[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 XN6$TNsD$  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of JIw?]xa*  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of %o4v} mzV  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear AX%}ip[PC  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 rNJU & .]  
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%fid=fopen('e21.dat','w'); tFc<f7k  
N = 128;                       % Number of Fourier modes (Time domain sampling points) !ht2*8$lQ  
M1 =3000;              % Total number of space steps 9d^m 7}2  
J =100;                % Steps between output of space ykJ+LS{+  
T =10;                  % length of time windows:T*T0 Dq<DW2It>  
T0=0.1;                 % input pulse width N%>h>HJ  
MN1=0;                 % initial value for the space output location F .Zk};lb  
dt = T/N;                      % time step ;+(_stxqV9  
n = [-N/2:1:N/2-1]';           % Index DZ\ '7%c  
t = n.*dt;   2A@oa9  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 [;7zg@Sa  
u20=u10.*0.0;                  % input to waveguide 2 B|"/bQ  
u1=u10; u2=u20;                 Ipq0 1 +  
U1 = u1;   ^'`(E_2u  
U2 = u2;                       % Compute initial condition; save it in U i ]8bj5j{  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. %XeN_ V  
w=2*pi*n./T; @VW1^{.do^  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T (y6q}#<  
L=4;                           % length of evoluation to compare with S. Trillo's paper G/FDD{y  
dz=L/M1;                       % space step, make sure nonlinear<0.05 iX{2U lF7  
for m1 = 1:1:M1                                    % Start space evolution WA1d8nl  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS Kr'?h'F  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; g(X`.0  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform QICxS
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   ca2 = fftshift(fft(u2)); j;E$7QH[  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation T%&vq6  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   %i/|}K  
   u2 = ifft(fftshift(c2));                        % Return to physical space ;`Xm?N  
   u1 = ifft(fftshift(c1)); Y$"
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if rem(m1,J) == 0                                 % Save output every J steps. $z*"@  
    U1 = [U1 u1];                                  % put solutions in U array d>mZY66P  
    U2=[U2 u2]; - EGZ  
    MN1=[MN1 m1]; ](Wa:U}Xs  
    z1=dz*MN1';                                    % output location |>xuH#Q  
  end g.di3GGi  
end *S.FM.r  
hg=abs(U1').*abs(U1');                             % for data write to excel gCPH>8JwS0  
ha=[z1 hg];                                        % for data write to excel [pp|*@1T  
t1=[0 t']; r,.j^a  
hh=[t1' ha'];                                      % for data write to excel file ,
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%dlmwrite('aa',hh,'\t');                           % save data in the excel format f42F@M(:  
figure(1) /;Hqv`X7  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn KMkD6g  
figure(2) QN$s%&O  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn ;b=diZE  
1aIGC9xQ`  
非线性超快脉冲耦合的数值方法的Matlab程序 *A8*FX>\F  
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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。   {_*G"A 9  
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 MG.c`t/w  
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%  This Matlab script file solves the nonlinear Schrodinger equations #[x*0K-h  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of /
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%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear CC"
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%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 DMsqTB`  
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C=1;                           5vR])T/S0  
M1=120,                       % integer for amplitude cMT:Ij];  
M3=5000;                      % integer for length of coupler }PBL  
N = 512;                      % Number of Fourier modes (Time domain sampling points) 'Z.C&6_  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. M\k[?i  
T =40;                        % length of time:T*T0. !lFNG:&`  
dt = T/N;                     % time step H.>EO&#|p  
n = [-N/2:1:N/2-1]';          % Index /0gr?I1wr7  
t = n.*dt;   ak_y:O|  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. Hc>yZ:c;  
w=2*pi*n./T; Zazs".  
g1=-i*ww./2; Z:AB(c  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; fa/o4S<  
g3=-i*ww./2; Qb)c>r  
P1=0; yF6AI@y  
P2=0; .5s58Hcg,  
P3=1; l1<=3+d  
P=0; Twd*HH  
for m1=1:M1                 *My9r.F5o  
p=0.032*m1;                %input amplitude t>N2K-8Qh  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 2SlL`hN>Z  
s1=s10; M6Xzyt|  
s20=0.*s10;                %input in waveguide 2 zY*~2|q,s  
s30=0.*s10;                %input in waveguide 3 zGz}.-F  
s2=s20; YRBJ(v"9  
s3=s30; '-N5F  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   MS#*3Md&y  
%energy in waveguide 1 u tkdL4G}'  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   sxRKWM@4  
%energy in waveguide 2 ackeq#  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   Z}vDP^rf  
%energy in waveguide 3 cU ?F D  
for m3 = 1:1:M3                                    % Start space evolution UNiK6h_%  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS ]v>[r?X#V  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; pi#a!Quf\  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; Z+6WG  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform d6[' [
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   sca2 = fftshift(fft(s2)); j-**\.4a~  
   sca3 = fftshift(fft(s3)); 7 qn=W  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   z(%tu  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); wY%t# [T3  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); 6[R6P:v&'G  
   s3 = ifft(fftshift(sc3)); 8`)* ?Q9~  
   s2 = ifft(fftshift(sc2));                       % Return to physical space }xBO;  
   s1 = ifft(fftshift(sc1)); FF^h(E
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end xgkCN$zQ`  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); i g7|kl  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); RkF^V(  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); Pke8RLg2A  
   P1=[P1 p1/p10]; 9a]o?>`E  
   P2=[P2 p2/p10]; $]};EI#  
   P3=[P3 p3/p10]; {4/*2IRN9h  
   P=[P p*p]; d&|5Rk ~  
end u$5.GmKm  
figure(1) ~Yl.(R  
plot(P,P1, P,P2, P,P3); `5Z'8^  
*3={s"a.(  
转自：http://blog.163.com/opto_wang/

谢谢哈~！~