[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 P^-9?uBno  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of 4F!d V;"Z(  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of e vuP4-[y  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear b"9,DQB=i  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 s6uAF(4,  
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%fid=fopen('e21.dat','w'); (7,Awf5D~  
N = 128;                       % Number of Fourier modes (Time domain sampling points) bux-t3g7+  
M1 =3000;              % Total number of space steps L~~Yh{<  
J =100;                % Steps between output of space
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T =10;                  % length of time windows:T*T0 ?Y* PVx9Y  
T0=0.1;                 % input pulse width o5R40["  
MN1=0;                 % initial value for the space output location @Iu-F4YT  
dt = T/N;                      % time step :_ox8xS4  
n = [-N/2:1:N/2-1]';           % Index _#B/#^a  
t = n.*dt;   W^f#xrq>  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 SGm?"esEt  
u20=u10.*0.0;                  % input to waveguide 2 x
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u1=u10; u2=u20;                 = ;d<Ikj  
U1 = u1;   K-3 _4As  
U2 = u2;                       % Compute initial condition; save it in U /+msrrpD  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. Lw`\J|%p  
w=2*pi*n./T; |sz9l/,lG  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T |{T2|iJI  
L=4;                           % length of evoluation to compare with S. Trillo's paper `Fj(g!`  
dz=L/M1;                       % space step, make sure nonlinear<0.05 stPCw$@  
for m1 = 1:1:M1                                    % Start space evolution (6nw8vQ  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS lDeWs%n  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; se[};t:  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform 0J~4   
   ca2 = fftshift(fft(u2)); -}@9lhS,  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation -wB AFr  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   hr5)$qZW  
   u2 = ifft(fftshift(c2));                        % Return to physical space }T,uw8?f!  
   u1 = ifft(fftshift(c1)); hh9{md\  
if rem(m1,J) == 0                                 % Save output every J steps. [@6iStRg7  
    U1 = [U1 u1];                                  % put solutions in U array @#apOoVW>  
    U2=[U2 u2]; V_!i KEU  
    MN1=[MN1 m1]; nP^$p C  
    z1=dz*MN1';                                    % output location o6 /?WR9  
  end zKNk(/y  
end H^G*5EQK  
hg=abs(U1').*abs(U1');                             % for data write to excel jPfoI-  
ha=[z1 hg];                                        % for data write to excel @zbXG_J  
t1=[0 t'];
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hh=[t1' ha'];                                      % for data write to excel file <T).+ M/  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format P*>V6SK>b  
figure(1) 7 <xxOY>y  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn U{EW +>  
figure(2) 9\F^\h{  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn U,'n}]=4A3  

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非线性超快脉冲耦合的数值方法的Matlab程序 w8qI7/  
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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。   `
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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 K_i2%t3  
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%  This Matlab script file solves the nonlinear Schrodinger equations )-(NL!?`  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of DjIs"5Iei  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear (rJ
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%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 (k?OYz]c  
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C=1;                           Dng^4VRd  
M1=120,                       % integer for amplitude GOt@x9%  
M3=5000;                      % integer for length of coupler nV,a|V5Xm  
N = 512;                      % Number of Fourier modes (Time domain sampling points) (I$hw"%&  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. F<$&G'% H  
T =40;                        % length of time:T*T0. -8IiQRS  
dt = T/N;                     % time step nMhc3t  
n = [-N/2:1:N/2-1]';          % Index Z]tz<YSkG  
t = n.*dt;   y;;@T X  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. L|<Mtw  
w=2*pi*n./T; Oe$C5KA>LW  
g1=-i*ww./2; 4t":WutC  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; 9c
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g3=-i*ww./2; du !.j  
P1=0; <XNLeJdY  
P2=0; D<MtLwH  
P3=1; 9;PtYdJ8  
P=0; IY'S<)vOY  
for m1=1:M1                 tm$3ZzP4  
p=0.032*m1;                %input amplitude !Ej<J&e  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 {?8rvAjY  
s1=s10; 4 QWHGh"  
s20=0.*s10;                %input in waveguide 2 @c.pOX[]m,  
s30=0.*s10;                %input in waveguide 3 %\A
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s2=s20; i[B%:q:&  
s3=s30; M-n +3E9  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   D3]_AS&\  
%energy in waveguide 1 'G&w[8mqY  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   Q]8r72uSk  
%energy in waveguide 2 `!i>fo~  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   ~%]+5^Ka]  
%energy in waveguide 3 o\N),;
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for m3 = 1:1:M3                                    % Start space evolution ]]+"`t,-  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS 2'D2>^os  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; >">-4L17m  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; .L}ar7  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform C`fQ` RL\  
   sca2 = fftshift(fft(s2)); /wQD
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   sca3 = fftshift(fft(s3));
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   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   dwRJ0D]&  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); ~!I \{(  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); i9d.Ls  
   s3 = ifft(fftshift(sc3)); =dPrG=A  
   s2 = ifft(fftshift(sc2));                       % Return to physical space &a V`u?'e  
   s1 = ifft(fftshift(sc1)); &W1cc#(  
end \QVL%,.%M  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); :>|[ o&L  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); a$ Z06j  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); Gd!y,n&s  
   P1=[P1 p1/p10]; j s
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   P2=[P2 p2/p10]; /0
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   P3=[P3 p3/p10]; OmsNo0OA  
   P=[P p*p]; qTG/7tn "  
end 2TdcZ<k}J  
figure(1) -{^Gzui  
plot(P,P1, P,P2, P,P3); -Wf 2m6t  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~