[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 b]+F/@h~]  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of /8h=6"  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of ssi7)0  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear LSJ?;Zg(=z  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 6@J=n@J$p  
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%fid=fopen('e21.dat','w'); ~.m<`~u  
N = 128;                       % Number of Fourier modes (Time domain sampling points) #dA$k+3  
M1 =3000;              % Total number of space steps vjGQ!xF  
J =100;                % Steps between output of space )#}>,,S  
T =10;                  % length of time windows:T*T0 -1g:3'% P  
T0=0.1;                 % input pulse width 3yZmW$E.  
MN1=0;                 % initial value for the space output location DYD<?._I  
dt = T/N;                      % time step V0\[|E;F  
n = [-N/2:1:N/2-1]';           % Index smQ^(S^  
t = n.*dt;   Iry$z^  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 *glZb;_  
u20=u10.*0.0;                  % input to waveguide 2 18>cfDh;N  
u1=u10; u2=u20;                 Z',!LK!  
U1 = u1;   u*l|MIi6J  
U2 = u2;                       % Compute initial condition; save it in U $1an#~  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. /~[Lr   
w=2*pi*n./T; S\e&xUA;|  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T Z4j6z>qE  
L=4;                           % length of evoluation to compare with S. Trillo's paper t;&XIG~  
dz=L/M1;                       % space step, make sure nonlinear<0.05 &_ekA44E  
for m1 = 1:1:M1                                    % Start space evolution I &t~o  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS g{65QP  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; ,fVD`RR(W?  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform wHc my  
   ca2 = fftshift(fft(u2)); $cCC 1=dW  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation \*xB<mq  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   ~U9K<_U  
   u2 = ifft(fftshift(c2));                        % Return to physical space 0s#72}n  
   u1 = ifft(fftshift(c1)); %@/^UE:  
if rem(m1,J) == 0                                 % Save output every J steps. m~ tvuz I  
    U1 = [U1 u1];                                  % put solutions in U array sHP-@  
    U2=[U2 u2]; ~Iu!B Y  
    MN1=[MN1 m1]; z$32rt8{`v  
    z1=dz*MN1';                                    % output location gE-y`2SU  
  end WSkGVQu  
end _u`YjzK  
hg=abs(U1').*abs(U1');                             % for data write to excel O !L`0 =%c  
ha=[z1 hg];                                        % for data write to excel +L(amq;S  
t1=[0 t']; +eM${JyXH  
hh=[t1' ha'];                                      % for data write to excel file )ZJvx%@i  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format ^QB[;g.O  
figure(1) C6_(j48&  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn vJkc/7  
figure(2) 7|P kc(O  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn Y::0v@&(  
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非线性超快脉冲耦合的数值方法的Matlab程序 ^URCnJ67Se  
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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。   t8Zo9q>  
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 Hd|l6/[xz  
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%  This Matlab script file solves the nonlinear Schrodinger equations z*y!Ml1  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of 5jdZC(q5a  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear ^4y]7p  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 S;Bk/\2  
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C=1;                            R$a<=  
M1=120,                       % integer for amplitude AKNx~!%2  
M3=5000;                      % integer for length of coupler XC4Z,,ah"  
N = 512;                      % Number of Fourier modes (Time domain sampling points) K~x,so  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. 8!g `bC#%  
T =40;                        % length of time:T*T0. ^S9y7b^;r  
dt = T/N;                     % time step VSj!Gm0LB  
n = [-N/2:1:N/2-1]';          % Index B~Q-V&@o  
t = n.*dt;   /'O8RUjN  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. XX;4A  
w=2*pi*n./T; ^?69|,  
g1=-i*ww./2; $EMOz=)I#  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; adON&<  
g3=-i*ww./2; ?mQ^"
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P1=0; G4&s_M$
 
P2=0; ZO}Og&%  
P3=1; _`$LdqgE  
P=0; q!c(~UVw  
for m1=1:M1                 0bNvmZ$  
p=0.032*m1;                %input amplitude 6Z/`p~e  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 ]`E+HLEQ'  
s1=s10; Nz{dnV{&x;  
s20=0.*s10;                %input in waveguide 2 OI R5QH  
s30=0.*s10;                %input in waveguide 3 ;?6vKpj;  
s2=s20; WKf<% E$  
s3=s30; #F*|@  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   K,f:X g!:  
%energy in waveguide 1 mgxIxusR  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   w7nt $L5  
%energy in waveguide 2 Zw]`z*,yRA  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   @0`A!5h?u  
%energy in waveguide 3 e_BG%+;G,  
for m3 = 1:1:M3                                    % Start space evolution $o"
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   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS ^}3^|
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   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; ,m=F H?5  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; *2X6;~  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform 8$Q`wRt(%  
   sca2 = fftshift(fft(s2)); HN47/]"*  
   sca3 = fftshift(fft(s3)); WSThhI  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   x_PO;  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); Z1Qz LvWs  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); ^<]'?4m]  
   s3 = ifft(fftshift(sc3)); e r" w{  
   s2 = ifft(fftshift(sc2));                       % Return to physical space (su,=Z  
   s1 = ifft(fftshift(sc1)); y48]|%73  
end Nk~}aj  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); J5@08bZm  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); )W@ug,y  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));  Xo^8o0xi  
   P1=[P1 p1/p10]; +^I0>\  
   P2=[P2 p2/p10]; 6K2e]r  
   P3=[P3 p3/p10]; p_r`"  
   P=[P p*p]; 4Z)4WGp!  
end 3WV(Ok  
figure(1) |%_C$s%  
plot(P,P1, P,P2, P,P3); {N(qS'N  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~