A=1*exp(-tau.^2.*0.5);
A2=1;
M=fftshift(fft(A));
%---Plot input pulse shape and spectrum
tempo =(M).*(nt*dtau)/sqrt(2*pi); % spectrum
figure;
subplot(2,1,1);
plot(tau, abs(A).^2,'--k'); hold on;
axis([-10 10 0 inf]);
xlabel('Normalized Time');
ylabel('Normalized Power');
title('Input and Output Pulse Shape and Spectrum');
subplot(2,1,2);
plot(fftshift(w)/(2*pi),abs(tempo).^2, '--k');
hold on;
axis([-10 10 0 inf]);
xlabel('Normalized Frequency');
ylabel('Spectral Power');
%%%%calculating pulse multiplied by the dispersion factor%%
gamma=1;% gamma=(2*pi*n2)/lamda*Aeff also Beta2=-lamdazero*D/(2*pi*c) also beta3=(lamdazero/2*pi*c)^2;{(2*lamdazero*D)+(lamdazero^2 * derivative of D)}
%temp3=temp2.*exp(h.*0);
temp2=fft(A);
temp3=temp2.*exp(D.*h.*0.5);
temp4=ifft(temp3);
%%%%%%%%%
for m=1:step_num
Nonlinear=exp(1i.*h*gamma.*A.^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*dtau)/sqrt(2*pi); %Final spectrum
%----Plot output pulse shape and spectrum
figure;
subplot(2,1,1);
plot(tau, abs(temp10).^2,'-k'); hold on;
axis([-20 20 0 inf]);
xlabel('Normalized Time');
ylabel('Normalized Power');
title('Input and Output Pulse Shape and Spectrum');
subplot(2,1,2);
plot(fftshift(w)/(2*pi), abs(tempo).^2, '-k');
hold on;
axis([-10 10 0 inf]);
xlabel('Normalized Frequency');
ylabel('Spectral Power');

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