[分享]求解光孤子或超短脉冲耦合方程的Matlab程序 [复制链接]

计算脉冲在非线性耦合器中演化的Matlab 程序 SA7(EJ95  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of zy5FO<->  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of Q8MIpa!:  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 3{fg3?  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 bF6J>&]!  
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%fid=fopen('e21.dat','w'); 6tFi\,)E  
N = 128;                       % Number of Fourier modes (Time domain sampling points) $1g1Bn  
M1 =3000;              % Total number of space steps H8B$#.  
J =100;                % Steps between output of space "Kdn`zN{  
T =10;                  % length of time windows:T*T0 :AS`1\ C  
T0=0.1;                 % input pulse width em'ADRxG+  
MN1=0;                 % initial value for the space output location `XpQR=IOMb  
dt = T/N;                      % time step S*$?~4{R  
n = [-N/2:1:N/2-1]';           % Index +:"0%(  
t = n.*dt;   X'-Yz7J?o  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 xJ2I@*DN  
u20=u10.*0.0;                  % input to waveguide 2 BM`6<Z"3q  
u1=u10; u2=u20;                 &7oL2Wf  
U1 = u1;   1[T7;i$  
U2 = u2;                       % Compute initial condition; save it in U *= ?|n  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. vENf3;o0  
w=2*pi*n./T; B0%=!&  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T xEk8oc  
L=4;                           % length of evoluation to compare with S. Trillo's paper FF~r&h8H  
dz=L/M1;                       % space step, make sure nonlinear<0.05 VX&Pk
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for m1 = 1:1:M1                                    % Start space evolution 0~z\WSo  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS @0 /qP<E  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; r5Tdp)S  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform n{i,`oQ"  
   ca2 = fftshift(fft(u2)); 2 U]d1  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation 6tndC o;`  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   L-!1ybB^  
   u2 = ifft(fftshift(c2));                        % Return to physical space z V\+za,  
   u1 = ifft(fftshift(c1)); U!`iKy-  
if rem(m1,J) == 0                                 % Save output every J steps. Pal=I)  
    U1 = [U1 u1];                                  % put solutions in U array Be=rBrI>  
    U2=[U2 u2]; |PlNVd2  
    MN1=[MN1 m1]; kJp~'\b  
    z1=dz*MN1';                                    % output location O|~C qb  
  end
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end `r-jWK\  
hg=abs(U1').*abs(U1');                             % for data write to excel d.^g#&h
 
ha=[z1 hg];                                        % for data write to excel [104;g <  
t1=[0 t']; Vh;zV Y  
hh=[t1' ha'];                                      % for data write to excel file weSq|f  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format b.@a,:"  
figure(1)  D**GC  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn QCF'/G
 
figure(2) n+Kv^Y`qxO  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn +7^p d9F.  
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非线性超快脉冲耦合的数值方法的Matlab程序 *L$2M?xkY  
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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。   `daqzn  
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 $Sgf jm  
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%  This Matlab script file solves the nonlinear Schrodinger equations ba);f[>  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of K"H\gmV_g  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 6t6Z&0$h~  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 /.Ak'Vmi  
*[3xc*5F/A  
C=1;                           &$F<]]&  
M1=120,                       % integer for amplitude }OL"38P  
M3=5000;                      % integer for length of coupler N8b\OTk2  
N = 512;                      % Number of Fourier modes (Time domain sampling points) xi=ApwNj  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. kg[%Q]]  
T =40;                        % length of time:T*T0. 6'r8.~O  
dt = T/N;                     % time step t?W}=%M[  
n = [-N/2:1:N/2-1]';          % Index *h!fqT%9  
t = n.*dt;   qW0:q.   
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. .B# .   
w=2*pi*n./T; //U1mDFT  
g1=-i*ww./2; aa`(2%(:  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; U]iI8c  
g3=-i*ww./2; @h%V:c  
P1=0; 2Wz8E2.  
P2=0; a/sjW  
P3=1; G^~[|a4`  
P=0; :$MOdLr  
for m1=1:M1                 &12KpEyf  
p=0.032*m1;                %input amplitude
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s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 =|S%Rzsk  
s1=s10; [1VA`:?W  
s20=0.*s10;                %input in waveguide 2 +jGHR&A t  
s30=0.*s10;                %input in waveguide 3 *1b|j|5v  
s2=s20; .$qa?$@  
s3=s30; |h>PUt@LL  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   fFjpQ~0  
%energy in waveguide 1 z-5`6aE9<  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   (^d7K:-'  
%energy in waveguide 2 mL{P4a 1xf  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   "is(  
%energy in waveguide 3 @ _Ey"k<  
for m3 = 1:1:M3                                    % Start space evolution W$rWg>4>  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS 0 &zp
 
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; GXtMX ha,  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; `>gG"1,]  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform UN]gn>~j  
   sca2 = fftshift(fft(s2)); 94u{k1d x  
   sca3 = fftshift(fft(s3)); ;b$P*dSG}  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   ,
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   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); 1 em,/>"  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); Z/#_Swv  
   s3 = ifft(fftshift(sc3)); iC gZ3M]  
   s2 = ifft(fftshift(sc2));                       % Return to physical space m&UP@hUV-  
   s1 = ifft(fftshift(sc1)); uJ!&T  
end B$4*U"tk  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); ,fkvvM{mq  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); > ;,S||  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); uN|A}/hr]  
   P1=[P1 p1/p10]; l!mbpFt  
   P2=[P2 p2/p10]; Mt[yY|Ec|  
   P3=[P3 p3/p10]; 3Vb4zZsl  
   P=[P p*p]; "yn~axk7  
end k ut=(;  
figure(1) -aoYoJ '  
plot(P,P1, P,P2, P,P3); rf.pT+g.P  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~