[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 Mvh_>-i  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of e.GzGX  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of +J4t0x  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear j&pgq2Kl  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 mN*P2*  
ybG)=0  
%fid=fopen('e21.dat','w'); rh_({rvQ  
N = 128;                       % Number of Fourier modes (Time domain sampling points)
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M1 =3000;              % Total number of space steps >`uSNY"tO  
J =100;                % Steps between output of space 8#Z5-",iw  
T =10;                  % length of time windows:T*T0 Dn3~8  
T0=0.1;                 % input pulse width N [
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MN1=0;                 % initial value for the space output location M5V1j(URE  
dt = T/N;                      % time step %ze1ZWO{  
n = [-N/2:1:N/2-1]';           % Index |@HdTGD  
t = n.*dt;   aVYUk7_<  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 <X |h*  
u20=u10.*0.0;                  % input to waveguide 2 F%d"gF
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u1=u10; u2=u20;                 #c>MUC(?s:  
U1 = u1;   }BrE|'.j'  
U2 = u2;                       % Compute initial condition; save it in U <.B s`P  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. 20qVzXi  
w=2*pi*n./T; o%%fO  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T w0!,1 Ry  
L=4;                           % length of evoluation to compare with S. Trillo's paper S\ZAcz4  
dz=L/M1;                       % space step, make sure nonlinear<0.05 SA1/U  
for m1 = 1:1:M1                                    % Start space evolution ,
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   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS =R.9"7~2x  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; VW
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   ca1 = fftshift(fft(u1));                        % Take Fourier transform DV\ei")  
   ca2 = fftshift(fft(u2)); eLny-.i,7  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation 2&fwr>!$  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   tl5IwrF6;  
   u2 = ifft(fftshift(c2));                        % Return to physical space 7]j-zv  
   u1 = ifft(fftshift(c1)); h$k3MhYDes  
if rem(m1,J) == 0                                 % Save output every J steps. 7nz
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    U1 = [U1 u1];                                  % put solutions in U array m[j3s=Gr  
    U2=[U2 u2]; A*~1Uz\t  
    MN1=[MN1 m1]; i)i)3K2  
    z1=dz*MN1';                                    % output location &>l8SlC?  
  end B?yt%f1  
end 77d`N  
hg=abs(U1').*abs(U1');                             % for data write to excel Ib8i#DV  
ha=[z1 hg];                                        % for data write to excel EiN)TB^]  
t1=[0 t']; <WJ0St  
hh=[t1' ha'];                                      % for data write to excel file rcmAVl:$>  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format nln6:^w  
figure(1) ';,Bn9rv  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn +~Ay h[V  
figure(2) _vV&4>  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn vCSB8R  
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非线性超快脉冲耦合的数值方法的Matlab程序 y9li<u<PF  
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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。   KBR0p&MN  
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 |u r~s$8y-  
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%  This Matlab script file solves the nonlinear Schrodinger equations >Ryss@o  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of N"RYM~c7  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear LIC~Kehi  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 j& iL5J;  
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C=1;                           Ygi1"X}  
M1=120,                       % integer for amplitude ]}7rWs[|1  
M3=5000;                      % integer for length of coupler gQ=POJ=G  
N = 512;                      % Number of Fourier modes (Time domain sampling points) 36x:(-GFq  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. 4)+IO;  
T =40;                        % length of time:T*T0. ]Y&)98  
dt = T/N;                     % time step #7-@k-<|  
n = [-N/2:1:N/2-1]';          % Index zk'K.! `^  
t = n.*dt;   2{B(j&{  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. C%
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w=2*pi*n./T; 2HGD{;6>v{  
g1=-i*ww./2; rk,1am:cg  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; )YMlFzYr  
g3=-i*ww./2; w;@25= |  
P1=0; rgdQR^!l6  
P2=0; E<CxKY9  
P3=1; xGEmrE<;  
P=0; ;xO=Yhc+  
for m1=1:M1                 W0MnGzZ  
p=0.032*m1;                %input amplitude )d(0Y<e@  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 ).}k6v[4)  
s1=s10; Ivt} o_b*  
s20=0.*s10;                %input in waveguide 2 4:Xj-l^D  
s30=0.*s10;                %input in waveguide 3 +'['HQ)  
s2=s20; Cld<D5\|f+  
s3=s30; [j}7@Mr`\  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   |\%F(d330  
%energy in waveguide 1 AuDR |;i  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   .D,?u"fk|  
%energy in waveguide 2 x, Vh  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   HKiVEg  
%energy in waveguide 3 _TOi [GT  
for m3 = 1:1:M3                                    % Start space evolution 5+bFy.UW  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS ?S@R~y0K  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; S -
6"f/  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; <F)w=_%&  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform )y`TymM[F  
   sca2 = fftshift(fft(s2)); dT]L-uRZgy  
   sca3 = fftshift(fft(s3)); +t>*l>[  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   <,@H;|mZ  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); <DXmZ1  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); KIKq9*  
   s3 = ifft(fftshift(sc3)); 4aN+}TkH@G  
   s2 = ifft(fftshift(sc2));                       % Return to physical space 0n*rs=\VG  
   s1 = ifft(fftshift(sc1)); kQw
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end ?UZ$bz  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); 7~ *;=,mw  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); r}R^<y@I  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); E#<7\p>  
   P1=[P1 p1/p10]; J&63Z  
   P2=[P2 p2/p10]; U+.PuC[3  
   P3=[P3 p3/p10]; W1?!iE~tO  
   P=[P p*p]; gHvW e  
end np-T&Pz2  
figure(1) Na. nA  
plot(P,P1, P,P2, P,P3); T/wM(pr'   
v~V;+S=gz  
转自：http://blog.163.com/opto_wang/

谢谢哈~！~