How to plot Frequency domain of optical nonlinear Schrodinger equation

Hello, This code solves the nonlinear in optical communication but, it only plots the time domain, I need to plot that frequency domain as well for both 3D and 2D plot. Thank you for help

if true
 clc; 
clear all; 
close all;
clf;
cputime=0;
tic;
p0=6;
alpha=0.00;%Fiber loss value in dB/km
gamma=0;%fiber non linearity in /W/m
t0=1e-10;%%total initial pulse width in second
C=0;%Chirp parameter
s=0;
b2=-20e-22;%second oder dispersion 
N=1;% soliton oder
m=0;
ln=1;
i=sqrt(-1);
pi=3.1415926535;
alph=alpha/(4.343); % Fiber loss equation, Ref page#55 eqn 2.5.3 (Agrawal)
Ld=(t0^2)/(abs(b2)); %%Dispersion
Ao=sqrt(p0); %power amplitude
tau =- 4096e-12:1e-12: 4095e-12;%  dt=t/to
dt=1e-12;
h1=1000;%%step size
for ii=0.1:0.1:1.0;
z=ii*Ld;
u1=Ao*sech(tau/t0).*exp(-i*C*(tau/t0).^2); % 
% u1=N*exp(-((1+i*(-C))/2)*(tau/t0).^2)
u2=Ao*sech(tau/t0);
%     u=N*sech(tau/to);%fundamental soliton pulse % first order soliton N=3
%     u=Ao*exp(-((1+i*(-C))/2)*(tau/to).^2) %%%N=1
%     u = Ao*sech(tau/to+1.5).*exp((-i*C/2).*(tau/to+1.5).^2)% first order with Chirp parameter

%%%%%%%%%%Plot Input Pulse%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
A11=u1;
A12=u2;
%    figure(1)
%    plot(tau/1e-10,abs(u1).^2,'r'); % Plot input pulse (with dispersion)
% %    axis([min(tau)/1e-9 max(tau)/1e-9,0 Ao])
grid on;
% figure(2)
%    plot(tau/1e-9,abs(u2).^2,'r'); % Plot input pulse (without pulse)
%    axis([min(tau)/1e-10 max(tau)/1e-10,0 Ao])
h=h1/Ld;%soliton conditions
Z=z/Ld;%soliton conditions
l=max(size(u1));  
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
fwhm1=find(abs(u1)>abs(max(u1)/2));
fwhm1=length(fwhm1);
spectrum1=fft(fftshift(u1)); %Pulse spectrum
spectrum2=fft(fftshift(u2)); %Pulse spectrum

dw=(1/l)/dt*2*pi;
w=(-1*l/2:1:l/2-1)*dw;
 w=fftshift(w);
d=0;
for jj=h:h:Z
spectrum1=spectrum1.*exp(gamma*(h/2)+i*s/2*w.^2*(h/2)) ; 
f1=ifft(spectrum1);
f1=f1.*exp(i*(N^2)*((abs(f1)).^2)*(h));
% f=fftshift(f);
spectrum1=fft(f1);
spectrum1=spectrum1.*exp(gamma*(h/2)+i*s/2*w.^2*(h/2)) ; 

spectrum2=spectrum2.*exp(gamma*(h/2)+i*s/2*w.^2*(h/2)) ; 
f2=ifft(spectrum2);
f2=f2.*exp(i*(N^2)*((abs(f2)).^2)*(h));
% f=fftshift(f);
spectrum2=fft(f2);
spectrum2=spectrum2.*exp(gamma*(h/2)+i*s/2*w.^2*(h/2)) ; 

d=d+1;
end
f1=ifft(spectrum1);
f1=fftshift(f1);
op_pulse1(ln,:)=abs(f1);%saving output pulse at all intervals
fwhm=find(abs(f1)>abs(max(f1)/2));
fwhm=length(fwhm);
ratio=fwhm/fwhm1; %PBR at every value
pbratio1(ln)=ratio;%saving PBR at every step size
dd=atand((abs(imag(f1)))/(abs(real(f1))));
phadisp1(ln)=dd;%saving pulse phase

f2=ifft(spectrum2);
f2=fftshift(f2);
op_pulse2(ln,:)=abs(f2);%saving output pulse at all intervals
fwhm=find(abs(f2)>abs(max(f2)/2));
fwhm=length(fwhm);
ratio=fwhm/fwhm1; %PBR at every value
pbratio2(ln)=ratio;%saving PBR at every step size
dd=atand((abs(imag(f2)))/(abs(real(f2))));
phadisp2(ln)=dd;%saving pulse phase
ln=ln+1;
end
toc;
cputime=toc;
figure(3);
mesh(tau/1e-12,(1:1:ln-1)./12,op_pulse1(1:1:ln-1,:));
% axis([min(tau)/1e-12 max(tau)/1e-12,0 Ao])
axis([-500 500 0 1 0 inf]);
colormap([0,0,1]);
title('Pulse Evolution');
xlabel('Time (ps)'),ylabel('Distance(km)'); zlabel('Power (W)');
set(gca,'FontSize',24);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%frequency
% figure(110)
spectrum1=fft(fftshift(u1)).*(N*tau)/sqrt(2*pi); % spectrum
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%Add optisystem data%%%%%%%%%%%
figure(10)
plot(tau/1e-12,abs(op_pulse2(ln-1,:)).^2,'r-',tau/1e-12,abs(A12).^2,':b','Linewidth',12);
axis([min(tau)/1e-12 max(tau)/1e-12,0 Ao]);
axis([-300,300 0 6]);
grid on;
title('Pulse Evolution');
xlabel('Time (ps) ');
ylabel('Power (W)');
set(gca,'FontSize',24);
legend ('Matlab IN','Matlab SPM-OUT');
legend boxon;
grid on;
  end

[Ashwini S]

I am working to develop a modelocked laser pulse with different pulse repetition frequency .. Can you please give a matlab code to develop the modelocked output pulse with split step fourier method or with some other methods .. Please help me.. If you can explain the code also it will be great help for a matlab beginner like me.. Thank you..

[ruicheng zhao]

I'm a beginner，and fi you can explain the code ".*(N*tau)/sqrt(2*pi);" of "spectrum1=fft(fftshift(u1)).*(N*tau)/sqrt(2*pi);" ，I would be very grateful !!!

I am not good in my English and once again my sincere thanks！！

Answer 1

[Akira Agata]

Unfortunately, I could not run and check your code.

Previously, I have implemented split-step Fourier method (SSFM) to solve the following nonlinear Schrodinger equation (NLSE) with 3rd order chromatic dispersion effect in optical fiber. Since I believe this code would be some help for your task, I would attach the code here.

If you run the SSFMtest.m, you can find basic soliton waveform before and after transmission in optical fiber where beta1, beta3 and alpha were set to 0.

By slightly modifying the code, you can plot spectrum of signal for any distance. But before going forward, let me clarify your definition of '3D plot'. Do you mean 'waterfall plot', like in the following link?

https://jp.mathworks.com/help/matlab/ref/waterfall.html

[Fabrice shao]

Yes its waterfall, I need to see what happing at each distance thank you so much. But where I run there some error "undefined function". Do I need to run both BasicSSFM and SSFMtest at the same time or calling the function from a different file?

Please see the code attached. this code only run in time domain I need to covert it on frequency domain to see how pulse act while SPM occur and Beta 2 and Beta 3 is set to 0

[Akira Agata]

OK. I have slightly modified the code to plot waterfall for both time-domain and frequency-domain. Please save the attached SSFMtest.m and previously attached basicSSFM.m at the same folder, and run the SSFMtest.m. Then, you can obtain the figures as follows:

[Fabrice shao]

Thank you so much, how can i plot the SPM waterfall like in this figure

[Akira Agata]

I think "Spectral intensity" in your figure is same as (or, at least proportional to) my "(Normalized) spectrum", or "SPM-induced power spectra" in the following link (Fig. 3(b)).

https://www.researchgate.net/figure/a-Experimental-and-b-theoretical-SPM-induced-broadened-spectra-as-a-function-of-input_fig3_311862913

[oussama isaac]

can you help for solving this equation with simulink