[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 ?Mp1~{8  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of R1-k3;v^  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of /i)Hb`(S  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear I@l>w._.  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 T#O??3/%$1  
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%fid=fopen('e21.dat','w'); g8'DoHJ*  
N = 128;                       % Number of Fourier modes (Time domain sampling points) jFerYv&K~  
M1 =3000;              % Total number of space steps m/`IGT5J  
J =100;                % Steps between output of space r Db>&s3  
T =10;                  % length of time windows:T*T0 (H?ZSeWx  
T0=0.1;                 % input pulse width IB
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MN1=0;                 % initial value for the space output location OSzjK7:  
dt = T/N;                      % time step _B,_4}  
n = [-N/2:1:N/2-1]';           % Index E-1"+p  
t = n.*dt;   (}:C+p 'I  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 X;!D};;M  
u20=u10.*0.0;                  % input to waveguide 2 &D#+6M&LK{  
u1=u10; u2=u20;                 Z v0C@r  
U1 = u1;   dZGbC9  
U2 = u2;                       % Compute initial condition; save it in U =w<v3wWN4  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. /9Ilo\M
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w=2*pi*n./T; k:#6^!b1  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T Icp0A\L@  
L=4;                           % length of evoluation to compare with S. Trillo's paper y7<&vIEC  
dz=L/M1;                       % space step, make sure nonlinear<0.05 Pj7gGf6v  
for m1 = 1:1:M1                                    % Start space evolution 0p fnV%  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS v.W{x?5  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; ["3d
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   ca1 = fftshift(fft(u1));                        % Take Fourier transform ad!(z[F'Y  
   ca2 = fftshift(fft(u2)); w5]l1}rl  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation NE"jh_m-
 
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   oj}"H>tTp  
   u2 = ifft(fftshift(c2));                        % Return to physical space wUi(3g|A  
   u1 = ifft(fftshift(c1)); GL
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if rem(m1,J) == 0                                 % Save output every J steps. rdj@u47  
    U1 = [U1 u1];                                  % put solutions in U array bO49GEUT _  
    U2=[U2 u2]; #/j={*-  
    MN1=[MN1 m1]; 7SI)1_%G  
    z1=dz*MN1';                                    % output location +zWrLf_Rc  
  end ]2+g&ox4'  
end >kdM:MK  
hg=abs(U1').*abs(U1');                             % for data write to excel R V!o4"\]  
ha=[z1 hg];                                        % for data write to excel !W1eUY  
t1=[0 t']; UqX1E  
hh=[t1' ha'];                                      % for data write to excel file SZVV40w  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format xKp0r1}  
figure(1) gZ(O)uzv  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn M@?"t_e1  
figure(2) 0^]t"z5f0  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn 015Owi  
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非线性超快脉冲耦合的数值方法的Matlab程序 ;mO,3dV  
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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。   qmmv7==  
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 |*Ot/TvG  
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%  This Matlab script file solves the nonlinear Schrodinger equations $(>f8)Uku(  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of PI7IBI  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear oA3d^%(c  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 X9'xn 0n;  
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C=1;                           g'G8 3F  
M1=120,                       % integer for amplitude 'TEyP56  
M3=5000;                      % integer for length of coupler @;9()ad  
N = 512;                      % Number of Fourier modes (Time domain sampling points) *1;23BiH-  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. 0|2%# E  
T =40;                        % length of time:T*T0. jA2ofC  
dt = T/N;                     % time step ci7~KewJ*  
n = [-N/2:1:N/2-1]';          % Index \ j]~>9  
t = n.*dt;   w67xl  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. *4#on>  
w=2*pi*n./T; 3%NE/lw1  
g1=-i*ww./2; onzA7Gre  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; >5i?JUZ  
g3=-i*ww./2; }W "(cYN_  
P1=0; *?Wtj  
P2=0; hZ#\t  
P3=1; GUCM4jVT^  
P=0; nx :)k-p_[  
for m1=1:M1                 A;%kl`~iyz  
p=0.032*m1;                %input amplitude -HTL5  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 -q(:%;  
s1=s10; luF#OPC  
s20=0.*s10;                %input in waveguide 2 s<{GpWT8  
s30=0.*s10;                %input in waveguide 3 wU0K3qZL
 
s2=s20; s1@@o#r  
s3=s30; 2$ VTu+  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   f)tc4iV  
%energy in waveguide 1 ,'-?:`hP'  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   K|~AA"I;  
%energy in waveguide 2 g!`BXmW  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   !'PlDGD  
%energy in waveguide 3 ~mcZUiP9  
for m3 = 1:1:M3                                    % Start space evolution ]1Qi=2'  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS sVD([`Nmc  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; q+J0}y{#8)  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; 'WnpwY  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform *C/KM;&  
   sca2 = fftshift(fft(s2)); g!5#,kJM  
   sca3 = fftshift(fft(s3)); ULbP_y>(Y  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   O &\<FT5  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); 7`+UB>8  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); .ftUhg  
   s3 = ifft(fftshift(sc3)); /^QFqM;  
   s2 = ifft(fftshift(sc2));                       % Return to physical space \"bLE0~  
   s1 = ifft(fftshift(sc1)); eb7UoZw  
end q]?+By-0  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
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   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); s|p(KWo2U  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); I9:%@g]uYw  
   P1=[P1 p1/p10]; lzI/\%  
   P2=[P2 p2/p10]; L.Vq1RU\"  
   P3=[P3 p3/p10]; .n=xbx:=  
   P=[P p*p]; R_~F6O^EO  
end Z0z)  
figure(1) SOYDp;j  
plot(P,P1, P,P2, P,P3); 'iDu0LX  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~