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tianmen 2011-06-12 18:33

求解光孤子或超短脉冲耦合方程的Matlab程序

计算脉冲在非线性耦合器中演化的Matlab 程序 $ KAOJc4<  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of 3mCf>qj73  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of q2U8]V U)  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear = VFPZ  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ] l@Mo7|w  
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%fid=fopen('e21.dat','w'); dPx{9Y<FzU  
N = 128;                       % Number of Fourier modes (Time domain sampling points) +T,Yf/^Fn  
M1 =3000;              % Total number of space steps x<lY&KQ0  
J =100;                % Steps between output of space EsK.g/d  
T =10;                  % length of time windows:T*T0 O dWZYWj  
T0=0.1;                 % input pulse width fk)5TPc^  
MN1=0;                 % initial value for the space output location KN\*|)  
dt = T/N;                      % time step 9cMQ51k)E  
n = [-N/2:1:N/2-1]';           % Index f?[0I\V[$  
t = n.*dt;   8gK  <xp  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 6_vhBYLf  
u20=u10.*0.0;                  % input to waveguide 2 ynQ+yW74Z  
u1=u10; u2=u20;                 y2=`NG=  
U1 = u1;   a|5^4 J \%  
U2 = u2;                       % Compute initial condition; save it in U u}~jNV  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. xoQ;fVNp  
w=2*pi*n./T; n5e1k y*9w  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T 'Io2",~ M  
L=4;                           % length of evoluation to compare with S. Trillo's paper A6faRi703  
dz=L/M1;                       % space step, make sure nonlinear<0.05 R{3vPG  
for m1 = 1:1:M1                                    % Start space evolution vk>EFm8l  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS  =o? Q0  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; 5k]xi)%  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform >r8$vQGj  
   ca2 = fftshift(fft(u2)); S`?L\R.:  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation m_;<7W&p]  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   CG397Y^  
   u2 = ifft(fftshift(c2));                        % Return to physical space YZllfw$9  
   u1 = ifft(fftshift(c1)); \fjr`t]  
if rem(m1,J) == 0                                 % Save output every J steps. 7sglqf>  
    U1 = [U1 u1];                                  % put solutions in U array y'#i'0eeL  
    U2=[U2 u2]; 3l?-H|T  
    MN1=[MN1 m1]; +@5@`"Jry  
    z1=dz*MN1';                                    % output location h F4gz*Q  
  end |w)S &+  
end |(Q !$  
hg=abs(U1').*abs(U1');                             % for data write to excel \'[C_+;X  
ha=[z1 hg];                                        % for data write to excel c'Mi9,q  
t1=[0 t']; 'v?"TZ  
hh=[t1' ha'];                                      % for data write to excel file 1nAAs;`'  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format \7elqX`.yY  
figure(1) 9&VfbrBM  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn ^PrG5|,s  
figure(2) YVT\@+C'  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn 1.6Y=Mh=i[  
9@{=2 k  
非线性超快脉冲耦合的数值方法的Matlab程序 HgfeSH  
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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。   9u%S<F"  
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 Vh o3I[C  
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%  This Matlab script file solves the nonlinear Schrodinger equations iF!r}fUU6  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of \Ng|bWR>LQ  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear `j1(GQt  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ?VaAVxd29  
F?EAIL  
C=1;                           n)6mfoe  
M1=120,                       % integer for amplitude trAIh}Dj  
M3=5000;                      % integer for length of coupler 1,pg7L8H  
N = 512;                      % Number of Fourier modes (Time domain sampling points) 4qe!+!#$  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. Zwm2T3@e  
T =40;                        % length of time:T*T0. BH+@!H3 hf  
dt = T/N;                     % time step |',$5!:0O  
n = [-N/2:1:N/2-1]';          % Index 8<X,6  
t = n.*dt;   QT[yw6Z  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. ?Gr2@,jlD  
w=2*pi*n./T; PY{])z3N  
g1=-i*ww./2; T#:n7$M|?A  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; x+B7r& #:  
g3=-i*ww./2;  jcVK4jW  
P1=0; G;k#06  
P2=0; 8"5^mj  
P3=1; `zmj iC  
P=0; `:y {  
for m1=1:M1                 ER4j=O#  
p=0.032*m1;                %input amplitude b0n " J`  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 mO|YX/>  
s1=s10; fRT4,;  
s20=0.*s10;                %input in waveguide 2 KM o]J1o  
s30=0.*s10;                %input in waveguide 3 g[ dI%  
s2=s20; B!X;T9^d  
s3=s30; }}4u>1,~  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   o1B8_$aYgc  
%energy in waveguide 1 =MCQNyf+  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   u hJnDo  
%energy in waveguide 2 YKtF)N;m]  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   K[/sVaPZ  
%energy in waveguide 3 0S}ogU[k  
for m3 = 1:1:M3                                    % Start space evolution @}[yC['  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS `of` uB  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; G:k]tZ*`  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; (s?Rbd  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform c"H59 jE  
   sca2 = fftshift(fft(s2)); 7%g8&d  
   sca3 = fftshift(fft(s3)); 0%f}w0]:  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   sH_5.+,`  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); $wq[W,'#L  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); %D9,Femt  
   s3 = ifft(fftshift(sc3)); Sh(Ws2b7  
   s2 = ifft(fftshift(sc2));                       % Return to physical space LLlt9(^d  
   s1 = ifft(fftshift(sc1)); _RI!Z   
end A\IQM^i  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); r iuG,$EX  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); Rx\.x? &  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); l%^VBv> 2  
   P1=[P1 p1/p10]; ~,jBm^4  
   P2=[P2 p2/p10]; (^)" qs B  
   P3=[P3 p3/p10];  +?I 1Og  
   P=[P p*p]; oI2YJ2?Je8  
end VP\'p1a  
figure(1) S>y(3E]I  
plot(P,P1, P,P2, P,P3); AXmW7/Sj"  
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转自:http://blog.163.com/opto_wang/
ciomplj 2014-06-22 22:57
谢谢哈~!~
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