[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 X)S4rW%  
8%B @[YDe  
%  This Matlab script file solves the coupled nonlinear Schrodinger equations of T@.CwV  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of wAYc)u#  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear zQJbZ=5Bu"  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 f5v|}gMAX  
5+J/Qm8{bb  
%fid=fopen('e21.dat','w'); |xOOdy6 )~  
N = 128;                       % Number of Fourier modes (Time domain sampling points) `{":*V   
M1 =3000;              % Total number of space steps 'M{_S  
J =100;                % Steps between output of space Ws(>} qjy  
T =10;                  % length of time windows:T*T0 nq;)!Wry  
T0=0.1;                 % input pulse width :OM>z4mQ  
MN1=0;                 % initial value for the space output location 2}AV_]]  
dt = T/N;                      % time step f#jAjzmYL  
n = [-N/2:1:N/2-1]';           % Index gg9W7%t/  
t = n.*dt;   vPi+8)  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 "%Ak[04'  
u20=u10.*0.0;                  % input to waveguide 2 HT'dft #  
u1=u10; u2=u20;                 y;H 3g#  
U1 = u1;   _ U\vHa$#  
U2 = u2;                       % Compute initial condition; save it in U g;pymz  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. RzkJS9)m  
w=2*pi*n./T; (g\'Zw5bk  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T 4^5s\f B  
L=4;                           % length of evoluation to compare with S. Trillo's paper 6Jm4?ex  
dz=L/M1;                       % space step, make sure nonlinear<0.05 T+fU+GLD  
for m1 = 1:1:M1                                    % Start space evolution Q=[&~^Y)  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS mAMKCxz,  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; lF<(yF5  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform %rsW:nl  
   ca2 = fftshift(fft(u2)); K67x.PZ  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation wU3Q  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   wJ}8y4O!N  
   u2 = ifft(fftshift(c2));                        % Return to physical space 8c#*T%Vf  
   u1 = ifft(fftshift(c1)); n| %
{R|s  
if rem(m1,J) == 0                                 % Save output every J steps. [T|~Kh%#  
    U1 = [U1 u1];                                  % put solutions in U array _Z%C{~,7)x  
    U2=[U2 u2]; -4;u|0_  
    MN1=[MN1 m1]; !O\r[c  
    z1=dz*MN1';                                    % output location *KMCU m  
  end R~b$7jpd  
end "^\4xI  
hg=abs(U1').*abs(U1');                             % for data write to excel ~I'hiV^-  
ha=[z1 hg];                                        % for data write to excel v1:5r  
t1=[0 t']; g7F>o76M  
hh=[t1' ha'];                                      % for data write to excel file QwiC2}/  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format Uhf -}Jdw  
figure(1) 3,GSBiK3}  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn iL(E`_I<  
figure(2) s=q}XIWK  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn Wrlmo'31  
79Iz,_  
非线性超快脉冲耦合的数值方法的Matlab程序 J&5|'yVX  
Uc&0>_Z  
在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   eI@O9<.&  
Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 IL<5Suz:  
nQ mkDPjU  
J[9jNCq|  
u5lj+
?  
%  This Matlab script file solves the nonlinear Schrodinger equations g\ke,r6  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of /];F4AO5  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear .w0?  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 =U:iR  
Z/64E^  
C=1;                           >IRo
]-,  
M1=120,                       % integer for amplitude Axr'zc  
M3=5000;                      % integer for length of coupler P)T:6K  
N = 512;                      % Number of Fourier modes (Time domain sampling points) 5~qr+la  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. ]xuq2MU,l  
T =40;                        % length of time:T*T0. {#7t(:x  
dt = T/N;                     % time step XOxm<3gXn  
n = [-N/2:1:N/2-1]';          % Index I%%$O'S  
t = n.*dt;   [ML4<Eb+x  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. ohwQ%NDl  
w=2*pi*n./T; A
/'G.H  
g1=-i*ww./2; -wY6da*.W  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; '0[l'Dt'  
g3=-i*ww./2; 4kx#=MLt
 
P1=0; /({5x[  
P2=0; }!2|*Y  
P3=1; LG;xZQx'  
P=0; BKN]DxJ6  
for m1=1:M1                 pPh$Jvo]  
p=0.032*m1;                %input amplitude &4]%&mX)-  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 B6
4%| S  
s1=s10; g|W~0A@D  
s20=0.*s10;                %input in waveguide 2 ;]p#PNQ0  
s30=0.*s10;                %input in waveguide 3 7%aB>uA  
s2=s20; 0O[q6!&]  
s3=s30; Nz2}M
a 2  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   0^hz1\g  
%energy in waveguide 1 8R)*8bb  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));    }UX>O  
%energy in waveguide 2 H>M0GL  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   Qg3 -%i/@  
%energy in waveguide 3 !j\yt  
for m3 = 1:1:M3                                    % Start space evolution wjY3:S~  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS ?onZ:s2  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; z]tvy).  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; F> ..eK  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform ww=< =  
   sca2 = fftshift(fft(s2)); ~aBALD0D;  
   sca3 = fftshift(fft(s3)); sjztT<{Q^-  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   W/fM0=!  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); d!,V"*S  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); ZQ@^(64  
   s3 = ifft(fftshift(sc3)); F+9|D  
   s2 = ifft(fftshift(sc2));                       % Return to physical space $lUZm\R|k  
   s1 = ifft(fftshift(sc1)); ,VbP$1t  
end Pf]L`haGN  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); KWM.b"WnXr  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); eml(F  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); `$Q $l  
   P1=[P1 p1/p10]; nAg|m,gA  
   P2=[P2 p2/p10];  8DyE  
   P3=[P3 p3/p10]; M7UVL&_z%  
   P=[P p*p]; ,>e)8  
end S__+S7]Nr  
figure(1) *|MPYxJ<  
plot(P,P1, P,P2, P,P3); ]l`?"X|^  
3xbA]u;gp  
转自：http://blog.163.com/opto_wang/

谢谢哈~！~