[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 */n)_  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of jl=<Q.Mm7  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of qDO4&NO  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 3Bz0B a  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 :xfD>K  
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%fid=fopen('e21.dat','w'); 0sRby!  
N = 128;                       % Number of Fourier modes (Time domain sampling points) 8ltHR]v  
M1 =3000;              % Total number of space steps *lg1iP{]  
J =100;                % Steps between output of space
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T =10;                  % length of time windows:T*T0 %,GY&hTw  
T0=0.1;                 % input pulse width &2{h]V6  
MN1=0;                 % initial value for the space output location nv(Pwb3B  
dt = T/N;                      % time step
k=O2s'F`  
n = [-N/2:1:N/2-1]';           % Index sD.bBz  
t = n.*dt;   Ay!=Yk^~  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 vt[4"eU  
u20=u10.*0.0;                  % input to waveguide 2 _`L,}=um'  
u1=u10; u2=u20;                 uYS?# g  
U1 = u1;   UHz*
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U2 = u2;                       % Compute initial condition; save it in U EW1L!3K  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. 3KfZI&g  
w=2*pi*n./T; abUn{X+f~  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T 7Rj!vj/  
L=4;                           % length of evoluation to compare with S. Trillo's paper 2s;/*<WM  
dz=L/M1;                       % space step, make sure nonlinear<0.05 BUv;BzyV  
for m1 = 1:1:M1                                    % Start space evolution L*9^-,  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS %L{H_;z  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; dZRz'd  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform *J?QXsg  
   ca2 = fftshift(fft(u2)); Lm9y!>1"O  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation *~M=2Fj;i  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   BN@*CG  
   u2 = ifft(fftshift(c2));                        % Return to physical space >\8Bu#&s4  
   u1 = ifft(fftshift(c1)); i)\`"&.j>N  
if rem(m1,J) == 0                                 % Save output every J steps. 0^|)[2m!  
    U1 = [U1 u1];                                  % put solutions in U array -c%GlpZw  
    U2=[U2 u2]; LS4c|Dv  
    MN1=[MN1 m1]; bc5+}&W  
    z1=dz*MN1';                                    % output location ,v$gQU2  
  end \*!?\Ko`W  
end yEtSyb~GK  
hg=abs(U1').*abs(U1');                             % for data write to excel JTpKF_Za<  
ha=[z1 hg];                                        % for data write to excel KSuP'.l  
t1=[0 t']; ,m!j2H}8  
hh=[t1' ha'];                                      % for data write to excel file &7T0nB/)  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format ;or(:Yoc-  
figure(1) {LY$  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn ? 8S0  
figure(2) N6$pOQ  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn 6CLrP} u  
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非线性超快脉冲耦合的数值方法的Matlab程序 vAq`*]W+  
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在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。  
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Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 Mvrc[s+o  
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%  This Matlab script file solves the nonlinear Schrodinger equations u1ggLH!U  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of [U]*OQH`e  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear wQ*vcbQX*  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 Jj|HeZ1C f  
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C=1;                           9cWl/7;zXO  
M1=120,                       % integer for amplitude z*YkD"]B  
M3=5000;                      % integer for length of coupler p<'#f,o  
N = 512;                      % Number of Fourier modes (Time domain sampling points) kG &.|  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. PLKp<kg  
T =40;                        % length of time:T*T0. wS <d8gw  
dt = T/N;                     % time step '[~NRKQJ  
n = [-N/2:1:N/2-1]';          % Index Bra>C  
t = n.*dt;   ^u:7U4  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. 782be-n  
w=2*pi*n./T; -
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g1=-i*ww./2; /0d_{Y+9  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; J8J~$DU\Gv  
g3=-i*ww./2; V? w;YTg  
P1=0; 5 1@V""m  
P2=0; *&+e2itm
p  
P3=1; ]=2Ba<)m  
P=0; %8
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for m1=1:M1                 {%9)l,  
p=0.032*m1;                %input amplitude \^iJv~d  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 ~+A?!f;-J  
s1=s10; x %L2eXL  
s20=0.*s10;                %input in waveguide 2 xpx=t71Hq  
s30=0.*s10;                %input in waveguide 3 Z2(z,pK  
s2=s20; 7UejK r  
s3=s30; 0_}OKn)J  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   $}jp=?,t  
%energy in waveguide 1 8t!(!<iF0  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   4v33{sp  
%energy in waveguide 2 >t)vQ&:;u  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   f/~"_O%  
%energy in waveguide 3 *j?tcxq
 
for m3 = 1:1:M3                                    % Start space evolution ,u#uk7V  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS <MB]W
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   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
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   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; 2xhwi.u  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform BDNn~aU#m  
   sca2 = fftshift(fft(s2)); z~L''X7g  
   sca3 = fftshift(fft(s3)); sD7Qt  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   9 #TzW9  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); MGfDxHg]  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); -GD_xk  
   s3 = ifft(fftshift(sc3)); %2f``48#  
   s2 = ifft(fftshift(sc2));                       % Return to physical space n`2d  
   s1 = ifft(fftshift(sc1)); d=o|)kV  
end jA$g0>  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); 9JBPE  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); ;o8C(5xE|  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); 2qo=ud  
   P1=[P1 p1/p10]; K}tl,MMU  
   P2=[P2 p2/p10]; &M,a+|yuY  
   P3=[P3 p3/p10]; 1"?KQU  
   P=[P p*p]; Y;8Ys&/t  
end "=@b>d6U+  
figure(1) l~;H~h!h/  
plot(P,P1, P,P2, P,P3); PUV)w\!&is  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~