[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 ya8MjGo  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of LK5,GWF;  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of ~fbFA?g3  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
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%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 v#J2yg  
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%fid=fopen('e21.dat','w'); HfEU[p7)  
N = 128;                       % Number of Fourier modes (Time domain sampling points) KfD=3h=  
M1 =3000;              % Total number of space steps &g%9$*gmT  
J =100;                % Steps between output of space PLlad\  
T =10;                  % length of time windows:T*T0 },zP,y:cH  
T0=0.1;                 % input pulse width |X@ZM  
MN1=0;                 % initial value for the space output location _3v6c  
dt = T/N;                      % time step Wv!#B$J~U  
n = [-N/2:1:N/2-1]';           % Index a~jU~('4}w  
t = n.*dt;   ;G_{$)P.o  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 t[/WGF&(R  
u20=u10.*0.0;                  % input to waveguide 2 }}L :6^  
u1=u10; u2=u20;                 r/o1a't;  
U1 = u1;   MHNuA,cz  
U2 = u2;                       % Compute initial condition; save it in U M,nX@8 _h  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. 3VNYDY`>  
w=2*pi*n./T; x{y}pH"H  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T .)J7 \z8m  
L=4;                           % length of evoluation to compare with S. Trillo's paper :98<dQIG  
dz=L/M1;                       % space step, make sure nonlinear<0.05 2H+!78  
for m1 = 1:1:M1                                    % Start space evolution h$
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   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS
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   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; 3[`/rg,  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform W6STjtT3P  
   ca2 = fftshift(fft(u2)); >G`Uc&=  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation IqEE.XhaK  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   UqHk
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   u2 = ifft(fftshift(c2));                        % Return to physical space 84(NylZ  
   u1 = ifft(fftshift(c1)); S~L;oX?(!  
if rem(m1,J) == 0                                 % Save output every J steps. nX 4WlH  
    U1 = [U1 u1];                                  % put solutions in U array kF{'?R5w  
    U2=[U2 u2]; gt]
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    MN1=[MN1 m1]; $=&a0O#  
    z1=dz*MN1';                                    % output location qaE>])  
  end [\|`C4@3a  
end s}3g+T\l1w  
hg=abs(U1').*abs(U1');                             % for data write to excel  rvPY  
ha=[z1 hg];                                        % for data write to excel ol^uM .k%_  
t1=[0 t']; B<^yT@Wc  
hh=[t1' ha'];                                      % for data write to excel file 8<0
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%dlmwrite('aa',hh,'\t');                           % save data in the excel format 1{%3OG^'  
figure(1) \.!+'2!m  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn :'hc&wk`  
figure(2) ~1xfE C/  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn gl.uDO%.  
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非线性超快脉冲耦合的数值方法的Matlab程序 | R\PQ/)  
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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。   wAt|'wP :  
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 >a
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%  This Matlab script file solves the nonlinear Schrodinger equations >]/RlW[  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of 8/i];/,v*M  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear st4WjX_Q  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 Z|t`}lK  
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C=1;                           ,1|Qm8O  
M1=120,                       % integer for amplitude d1[;~)  
M3=5000;                      % integer for length of coupler /w|!SZB  
N = 512;                      % Number of Fourier modes (Time domain sampling points) ?ZF~U  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. MP LgE.n  
T =40;                        % length of time:T*T0. :r+BL@9  
dt = T/N;                     % time step ,_wpYTl*X  
n = [-N/2:1:N/2-1]';          % Index GMv.G  
t = n.*dt;   Fy6(N{hql  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. .5_zh; `  
w=2*pi*n./T; ScCp88KpFI  
g1=-i*ww./2; Qq7%{`<}  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; o&U'zaj
 
g3=-i*ww./2; )I{~Pcq  
P1=0; #B$r|rqamq  
P2=0; "z8iuF  
P3=1; GZq~Pl  
P=0; TWU[/>K  
for m1=1:M1                 " J4?Sb<  
p=0.032*m1;                %input amplitude g6D7Y<}d  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 &mPR[{  
s1=s10; L\cbY6b  
s20=0.*s10;                %input in waveguide 2 ,%^qzoZnT  
s30=0.*s10;                %input in waveguide 3 h 2QJQ|7a  
s2=s20; [gkOwU=?  
s3=s30; F!RzF7h1  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   C CDO8  
%energy in waveguide 1 0F5QAR O  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   SuJa?VU1w  
%energy in waveguide 2 y 1I(^<qO=  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   AqZ()p*z  
%energy in waveguide 3
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for m3 = 1:1:M3                                    % Start space evolution 'pa8h L  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS V\m51H1mqo  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; [G<SAWFg7  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; j>I.d+  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform IW>\\&pJ  
   sca2 = fftshift(fft(s2)); uS|f|)U&  
   sca3 = fftshift(fft(s3)); =XhxD<kI  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   S-7ryHH*0  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); Ly~s84k_po  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); 3?x}48  
   s3 = ifft(fftshift(sc3)); zI&).  
   s2 = ifft(fftshift(sc2));                       % Return to physical space @xkI?vK6  
   s1 = ifft(fftshift(sc1)); P3_&(  
end 3E$h W  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); +ab#2~,)  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); 5T-CAkR{n  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); 8(@Y@`/  
   P1=[P1 p1/p10]; 1,Uf-i  
   P2=[P2 p2/p10]; @wTRoMHPQ  
   P3=[P3 p3/p10]; NGp^/PZX0  
   P=[P p*p]; &eIwlynm  
end 0ZJN<AzbA  
figure(1) J,_IHzO~Z  
plot(P,P1, P,P2, P,P3); ~E3"
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~