[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 icb*L~qm  

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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of =?Ui(?tI  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of "7'P Lo3O  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear p8 Ao{  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 iCLH  
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%fid=fopen('e21.dat','w'); 1$+8wDVwad  
N = 128;                       % Number of Fourier modes (Time domain sampling points) *AP"[W  
M1 =3000;              % Total number of space steps 684d&\(s  
J =100;                % Steps between output of space Bgn%d4W;G  
T =10;                  % length of time windows:T*T0 _-3n'i8  
T0=0.1;                 % input pulse width ``eam8Az_U  
MN1=0;                 % initial value for the space output location zvVo-{6  
dt = T/N;                      % time step w$Fg0JS  
n = [-N/2:1:N/2-1]';           % Index Rj4C-X4=  
t = n.*dt;   YYT#{>&  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 <_ENC>NP  
u20=u10.*0.0;                  % input to waveguide 2 D6H?*4f]  
u1=u10; u2=u20;                 R7U%v"F>`  
U1 = u1;   O@4J=P=w  
U2 = u2;                       % Compute initial condition; save it in U gO)":!_n W  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. jCXBp>9$M  
w=2*pi*n./T; N#ZWW6  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T 22=sh;y+2  
L=4;                           % length of evoluation to compare with S. Trillo's paper Rk[a|T&  
dz=L/M1;                       % space step, make sure nonlinear<0.05 Uqb]&2  
for m1 = 1:1:M1                                    % Start space evolution &x[7?Y L  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS ":vEWp+g  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; El@*Fo  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform ZX64kk+
 
   ca2 = fftshift(fft(u2)); [`oVMR  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation <e?Eva%t`  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   8#VD u(  
   u2 = ifft(fftshift(c2));                        % Return to physical space "TJ*mN.i{}  
   u1 = ifft(fftshift(c1)); g&85L$   
if rem(m1,J) == 0                                 % Save output every J steps. A=5Ebu!z  
    U1 = [U1 u1];                                  % put solutions in U array } ck<R
  
    U2=[U2 u2]; C l,vBjl h  
    MN1=[MN1 m1]; 8*@{}O##  
    z1=dz*MN1';                                    % output location fggs ;Le  
  end gFKJbjT|  
end pmvd%X\f  
hg=abs(U1').*abs(U1');                             % for data write to excel Ei):\,Nv  
ha=[z1 hg];                                        % for data write to excel  5QLK  
t1=[0 t']; 4l%1D.3-O  
hh=[t1' ha'];                                      % for data write to excel file /1v9U|j  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format tV
`=o$`  
figure(1) ^a_a%ws
 
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn *;]}`r  
figure(2) L/r_MtN  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn fO&`A:JY  
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非线性超快脉冲耦合的数值方法的Matlab程序 BhzDV
 
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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。   CDRbYO  
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 flo$[]`.7  
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%  This Matlab script file solves the nonlinear Schrodinger equations n)98NSVDbT  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of - ~|Gwr"  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear j}eb _K+I  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ESIP+  
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C=1;                           twq~.:<o  
M1=120,                       % integer for amplitude NFZ(*v1U  
M3=5000;                      % integer for length of coupler [i/!o
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N = 512;                      % Number of Fourier modes (Time domain sampling points) DJL
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dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. ,M;9|kE*  
T =40;                        % length of time:T*T0. uW(-?  
dt = T/N;                     % time step JRo/ HY+  
n = [-N/2:1:N/2-1]';          % Index ^0}ma*gi~  
t = n.*dt;   +h4W<YnW  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. BZ?Ck[E]Z  
w=2*pi*n./T; #mw!_]  
g1=-i*ww./2; o+A1-&qhN  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; $M 8&&M  
g3=-i*ww./2; 8YQuq.(>a  
P1=0; B5;%R01A  
P2=0; ,UMr_ e{|  
P3=1; Giv,%3'  
P=0; eZa*WI=  
for m1=1:M1                 vTO9XHc E  
p=0.032*m1;                %input amplitude q2vD)r  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 OL
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s1=s10; @@Ybg6.+*  
s20=0.*s10;                %input in waveguide 2 *9EwZwE_K  
s30=0.*s10;                %input in waveguide 3 q>.7VN[ vE  
s2=s20; #dWz,e3   
s3=s30; tF`L]1r>  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   \Y)HSJR;e  
%energy in waveguide 1 pT]hPuC  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   _xaum  
%energy in waveguide 2 #T_!-;(Z  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   Uz^N6q  
%energy in waveguide 3 #&}- q RA  
for m3 = 1:1:M3                                    % Start space evolution vn^O m-\  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS #cfiN b}GX  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; SN}K=)KF#  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; xz8e1M  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform )t|:_Z  
   sca2 = fftshift(fft(s2)); 2`$*HPj+G  
   sca3 = fftshift(fft(s3)); 0+FPAqX  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   )4 4Y`v  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); Xxg|01  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); sm/aL^4  
   s3 = ifft(fftshift(sc3)); f,TW|Y'{g  
   s2 = ifft(fftshift(sc2));                       % Return to physical space AOR?2u  
   s1 = ifft(fftshift(sc1)); u /F!8#  
end F?Lt-a+  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); avRtYL  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); f1 x&Fk  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); T7,]^ 1  
   P1=[P1 p1/p10]; *#Cx-J  
   P2=[P2 p2/p10]; _`udd)Y2  
   P3=[P3 p3/p10]; +#FqC/`l  
   P=[P p*p]; 6dIPgie3w  
end bej(Ds0  
figure(1) Te+(7 Z  
plot(P,P1, P,P2, P,P3); l
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~