[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 mTb2d?NS  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of 4/mj"PBKL  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of x9{Sl[2&  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear EkgN6S`}  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 8YJqM,t5)  

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%fid=fopen('e21.dat','w');
J4K|KS7   
N = 128;                       % Number of Fourier modes (Time domain sampling points) j.yr5%  
M1 =3000;              % Total number of space steps l66ipgw_^I  
J =100;                % Steps between output of space y!{/'{?P  
T =10;                  % length of time windows:T*T0 ui#1+p3G  
T0=0.1;                 % input pulse width 9{]r+z:  
MN1=0;                 % initial value for the space output location XM5;AcD  
dt = T/N;                      % time step 5sV/N] !  
n = [-N/2:1:N/2-1]';           % Index _ /28Cw  
t = n.*dt;   ~:RDw<PWp  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 ~1wdAq`'a  
u20=u10.*0.0;                  % input to waveguide 2 +D{*L0$D"  
u1=u10; u2=u20;                 M@LaD 5  
U1 = u1;   '\E*W!R.]  
U2 = u2;                       % Compute initial condition; save it in U oE|{|27X  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. (j"~]T!)1  
w=2*pi*n./T; ,*}g r  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T %Cbc@=k  
L=4;                           % length of evoluation to compare with S. Trillo's paper XKPt[$ab  
dz=L/M1;                       % space step, make sure nonlinear<0.05 Y[8co<p  
for m1 = 1:1:M1                                    % Start space evolution krnk%
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   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS @*`UOgP7
 
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; z&HN>7  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform tU~H@'  
   ca2 = fftshift(fft(u2)); W0?Y%Da(4m  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation cI4qgV  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   RT+30Q?  
   u2 = ifft(fftshift(c2));                        % Return to physical space f6_|dvY3  
   u1 = ifft(fftshift(c1)); lt(-,md  
if rem(m1,J) == 0                                 % Save output every J steps. J/&*OC  
    U1 = [U1 u1];                                  % put solutions in U array ]2sZu7  
    U2=[U2 u2]; Qj~W-^/ -  
    MN1=[MN1 m1]; ,;ruH^  
    z1=dz*MN1';                                    % output location '8pPGh9D
 
  end u{lDof>  
end fOjt` ~ToI  
hg=abs(U1').*abs(U1');                             % for data write to excel D(ntVR  
ha=[z1 hg];                                        % for data write to excel 8!fAv$g0  
t1=[0 t']; %IH|zSr)EM  
hh=[t1' ha'];                                      % for data write to excel file GHsdLe=t0#  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format D!E 9@*Lf  
figure(1) 'FA)LuAok  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn U@t?jTMBkO  
figure(2) g#<?OFl  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn >D^7v(&  
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非线性超快脉冲耦合的数值方法的Matlab程序 AiHDoV+-  
YHv,Z|.w  
在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   T+`GOFx  
Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 -N
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%  This Matlab script file solves the nonlinear Schrodinger equations &l}xBQAL  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of &\D<n;3  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear ](6vG$\  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 X1PlW8pd  
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C=1;                           `[u>NEb  
M1=120,                       % integer for amplitude MKYE]D;  
M3=5000;                      % integer for length of coupler D@1
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N = 512;                      % Number of Fourier modes (Time domain sampling points) 
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dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. 52R.L9Ai  
T =40;                        % length of time:T*T0. +q?0A^C>  
dt = T/N;                     % time step ^WYG?/{4  
n = [-N/2:1:N/2-1]';          % Index v@1Jhns  
t = n.*dt;   ^|12~d_.T  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. {.8)gVBmA  
w=2*pi*n./T; uC ;PP=z  
g1=-i*ww./2; 8i$`oMv[y  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; b0CaoSWo  
g3=-i*ww./2; [B;Ek\5W  
P1=0; I8wVvs;k  
P2=0; !_z>w6uR  
P3=1; $W]guG  
P=0; k 5kX  
for m1=1:M1                 >-WOw  
p=0.032*m1;                %input amplitude 4U1fPyt  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 a_MnQ@  
s1=s10; BQmafpp`  
s20=0.*s10;                %input in waveguide 2 DMpd(ws  
s30=0.*s10;                %input in waveguide 3 BJ2W}R  
s2=s20; l]=$<  
s3=s30; s|`)'  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   otVdx&%]  
%energy in waveguide 1 ,colGth54  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   6y!?xot  
%energy in waveguide 2 0s[3:bZ\Ia  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   >V=@[B(0  
%energy in waveguide 3 }n8;A;axi  
for m3 = 1:1:M3                                    % Start space evolution $=a$z"  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS \(t>(4s_~  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; ,+evP=(cX  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; $d[:4h~  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform 4^9_E&Fa  
   sca2 = fftshift(fft(s2)); Eu~wbU"%  
   sca3 = fftshift(fft(s3)); q)y8Bv|  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   {/!"}{G1e  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); 7}85o J  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); J~`%Nj5>  
   s3 = ifft(fftshift(sc3)); vK~KeZ\,p=  
   s2 = ifft(fftshift(sc2));                       % Return to physical space L 'Rapu  
   s1 = ifft(fftshift(sc1)); \`# 0,pLr  
end iFchD\E*o  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); m3e49 bP  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); =xP{f<`
 
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); mQuaO# I,  
   P1=[P1 p1/p10]; |^!@
  
   P2=[P2 p2/p10]; 6;V1PK>9  
   P3=[P3 p3/p10]; IcA~f@  
   P=[P p*p]; 1<e%)? G  
end K0a 50@B]
 
figure(1) SXF_)1QO\W  
plot(P,P1, P,P2, P,P3); sUMn (@r  
'~a$f;: Dv  
转自：http://blog.163.com/opto_wang/

谢谢哈~！~