[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 ;r XhK$  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of Cb/?hT  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of ofA6EmQ37  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear |~3$L\X  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 .+cYzS]!  
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%fid=fopen('e21.dat','w');
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N = 128;                       % Number of Fourier modes (Time domain sampling points) |u
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M1 =3000;              % Total number of space steps f{[,
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J =100;                % Steps between output of space %C8fv|@:f  
T =10;                  % length of time windows:T*T0 D3emO'`gQ  
T0=0.1;                 % input pulse width XT5Vo  
MN1=0;                 % initial value for the space output location {\HE'C/?  
dt = T/N;                      % time step 6}6ky9  
n = [-N/2:1:N/2-1]';           % Index ,`JXBI~  
t = n.*dt;   t(:6S$6{e  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 fKY1=3  
u20=u10.*0.0;                  % input to waveguide 2 WPM<Qv L  
u1=u10; u2=u20;                 fJ3qL#'  
U1 = u1;   uPpRzp  
U2 = u2;                       % Compute initial condition; save it in U y'k4>,`9e  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. I({ 7a i  
w=2*pi*n./T; %KmB>9  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T |k4ZTr]?  
L=4;                           % length of evoluation to compare with S. Trillo's paper zA/W+j$:  
dz=L/M1;                       % space step, make sure nonlinear<0.05 Q nqU!6k@  
for m1 = 1:1:M1                                    % Start space evolution #dGg !D  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS r4xq%hy  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; s `r tr  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform :6z0Ep"  
   ca2 = fftshift(fft(u2)); xIo7f  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation NOa.K)^k  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   XabrX|B#  
   u2 = ifft(fftshift(c2));                        % Return to physical space F*
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   u1 = ifft(fftshift(c1)); IfZaK([  
if rem(m1,J) == 0                                 % Save output every J steps. CW=-@W7  
    U1 = [U1 u1];                                  % put solutions in U array >gr6H1  
    U2=[U2 u2]; (t9qwSS8z  
    MN1=[MN1 m1]; B!le=V,@,  
    z1=dz*MN1';                                    % output location ZtEHP`Iin  
  end *3
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end _+8$=k2nM  
hg=abs(U1').*abs(U1');                             % for data write to excel 6iFd[<.*j  
ha=[z1 hg];                                        % for data write to excel f41!+W=  
t1=[0 t']; <v('HLA  
hh=[t1' ha'];                                      % for data write to excel file {Pg7IYjH  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format M{7EFTy!y  
figure(1) \Rp)n=|  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn yg2~qa:dZ  
figure(2) d~|qx  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn xL>0&R  
@/JGC%!  
非线性超快脉冲耦合的数值方法的Matlab程序 {F k]X#j  
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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。   \FTvN  
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 ]'_z(s}  
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%  This Matlab script file solves the nonlinear Schrodinger equations nL+*Ja  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of =
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%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear uB,B%XHj  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 f8?K_K;\   
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C=1;                           8XJ%Yuu  
M1=120,                       % integer for amplitude ;gm){ g  
M3=5000;                      % integer for length of coupler 3 XfXMVm  
N = 512;                      % Number of Fourier modes (Time domain sampling points) z4-AOTo2y  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. H[,.nH_>+  
T =40;                        % length of time:T*T0. 4kg9
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dt = T/N;                     % time step 6g$04C3tHi  
n = [-N/2:1:N/2-1]';          % Index b9y E  
t = n.*dt;    ]NAPvw#p  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. RFK N,oB  
w=2*pi*n./T; A{6ZEQAh>  
g1=-i*ww./2; $
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g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; #zy,x  
g3=-i*ww./2; RL&3 P@r  
P1=0; h'-TZXs0e1  
P2=0; T>uLqd{hH  
P3=1; D}"GrY5  
P=0; ~hvhT}lE  
for m1=1:M1                 "W+4`A(/l  
p=0.032*m1;                %input amplitude RycEM|51V  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 Zo0&<QWj  
s1=s10; C}1(@$  
s20=0.*s10;                %input in waveguide 2 N'`*#UI+  
s30=0.*s10;                %input in waveguide 3 bY>o%L
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s2=s20; 6PMu;#  
s3=s30; pb{P[-f  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   AN~1E@"  
%energy in waveguide 1 J)fS2Ni+  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   VS).!;>z  
%energy in waveguide 2 K5.C*|w  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   sG VC+!E  
%energy in waveguide 3 e8lF$[i  
for m3 = 1:1:M3                                    % Start space evolution 95!xTf  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS C3_*o>8  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; 5;^8wh(  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; 8Peqm?{5Y5  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform }dXL= ul  
   sca2 = fftshift(fft(s2)); ttw@nv% @  
   sca3 = fftshift(fft(s3)); |;_ yAL  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   by06!-P0[  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); 9xKFX|*$  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); cn\_;TYiJ  
   s3 = ifft(fftshift(sc3)); g]ihwm~  
   s2 = ifft(fftshift(sc2));                       % Return to physical space e.jgV=dT-  
   s1 = ifft(fftshift(sc1)); uyA9`~p=#  
end NFSPw`f  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); q
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   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); F@I_sGCcb  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); c"z%AzUV'  
   P1=[P1 p1/p10]; Yj"UD:p  
   P2=[P2 p2/p10]; { &qBr&kg  
   P3=[P3 p3/p10]; OKU P  
   P=[P p*p]; |(V%(_s  
end y1'/@A1  
figure(1) S77Gc:[;8  
plot(P,P1, P,P2, P,P3); o&AUB`.9~  
l1:j/[B=  
转自：http://blog.163.com/opto_wang/

谢谢哈~！~