[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 nMDxH$O  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of U~{du;\  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of { pu85'DV  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear =U[3PC-N@  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 c,so`I3rI  
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%fid=fopen('e21.dat','w'); UT~a&u  
N = 128;                       % Number of Fourier modes (Time domain sampling points) Qjx?ri//  
M1 =3000;              % Total number of space steps YDC mI@  
J =100;                % Steps between output of space wIkN9 f  
T =10;                  % length of time windows:T*T0 yJuQ8+vgR}  
T0=0.1;                 % input pulse width _0+0#! J!  
MN1=0;                 % initial value for the space output location 0!
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dt = T/N;                      % time step b[z]CP  
n = [-N/2:1:N/2-1]';           % Index f)]%.>  
t = n.*dt;   h%WE=\,Qp  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 PcB_oG g  
u20=u10.*0.0;                  % input to waveguide 2 01!s"wjf  
u1=u10; u2=u20;                 -(#I3h;I  
U1 = u1;   fQrhsuCrC  
U2 = u2;                       % Compute initial condition; save it in U 'c\iK
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ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. YV=QF J'  
w=2*pi*n./T; dd2[yKC`  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T =U|N=/y#hJ  
L=4;                           % length of evoluation to compare with S. Trillo's paper !=;XBd-  
dz=L/M1;                       % space step, make sure nonlinear<0.05 k6`6Mjbc  
for m1 = 1:1:M1                                    % Start space evolution TJE\A)|>g  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS XC{eX&,2x  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; zf3v5Hk  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform 5cx#SD&5/  
   ca2 = fftshift(fft(u2)); V"cKJ;s  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation IwGqf.!.>  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   A^Kbsc  
   u2 = ifft(fftshift(c2));                        % Return to physical space O1')nYF7  
   u1 = ifft(fftshift(c1)); TW !&p"Us+  
if rem(m1,J) == 0                                 % Save output every J steps. "#mBcQ;QLV  
    U1 = [U1 u1];                                  % put solutions in U array k X {0y  
    U2=[U2 u2]; :JlP[I  
    MN1=[MN1 m1]; c1X1+b,  
    z1=dz*MN1';                                    % output location u!1{Vt87  
  end j*xV!DqC  
end bINvqv0v  
hg=abs(U1').*abs(U1');                             % for data write to excel =4d (b ;  
ha=[z1 hg];                                        % for data write to excel hsu{eyp  
t1=[0 t']; oyo(1>  
hh=[t1' ha'];                                      % for data write to excel file J>d.dq>r  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format (a9d
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figure(1) j,]Y$B  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn 1CLL%\V  
figure(2) fM^[7;]7e  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn /VG2.:  
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非线性超快脉冲耦合的数值方法的Matlab程序 q -8t'7  
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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。   A!^q J#  
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 .k,YlFvj  
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%  This Matlab script file solves the nonlinear Schrodinger equations 2wF8 P)  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of uwlr9nB  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear  }-~l!  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 dH
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C=1;                           -*.-9B~u  
M1=120,                       % integer for amplitude 4@xE8`+bG  
M3=5000;                      % integer for length of coupler n]he-NHP  
N = 512;                      % Number of Fourier modes (Time domain sampling points) eYx Kp!f  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. [$[:"N_  
T =40;                        % length of time:T*T0. +{
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dt = T/N;                     % time step 7g_]mG[6  
n = [-N/2:1:N/2-1]';          % Index I!^O)4QRx  
t = n.*dt;   3Gkv4,w<  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. b+Br=Fv"T  
w=2*pi*n./T; qWb+r  
g1=-i*ww./2; Agrk|wPK  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; *2jK#9"MP  
g3=-i*ww./2; w6j/ Dq!  
P1=0; $MJm*6h  
P2=0; $ `7^+8vHV  
P3=1; 7g3>jh  
P=0; /hO1QT}xd  
for m1=1:M1                 GgKEP,O  
p=0.032*m1;                %input amplitude 0wS+++n$5  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 .9.2Be  
s1=s10; yr,=.?C-  
s20=0.*s10;                %input in waveguide 2 Sfdu`MQR  
s30=0.*s10;                %input in waveguide 3 R LD`O9#j  
s2=s20; }V\N16f  
s3=s30; }l=xiAF  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));  
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%energy in waveguide 1 R4-~jgzx  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   m)oJFF  
%energy in waveguide 2 ={u0_j W  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   ge8/``=  
%energy in waveguide 3 -44&#l^}_u  
for m3 = 1:1:M3                                    % Start space evolution #KO,~]k5|e  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS ^aW Z!gi  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; CD8}I85K  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; t%8d-+$  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform tor!Dl@Mo  
   sca2 = fftshift(fft(s2));  Tgl}  
   sca3 = fftshift(fft(s3)); Q$fmD  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   H*r
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   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); 7VP32Eh[  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); [<KM?\"1<  
   s3 = ifft(fftshift(sc3)); 9+pmS#>_  
   s2 = ifft(fftshift(sc2));                       % Return to physical space Si~vDQ7"  
   s1 = ifft(fftshift(sc1)); QPq7R  
end 3)RsLI9  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); '}9JCJ  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); &y#r;L<9  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); KI+VXH}Y5{  
   P1=[P1 p1/p10]; F;>!&[h}G  
   P2=[P2 p2/p10]; 9VbOQ{8  
   P3=[P3 p3/p10]; Sfr&p>{,  
   P=[P p*p]; Pfs;0}h5  
end wiBVuj#  
figure(1) nWHa.H#  
plot(P,P1, P,P2, P,P3); T'~!9Q  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~