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[分享]求解光孤子或超短脉冲耦合方程的Matlab程序 [复制链接]

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离线tianmen

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只看楼主倒序阅读楼主发表于: 2011-06-12

计算脉冲在非线性耦合器中演化的Matlab 程序

%  This Matlab script file solves the coupled nonlinear Schrodinger equations of
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004

%fid=fopen('e21.dat','w');
N = 128;                       % Number of Fourier modes (Time domain sampling points)
M1 =3000;              % Total number of space steps
J =100;                % Steps between output of space
T =10;                  % length of time windows:T*T0
T0=0.1;                 % input pulse width
MN1=0;                 % initial value for the space output location
dt = T/N;                      % time step
n = [-N/2:1:N/2-1]';           % Index
t = n.*dt;
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10
u20=u10.*0.0;                  % input to waveguide 2
u1=u10; u2=u20;
U1 = u1;
U2 = u2;                       % Compute initial condition; save it in U
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1.
w=2*pi*n./T;
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
L=4;                           % length of evoluation to compare with S. Trillo's paper
dz=L/M1;                       % space step, make sure nonlinear<0.05
for m1 = 1:1:M1                                    % Start space evolution
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
   ca1 = fftshift(fft(u1));                        % Take Fourier transform
   ca2 = fftshift(fft(u2));
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift
   u2 = ifft(fftshift(c2));                        % Return to physical space
   u1 = ifft(fftshift(c1));
if rem(m1,J) == 0                                 % Save output every J steps.
    U1 = [U1 u1];                                  % put solutions in U array
    U2=[U2 u2];
    MN1=[MN1 m1];
    z1=dz*MN1';                                    % output location
  end
end
hg=abs(U1').*abs(U1');                             % for data write to excel
ha=[z1 hg];                                        % for data write to excel
t1=[0 t'];
hh=[t1' ha'];                                      % for data write to excel file
%dlmwrite('aa',hh,'\t');                           % save data in the excel format
figure(1)
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn
figure(2)
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn

非线性超快脉冲耦合的数值方法的Matlab程序

在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的论文中，我们提出了一种简洁的数值方法。这里我们提供给大家用Matlab编写的计算程序。
Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004

%  This Matlab script file solves the nonlinear Schrodinger equations
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004

C=1;
M1=120,                       % integer for amplitude
M3=5000;                      % integer for length of coupler
N = 512;                      % Number of Fourier modes (Time domain sampling points)
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05.
T =40;                        % length of time:T*T0.
dt = T/N;                     % time step
n = [-N/2:1:N/2-1]';          % Index
t = n.*dt;
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1.
w=2*pi*n./T;
g1=-i*ww./2;
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
g3=-i*ww./2;
P1=0;
P2=0;
P3=1;
P=0;
for m1=1:M1
p=0.032*m1;                %input amplitude
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1
s1=s10;
s20=0.*s10;                %input in waveguide 2
s30=0.*s10;                %input in waveguide 3
s2=s20;
s3=s30;
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
%energy in waveguide 1
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
%energy in waveguide 2
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
%energy in waveguide 3
for m3 = 1:1:M3                                    % Start space evolution
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
   sca1 = fftshift(fft(s1));                       % Take Fourier transform
   sca2 = fftshift(fft(s2));
   sca3 = fftshift(fft(s3));
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
   s3 = ifft(fftshift(sc3));
   s2 = ifft(fftshift(sc2));                       % Return to physical space
   s1 = ifft(fftshift(sc1));
end
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
   P1=[P1 p1/p10];
   P2=[P2 p2/p10];
   P3=[P3 p3/p10];
   P=[P p*p];
end
figure(1)
plot(P,P1, P,P2, P,P3);

转自：http://blog.163.com/opto_wang/

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离线ciomplj

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只看该作者 1楼发表于: 2014-06-22

谢谢哈~！~

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[分享]求解光孤子或超短脉冲耦合方程的Matlab程序 [复制链接]