[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 2e-bt
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of )S`[ gK  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of K\8zhY  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear yqL"YD  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 PUZcb+%]h  
%eIaH!x:  
%fid=fopen('e21.dat','w'); tCGx]\  
N = 128;                       % Number of Fourier modes (Time domain sampling points) =_N[mR^  
M1 =3000;              % Total number of space steps BKb#\(95*  
J =100;                % Steps between output of space y06**f)  
T =10;                  % length of time windows:T*T0 qz3 Z'  
T0=0.1;                 % input pulse width TecMQ0 KD  
MN1=0;                 % initial value for the space output location IvY3iRq6  
dt = T/N;                      % time step { gs$pBu  
n = [-N/2:1:N/2-1]';           % Index qq<T~^  
t = n.*dt;   Ml{ ]{n  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 oaPWeM+  
u20=u10.*0.0;                  % input to waveguide 2 4KR`  
u1=u10; u2=u20;                 ISK 8t  
U1 = u1;   l:JVt`A4?  
U2 = u2;                       % Compute initial condition; save it in U v7KBYN  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. +WMXd.iN,  
w=2*pi*n./T; \f(zMP  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T -LUZ7,!/>o  
L=4;                           % length of evoluation to compare with S. Trillo's paper vyJ8" #]qY  
dz=L/M1;                       % space step, make sure nonlinear<0.05 w%iwxo  
for m1 = 1:1:M1                                    % Start space evolution ){'<67dK  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS _#&oQFdYR  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; S$$SLy:P  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform B&B:P  
   ca2 = fftshift(fft(u2));
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   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation 2PRiiL@  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   .Tq8Qdl  
   u2 = ifft(fftshift(c2));                        % Return to physical space /^k%sG@?  
   u1 = ifft(fftshift(c1)); 6_
u!{  
if rem(m1,J) == 0                                 % Save output every J steps. _6r[msH"  
    U1 = [U1 u1];                                  % put solutions in U array %g@\SR.  
    U2=[U2 u2]; "JLE  
    MN1=[MN1 m1]; n^l*oEl  
    z1=dz*MN1';                                    % output location 8OV=;aM?{  
  end jIrfJ*z  
end bfZt<-  
hg=abs(U1').*abs(U1');                             % for data write to excel uYg Q?*Z  
ha=[z1 hg];                                        % for data write to excel Z4As'a
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t1=[0 t']; (hZNWQ0  
hh=[t1' ha'];                                      % for data write to excel file qpCaW0]7  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format 4;AQ12<[1  
figure(1) m;{HlDez  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn rXMc0SPk  
figure(2) se2Y:v  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn hE`d@  
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非线性超快脉冲耦合的数值方法的Matlab程序 PI`Y%!P  
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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"-V6CA[  
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 )uo".n|n~B  
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%  This Matlab script file solves the nonlinear Schrodinger equations hHVAN3e  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of wL3RcXW``e  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear G7+{O7  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 @sZ7Ka  
k\T]*A  
C=1;                           0)b1'xt',  
M1=120,                       % integer for amplitude hFr+K1  
M3=5000;                      % integer for length of coupler iV?8'^  
N = 512;                      % Number of Fourier modes (Time domain sampling points) H!X*29nX  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. /.!&d^  
T =40;                        % length of time:T*T0. Y%eW6Y#  
dt = T/N;                     % time step >yn]h4
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n = [-N/2:1:N/2-1]';          % Index Yu_ eCq5/  
t = n.*dt;   cQThpgha  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. u?MhK#Mr  
w=2*pi*n./T; RfD#/G3|  
g1=-i*ww./2; OAW_c.)5D  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; |zP~/  
g3=-i*ww./2; CL7/J[TS  
P1=0; {fl[BX]kZ  
P2=0; ,P`GIGvkA  
P3=1; ts@$*  
P=0; 2W_[|.;'  
for m1=1:M1                 .-& =\}^2l  
p=0.032*m1;                %input amplitude DA>nYj-s  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 R[v<mo[s  
s1=s10; tB`"gC~  
s20=0.*s10;                %input in waveguide 2 i>CR{q  
s30=0.*s10;                %input in waveguide 3 #4LTUVH  
s2=s20; F-ofR]|)>  
s3=s30; tK{#kApHGG  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   K3tW Y 4-  
%energy in waveguide 1 iWr #H  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   noa+h<vGb  
%energy in waveguide 2 V?x&\<;,  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   <[}zw!z  
%energy in waveguide 3 4h--x~ @  
for m3 = 1:1:M3                                    % Start space evolution 'sa)_?Hy  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS F^!O\8PFd  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; AT3H
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   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; ^z,B}Nz  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform LCA+y1LP-_  
   sca2 = fftshift(fft(s2)); Y`-q[F?\y  
   sca3 = fftshift(fft(s3)); AU%Yr6  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   ( )ldn?v  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); <^{(?*  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); =B;qy7?  
   s3 = ifft(fftshift(sc3)); :KG=3un]  
   s2 = ifft(fftshift(sc2));                       % Return to physical space $J)`Ru6.  
   s1 = ifft(fftshift(sc1)); udr|6EjD.  
end *,O3@,+>H  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); <GQ=PrT|/  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); iS.gN&\z^  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); 4K`b?{){+a  
   P1=[P1 p1/p10]; KOXG=P0  
   P2=[P2 p2/p10]; f8r7SFwUv  
   P3=[P3 p3/p10]; `<<9A\Y-f  
   P=[P p*p]; &X` lh P  
end G}NqVbZ9]  
figure(1) &c&TQkx  
plot(P,P1, P,P2, P,P3); c>/7E-T  
saQ ~v@  
转自：http://blog.163.com/opto_wang/

谢谢哈~！~