[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 y_-0tI\J  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of T:yE(OBf  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of JL{VD /f  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 7~.9=I'A  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 u\;C;I-? '  
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%fid=fopen('e21.dat','w'); /@TF5]Ri  
N = 128;                       % Number of Fourier modes (Time domain sampling points) BUXpCxQ  
M1 =3000;              % Total number of space steps 'zuIBOH`j3  
J =100;                % Steps between output of space yl+gL?IES  
T =10;                  % length of time windows:T*T0 j'"J%e]  
T0=0.1;                 % input pulse width fuf"Ae  
MN1=0;                 % initial value for the space output location vV-`jsq20H  
dt = T/N;                      % time step 6mxfLlZ  
n = [-N/2:1:N/2-1]';           % Index \\;jw[P0  
t = n.*dt;   1K50Z.
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u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 `7V]y-  
u20=u10.*0.0;                  % input to waveguide 2 <}9lZEqY  
u1=u10; u2=u20;                 Ean5b>\  
U1 = u1;   ],Do6 @M-  
U2 = u2;                       % Compute initial condition; save it in U ^o&. fQ*  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. q#9RW(o  
w=2*pi*n./T; v;D~Pa  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T H8}oIA"b  
L=4;                           % length of evoluation to compare with S. Trillo's paper 7?w*]  
dz=L/M1;                       % space step, make sure nonlinear<0.05 HvJs1)Wo&  
for m1 = 1:1:M1                                    % Start space evolution {q^[a-h>  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS i5
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   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; >@ .  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform *_\_'@1|J)  
   ca2 = fftshift(fft(u2)); {8bSB.?R  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation _ZSR.w}j/  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   "b3"TPfK  
   u2 = ifft(fftshift(c2));                        % Return to physical space }y gD3:vN7  
   u1 = ifft(fftshift(c1)); 3"~!nn0;  
if rem(m1,J) == 0                                 % Save output every J steps. %YqEzlzF  
    U1 = [U1 u1];                                  % put solutions in U array ?)d~cJ  
    U2=[U2 u2]; 5#E`=C%  
    MN1=[MN1 m1]; ,/|T-Ka
 
    z1=dz*MN1';                                    % output location 5M*:}*  
  end (V2fRv  
end ml }{|Yz  
hg=abs(U1').*abs(U1');                             % for data write to excel Y9XEP7  
ha=[z1 hg];                                        % for data write to excel 1\I}2
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t1=[0 t']; AFE~ v\Gz  
hh=[t1' ha'];                                      % for data write to excel file LyFN.2q
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%dlmwrite('aa',hh,'\t');                           % save data in the excel format 6?c7$Y  
figure(1) mxdr,Idx  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn tf`^v6m%]  
figure(2) 28d'7El$  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn OYn}5RN  
Se =`N  
非线性超快脉冲耦合的数值方法的Matlab程序 c(s.5p ^  
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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。   I^$fM
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Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ]>Es4 s  
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%  This Matlab script file solves the nonlinear Schrodinger equations {&1/V  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of ~oY^;/ j  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear d>qY{Fdz  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 *u;Iw{.{  
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C=1;                           1=Z0w +v{  
M1=120,                       % integer for amplitude 0YDR1dO(*  
M3=5000;                      % integer for length of coupler '?(% Zxw%&  
N = 512;                      % Number of Fourier modes (Time domain sampling points) 1
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dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. t
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T =40;                        % length of time:T*T0. }:)&u|d_  
dt = T/N;                     % time step ER.}CM6{[  
n = [-N/2:1:N/2-1]';          % Index FVJGL  
t = n.*dt;   hM@>q&q_  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. @b2aNS<T  
w=2*pi*n./T; A6(/;+n  
g1=-i*ww./2; +TDw+  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; -e:`|(Mo  
g3=-i*ww./2; P+/e2Y  
P1=0; o!A+&{  
P2=0; ;u)I\3`*!  
P3=1; DN:EB@  
P=0; [Z$[rOF  
for m1=1:M1                 20Wg=p9L  
p=0.032*m1;                %input amplitude 7zG_(83)K  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 {3aua:q  
s1=s10; YNi.SXH  
s20=0.*s10;                %input in waveguide 2
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s30=0.*s10;                %input in waveguide 3 $6SW;d+>n  
s2=s20; dvUic-w<j  
s3=s30; $qj2w"'  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   P/_['7  
%energy in waveguide 1 @~a%/GQ#n*  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   ZPYS$Ydy  
%energy in waveguide 2 (SAs-  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   KPUV@eQ,  
%energy in waveguide 3 /m

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for m3 = 1:1:M3                                    % Start space evolution <wD-qTW  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS $(x]  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; e$rZ5X  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; IjnU?Bf  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform g[4WzDF*  
   sca2 = fftshift(fft(s2)); }@d@
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   sca3 = fftshift(fft(s3)); lrIe"H@  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   --BW9]FW  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); 7B66]3v  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); K]w'&Qm8W  
   s3 = ifft(fftshift(sc3)); /N.U/
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   s2 = ifft(fftshift(sc2));                       % Return to physical space X#
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   s1 = ifft(fftshift(sc1)); z<' u1l3  
end |P?*5xPB  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); nAlQ7'  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); :Zw2'IV  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); >i?oC^QM  
   P1=[P1 p1/p10]; [(7S.5I  
   P2=[P2 p2/p10]; FGq[\B  
   P3=[P3 p3/p10]; .HABNPNg(  
   P=[P p*p]; 7
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end U|R_OLWAg  
figure(1) KF:78C  
plot(P,P1, P,P2, P,P3); ~*];pV]A[  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~