[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 )#0Llx!  

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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of |W;EPQ+<  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of ibxtrt=  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear x-Fl|kwX.5  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ?
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%fid=fopen('e21.dat','w'); M
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N = 128;                       % Number of Fourier modes (Time domain sampling points) Mb\[` 4z  
M1 =3000;              % Total number of space steps q,fk@GI'2  
J =100;                % Steps between output of space :qxd s>Xm  
T =10;                  % length of time windows:T*T0 kOLS<>.  
T0=0.1;                 % input pulse width #e5*Dr8  
MN1=0;                 % initial value for the space output location ghVxcK  
dt = T/N;                      % time step }< m@82\  
n = [-N/2:1:N/2-1]';           % Index r57rH^Hc  
t = n.*dt;   TM$Ek^fQ.  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 *h Bo,   
u20=u10.*0.0;                  % input to waveguide 2 5%%A2FrB.S  
u1=u10; u2=u20;                 DOGg=`XK1  
U1 = u1;   #7dM %  
U2 = u2;                       % Compute initial condition; save it in U !Z`xwk"!  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. Nk/Ms:57y  
w=2*pi*n./T; 2apQ4)6#[H  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T oQ_n
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L=4;                           % length of evoluation to compare with S. Trillo's paper *l\vqgv.Z  
dz=L/M1;                       % space step, make sure nonlinear<0.05 'P,F)*kh  
for m1 = 1:1:M1                                    % Start space evolution Ykt(%2L  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS $jKeJn8,  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; bmu<V1[W  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform G##^xFx  
   ca2 = fftshift(fft(u2)); xrky5[XoD  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation Gj(UA1~1  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   ||vQW\g  
   u2 = ifft(fftshift(c2));                        % Return to physical space js8GK  
   u1 = ifft(fftshift(c1)); ;3k6_ub  
if rem(m1,J) == 0                                 % Save output every J steps. tmf=1M  
    U1 = [U1 u1];                                  % put solutions in U array DU: sQS4  
    U2=[U2 u2]; Zjh9jvsW  
    MN1=[MN1 m1]; DozC>  
    z1=dz*MN1';                                    % output location !B\[Q$  
  end )#n>))   
end %D:5 S?{  
hg=abs(U1').*abs(U1');                             % for data write to excel >5!/&D.q  
ha=[z1 hg];                                        % for data write to excel Cb/?hT  
t1=[0 t']; m K@a7fF?  
hh=[t1' ha'];                                      % for data write to excel file |~3$L\X  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format .+cYzS]!  
figure(1) 3((53@s98  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn *>XY' -;2e  
figure(2) 6lc/_&
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waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn ^. i;,  
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非线性超快脉冲耦合的数值方法的Matlab程序 i|Y_X  
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在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   "yCe
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Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 tKUy&]T  
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%  This Matlab script file solves the nonlinear Schrodinger equations SEXLi8;/  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of r6-'p0|   
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear UVD::  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 9/k?Lv  
!u#o"e<qh  
C=1;                           s=nE'/q1|  
M1=120,                       % integer for amplitude q[3b i!Q  
M3=5000;                      % integer for length of coupler pPG@_9qf  
N = 512;                      % Number of Fourier modes (Time domain sampling points) "lf_`4  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. (A*r&Ak[  
T =40;                        % length of time:T*T0. rS 4'@a  
dt = T/N;                     % time step &xqe8!FeA  
n = [-N/2:1:N/2-1]';          % Index #:68}f"$  
t = n.*dt;   NOa.K)^k  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. XabrX|B#  
w=2*pi*n./T; F*
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g1=-i*ww./2; IfZaK([  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; CW=-@W7  
g3=-i*ww./2; >gr6H1  
P1=0; j1>77C3  
P2=0; | ~G;M*q  
P3=1; ~^"cq S(  
P=0; .6E7 R  
for m1=1:M1                 Ac.z6]p  
p=0.032*m1;                %input amplitude XY|-qd}A  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 5Wi5`8m  
s1=s10; R^F99L  
s20=0.*s10;                %input in waveguide 2 /d >fp  
s30=0.*s10;                %input in waveguide 3 8}Y( @ %4  
s2=s20; nu$LWC-  
s3=s30; rDYq]`  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   j86s[Dty  
%energy in waveguide 1 %'* |N[  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   JPUDnPr  
%energy in waveguide 2 ,[bcyf  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   SAG)vmm  
%energy in waveguide 3 -JZl?hY(  
for m3 = 1:1:M3                                    % Start space evolution !*|CIxk(  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS G-n`X":$DT  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; 7B%@f9g  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; #OWwg`AWv  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform r+0)l:{.  
   sca2 = fftshift(fft(s2)); YQN=.Wtc  
   sca3 = fftshift(fft(s3)); .(S,dG0P  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   @;<w"j`r  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); &r<<4J(t  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); }C#YR(]  
   s3 = ifft(fftshift(sc3)); NE9e brK  
   s2 = ifft(fftshift(sc2));                       % Return to physical space v&XG4 &  
   s1 = ifft(fftshift(sc1)); !gf&l ^)  
end p]+W1v}V!  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); &9s6p6eb  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); hkU# lt  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); il-&d]AP  
   P1=[P1 p1/p10]; Vn/6D[}Tu  
   P2=[P2 p2/p10]; XY4s  
   P3=[P3 p3/p10]; }UGPEf\  
   P=[P p*p]; i]$d3J3  
end (Z,,H1L  
figure(1) K.z}%a  
plot(P,P1, P,P2, P,P3); :za!!^  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~