[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 s4[PwD  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of LDY3Ya`6m  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of %j/}e>$"Nk  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear WXQ+`OH7  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 O?t49=uB}  
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%fid=fopen('e21.dat','w'); 7d^ ~.F  
N = 128;                       % Number of Fourier modes (Time domain sampling points) * /^}  
M1 =3000;              % Total number of space steps yVe<+Z\7  
J =100;                % Steps between output of space Om(Ir&0  
T =10;                  % length of time windows:T*T0 qH(HcsgD  
T0=0.1;                 % input pulse width z#B(1uI  
MN1=0;                 % initial value for the space output location %J8uVD.2  
dt = T/N;                      % time step tu's]3RE  
n = [-N/2:1:N/2-1]';           % Index 8osP$"/o  
t = n.*dt;   v Q51-.g  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 @^.o8+Pp  
u20=u10.*0.0;                  % input to waveguide 2 ldnKV&N  
u1=u10; u2=u20;                 bTMgEY  
U1 = u1;   TPn#cIPG  
U2 = u2;                       % Compute initial condition; save it in U 7$mB.\|  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. eig{~
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w=2*pi*n./T; ?4
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g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T >U)>~SQf  
L=4;                           % length of evoluation to compare with S. Trillo's paper Zi}jf25  
dz=L/M1;                       % space step, make sure nonlinear<0.05 s6k(K>Pl  
for m1 = 1:1:M1                                    % Start space evolution [)?yH3  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS 2B"tT"f  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; ioUO0  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform X>%li$9J.  
   ca2 = fftshift(fft(u2)); hi/Z>1ZOX  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation &88c@Ksn  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   J7HY(7Nx  
   u2 = ifft(fftshift(c2));                        % Return to physical space LIll@2[  
   u1 = ifft(fftshift(c1)); -<:w{
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if rem(m1,J) == 0                                 % Save output every J steps. v]#[bqB.b  
    U1 = [U1 u1];                                  % put solutions in U array F*_+k  
    U2=[U2 u2]; qJE_4/<^!  
    MN1=[MN1 m1]; rv c%[HfW;  
    z1=dz*MN1';                                    % output location 49e
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  end [X7gP4  
end A b+qLh&?  
hg=abs(U1').*abs(U1');                             % for data write to excel -O\fy!  
ha=[z1 hg];                                        % for data write to excel ~UHjc0  
t1=[0 t']; Dutc#?bT  
hh=[t1' ha'];                                      % for data write to excel file @hwNM#>`  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format 0mNL!"  
figure(1) V
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waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn mkq246<D~  
figure(2) Vh
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waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn 4dy!2KZN  
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非线性超快脉冲耦合的数值方法的Matlab程序 bB)$=7\  

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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。   L)qUBp@MW  
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 qHvU4v  
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%  This Matlab script file solves the nonlinear Schrodinger equations
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%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of (*kKfg4Wj  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear G'`^U}9V\  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 7yjun|Lt}X  
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C=1;                           {yB0JL}n  
M1=120,                       % integer for amplitude zN9#qlfv  
M3=5000;                      % integer for length of coupler iRx`Nx<@  
N = 512;                      % Number of Fourier modes (Time domain sampling points) eJ6 #x$I,  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. hAsReZ?  
T =40;                        % length of time:T*T0. /N#=Tol  
dt = T/N;                     % time step ,f@j4*)  
n = [-N/2:1:N/2-1]';          % Index V`9*_8Dx2  
t = n.*dt;   zG{jRth  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. $@l=FV_;  
w=2*pi*n./T; .IM]B4m  
g1=-i*ww./2; NwdrJw9  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; 1CR\!?  
g3=-i*ww./2; g W_E  
P1=0; *sau['Ha  
P2=0; !p76I=H%  
P3=1; maa$kg8U*!  
P=0; u8t|!pMF8  
for m1=1:M1                 zeq")A
 
p=0.032*m1;                %input amplitude "G,,:H9v  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 T]/5aA4  
s1=s10; + )z5ai0m  
s20=0.*s10;                %input in waveguide 2 (P=WKZMPN  
s30=0.*s10;                %input in waveguide 3 g7^|(!Y%  
s2=s20; 0FLCN!i1  
s3=s30; @e
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p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   f96`n+>xi  
%energy in waveguide 1 9_4(}|"N|  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   6QJ.=.>b  
%energy in waveguide 2 =qbN?a/?2  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   L8H:,} 2  
%energy in waveguide 3 FS=LpvOG)  
for m3 = 1:1:M3                                    % Start space evolution n).*=YLN  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS IuA4eDr^Y%  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; s:iBl/N}  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; u+ hRaI;v  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform cNN0-<#c  
   sca2 = fftshift(fft(s2)); Z9MR"!0  
   sca3 = fftshift(fft(s3)); ]Yf^O @<<>  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   !@wUARQ  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); U
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   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); Jw#7b[a  
   s3 = ifft(fftshift(sc3)); bBV03_*  
   s2 = ifft(fftshift(sc2));                       % Return to physical space J}+N\V~
 
   s1 = ifft(fftshift(sc1)); +0j{$MPZ  
end Om;aE1sW  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); UbGnU_}  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); pQ!lY  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); Lb?q5_  
   P1=[P1 p1/p10]; [La}h2gz  
   P2=[P2 p2/p10]; US=K}B=g  
   P3=[P3 p3/p10]; jl]3B  
   P=[P p*p]; Q`NdsS2  
end j
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figure(1) wc~s:  
plot(P,P1, P,P2, P,P3); s$,G5Feub  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~