[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 g%1!YvS3v  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of 7$,["cJX  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of DtXXfp@;  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear w v9s{I{P  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 h7[V
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%fid=fopen('e21.dat','w'); 1fViW^l_  
N = 128;                       % Number of Fourier modes (Time domain sampling points) 7ABHgw~?8r  
M1 =3000;              % Total number of space steps }1z= C<  
J =100;                % Steps between output of space %jqBYn0q'  
T =10;                  % length of time windows:T*T0 *z` {$hc  
T0=0.1;                 % input pulse width :}UWy?F  
MN1=0;                 % initial value for the space output location 5(u7b  
dt = T/N;                      % time step QbxjfW"/+  
n = [-N/2:1:N/2-1]';           % Index ;9=9D{-4+  
t = n.*dt;   p Ic;9  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 1g2%f9G  
u20=u10.*0.0;                  % input to waveguide 2 ;T-i+_  
u1=u10; u2=u20;                 j3Cpo x  
U1 = u1;   (<itE3P  
U2 = u2;                       % Compute initial condition; save it in U \
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ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. T/)$}#w0i  
w=2*pi*n./T; Y]&HU) u  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T Q(oWaG  
L=4;                           % length of evoluation to compare with S. Trillo's paper uhQ
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dz=L/M1;                       % space step, make sure nonlinear<0.05 j%]i#iqF  
for m1 = 1:1:M1                                    % Start space evolution $M$oNOT}Y  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS Itj|0PGd  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; V6BCW;  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform EG7
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   ca2 = fftshift(fft(u2)); u9N?B* &{  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation i.0}qS?  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   h"#^0$f  
   u2 = ifft(fftshift(c2));                        % Return to physical space .7+_ubj&,  
   u1 = ifft(fftshift(c1)); pFGdm3pV  
if rem(m1,J) == 0                                 % Save output every J steps. lOI(+74  
    U1 = [U1 u1];                                  % put solutions in U array \1aj!)  
    U2=[U2 u2]; O0WzDD  
    MN1=[MN1 m1]; 67/hhO  
    z1=dz*MN1';                                    % output location 75Jh(hd(  
  end GB^Ch YOb  
end v|t^th,  
hg=abs(U1').*abs(U1');                             % for data write to excel v;?t=}NwF  
ha=[z1 hg];                                        % for data write to excel bveNd0hN  
t1=[0 t']; 1,,o_e\nn3  
hh=[t1' ha'];                                      % for data write to excel file 9);a0}*5  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format 7{."Y@  
figure(1) ;=F^G?p^  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn /LPSI^l!m  
figure(2) g9GE0DbT`  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn qJ5Y}/r  
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非线性超快脉冲耦合的数值方法的Matlab程序 9t7_7{Q+;  
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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。   /_26D0}UuF  
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 )q&uvfQ1(  
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%  This Matlab script file solves the nonlinear Schrodinger equations Q4CxtY  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of HQQc<7c",  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear .CQ IN]iD  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 jP@H$$-=wH  
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C=1;                           fo4j^,`  
M1=120,                       % integer for amplitude 2[qO;js  
M3=5000;                      % integer for length of coupler nC
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N = 512;                      % Number of Fourier modes (Time domain sampling points) BU<A+Pe>  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. ;u!>( QQ  
T =40;                        % length of time:T*T0. i7cMe8  
dt = T/N;                     % time step -'5:Cq  
n = [-N/2:1:N/2-1]';          % Index t9Pu:B6  
t = n.*dt;   "eZNci  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. BT`D|<  
w=2*pi*n./T; 0K@s_C=n#  
g1=-i*ww./2; }`h)+Im=  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; Ol{)U;,`  
g3=-i*ww./2; _Bb/~^  
P1=0; h1
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P2=0; EAj2uV  
P3=1; ?9OiF-:n  
P=0; F>96]71 2  
for m1=1:M1                 pWO,yxr:  
p=0.032*m1;                %input amplitude T% Kj >
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s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 ! Hdg $,  
s1=s10; HGh`O\f8  
s20=0.*s10;                %input in waveguide 2 2/E3~X7  
s30=0.*s10;                %input in waveguide 3 6EGh8H f  
s2=s20; W*}q;ub;  
s3=s30; _\"7  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   ~BDVmQa  
%energy in waveguide 1 1EyM,$On  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   u"?cmg<.1  
%energy in waveguide 2 z )a8 ^]`  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   %_KNAuM  
%energy in waveguide 3 CmY'[rI  
for m3 = 1:1:M3                                    % Start space evolution " F~uTo  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS -KCm#!  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; &owBmpz  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; ?UcW@B{  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform tceQn ^|<  
   sca2 = fftshift(fft(s2)); PfF7*}P  
   sca3 = fftshift(fft(s3)); CsQ}eW8uEf  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   Y\& 4`v'  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); b_W0tiyv%  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); )?K3nr  
   s3 = ifft(fftshift(sc3));  Ae<v  
   s2 = ifft(fftshift(sc2));                       % Return to physical space (`<l" @:_*  
   s1 = ifft(fftshift(sc1)); [NQ`S ~_:  
end w`CGDF\Oo  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); O<)"kj 7  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); BN|+2D+S  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); [`6|~E"F  
   P1=[P1 p1/p10]; V`l.F"<L  
   P2=[P2 p2/p10]; vaxNF%^~yN  
   P3=[P3 p3/p10]; qCc'w8A  
   P=[P p*p]; N|h`}*:x=  
end >(<OhS(  
figure(1) f)({;,q  
plot(P,P1, P,P2, P,P3); 1YTnOiYS1  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~