How to plot Frequency domain of optical nonlinear Schrodinger equation

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Fabrice shao
Fabrice shao 2018-11-11
评论： ruicheng zhao 2022-9-3
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
  2 个评论
Ashwini S
Ashwini S 2020-9-22
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
ruicheng zhao 2022-9-3
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！！

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采纳的回答

Akira Agata
Akira Agata 2018-11-12
编辑：Akira Agata 2018-11-12
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
  5 个评论
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Akira Agata
Akira Agata 2018-11-14
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

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