[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 G1K5J`"*  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of `f,SY  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of $vnshU8/v  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear h|$.`$  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 8_US.52V  
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%fid=fopen('e21.dat','w'); 8 ;y N  
N = 128;                       % Number of Fourier modes (Time domain sampling points) NRe{0U}nO  
M1 =3000;              % Total number of space steps |QHDg(   
J =100;                % Steps between output of space R#eY@N}\  
T =10;                  % length of time windows:T*T0 w[~O@:`]<o  
T0=0.1;                 % input pulse width O~N0JK_>  
MN1=0;                 % initial value for the space output location R#.FfWTZ  
dt = T/N;                      % time step ?xu5/r<  
n = [-N/2:1:N/2-1]';           % Index qn}4PVn4  
t = n.*dt;   W-ErzX  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 ;N6Euiz  
u20=u10.*0.0;                  % input to waveguide 2 vY&[=2=  
u1=u10; u2=u20;                 2fM*6CaS  
U1 = u1;   'gHa3:US  
U2 = u2;                       % Compute initial condition; save it in U 4loG$l+a1  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1.  3=@94i  
w=2*pi*n./T; 59A@~;.F  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T pJ!:mt  
L=4;                           % length of evoluation to compare with S. Trillo's paper p0U4#dD6  
dz=L/M1;                       % space step, make sure nonlinear<0.05 NI_.wB{  
for m1 = 1:1:M1                                    % Start space evolution Ea#wtow|-  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS \_;zm+ <{  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; ?s/]k#H  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform %;$zR}  
   ca2 = fftshift(fft(u2)); %
g1:yx  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation K;Qlg{v  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   lArYlR}  
   u2 = ifft(fftshift(c2));                        % Return to physical space T{-<G13  
   u1 = ifft(fftshift(c1)); Goa0OC,  
if rem(m1,J) == 0                                 % Save output every J steps. ]f#1G$  
    U1 = [U1 u1];                                  % put solutions in U array W'WZ@!!  
    U2=[U2 u2]; wN'Q\l+  
    MN1=[MN1 m1]; N]f"+  
    z1=dz*MN1';                                    % output location [9dW9[Z+!  
  end k`ulDQu
 
end |zhVl  
hg=abs(U1').*abs(U1');                             % for data write to excel w9h`8
pt  
ha=[z1 hg];                                        % for data write to excel `IL''eJug_  
t1=[0 t']; :%-xiv  
hh=[t1' ha'];                                      % for data write to excel file 3~v'Ev  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format *F7ksLH|q  
figure(1) l'TM^B)`c  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn y qDE|DIez  
figure(2) sTeW4Hnp  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn kH:! 7L_=  
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非线性超快脉冲耦合的数值方法的Matlab程序 ^UTQcm  
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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。   fy&vo~4i;  
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 X.TsOoy  
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%  This Matlab script file solves the nonlinear Schrodinger equations >HMuh)  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of *Xm$w  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear !##OQ  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 3zi(|B[,?  
Y)="of  
C=1;                           DPIIE2X  
M1=120,                       % integer for amplitude HAa$pGb  
M3=5000;                      % integer for length of coupler ~m4{GzB  
N = 512;                      % Number of Fourier modes (Time domain sampling points) c!#DD;<Q  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. q=Cc2|Ve  
T =40;                        % length of time:T*T0. m^hi}Am1  
dt = T/N;                     % time step =^  
n = [-N/2:1:N/2-1]';          % Index ,|RS]I>X  
t = n.*dt;   #{97<sU\  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. ?&v+-4%4PI  
w=2*pi*n./T; o\ss  
g1=-i*ww./2; zl~`>  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; (vL-Z[M!  
g3=-i*ww./2; wCT. (d_  
P1=0; aH@GhI
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P2=0; X'BFR]cm  
P3=1; .8[Uk^q  
P=0; ;Ohabbj*  
for m1=1:M1                 c*iZ6j"iI  
p=0.032*m1;                %input amplitude e
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s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 C9+`sFau@  
s1=s10; )<Cf,R  
s20=0.*s10;                %input in waveguide 2 eRV4XB:  
s30=0.*s10;                %input in waveguide 3 JQSp2b@'H  
s2=s20; aB@D-Y"HO  
s3=s30; k;aV4 0N9  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   aE]/w1a  
%energy in waveguide 1 !2]eVO  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   jV:Krk6T<  
%energy in waveguide 2 + Xc s<+b  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   5!GL"  
%energy in waveguide 3 urM=l5Sx  
for m3 = 1:1:M3                                    % Start space evolution 7-p9IFcA  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS % Q|
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   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; PWU8 9YXp  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; Q:U^):~  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform 53vnON#{*  
   sca2 = fftshift(fft(s2)); 70sb{)  
   sca3 = fftshift(fft(s3)); Rwu y!F  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   *CsRO  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); xV]eEOiL
M  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); AC`4n|,zJ;  
   s3 = ifft(fftshift(sc3)); os<YfMM<:/  
   s2 = ifft(fftshift(sc2));                       % Return to physical space I.V?O}   
   s1 = ifft(fftshift(sc1)); QOb+6qy:3  
end SEf:u  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); *RPdU.  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); fV}:eEo|Y  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); H)
;O.m  
   P1=[P1 p1/p10]; dS+/G9X^  
   P2=[P2 p2/p10]; ;;A8*\*$  
   P3=[P3 p3/p10]; P~"e=NL5  
   P=[P p*p]; .Oh4b5  
end pi/Jto25z  
figure(1) -o\o{?t,  
plot(P,P1, P,P2, P,P3); CJn{tP  
c,wYXnJ_t  
转自：http://blog.163.com/opto_wang/

谢谢哈~！~