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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 W CoF{ *  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of W'V@  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of 7y;u} 1  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear g#Mv&tU  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 5=m3J !?  
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%fid=fopen('e21.dat','w');  *0-v!\{  
N = 128;                       % Number of Fourier modes (Time domain sampling points) PC[cHgSYU  
M1 =3000;              % Total number of space steps IyT ?-R  
J =100;                % Steps between output of space <g*.p@o  
T =10;                  % length of time windows:T*T0 _l<| 1nH  
T0=0.1;                 % input pulse width 0w'|d@*wV  
MN1=0;                 % initial value for the space output location o|+E+l9\  
dt = T/N;                      % time step ;*.(.  
n = [-N/2:1:N/2-1]';           % Index %P(;8sS  
t = n.*dt;   -}<d(c  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 '1]+8E `Z  
u20=u10.*0.0;                  % input to waveguide 2  :4{Qh  
u1=u10; u2=u20;                 xHm/^C&px  
U1 = u1;   5pB^Y MP  
U2 = u2;                       % Compute initial condition; save it in U ]u;GNz}?  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. w/O<.8+  
w=2*pi*n./T; m,=)qex  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T @c0n2 Xcr  
L=4;                           % length of evoluation to compare with S. Trillo's paper a6k(9ZF  
dz=L/M1;                       % space step, make sure nonlinear<0.05 6GY32\Ac  
for m1 = 1:1:M1                                    % Start space evolution ,zG<7~m  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS D9,e3.?p  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; K q/~T7Ru  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform 'xQna+%h  
   ca2 = fftshift(fft(u2)); R04.K !  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation 'N*!>mZ<  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   Is<x31R  
   u2 = ifft(fftshift(c2));                        % Return to physical space ;x,+*%  
   u1 = ifft(fftshift(c1)); 0GS{F8f~,  
if rem(m1,J) == 0                                 % Save output every J steps. g)X7FxS,z  
    U1 = [U1 u1];                                  % put solutions in U array {3.*7gnY\L  
    U2=[U2 u2]; y#&$ f  
    MN1=[MN1 m1]; mMV2h|W   
    z1=dz*MN1';                                    % output location 7Nd*,DV_  
  end ]NbX`'  
end E]\D>[0O  
hg=abs(U1').*abs(U1');                             % for data write to excel 4}+xeGA$  
ha=[z1 hg];                                        % for data write to excel `i=JjgG@  
t1=[0 t']; Z+r%_|kZ  
hh=[t1' ha'];                                      % for data write to excel file bd,Uz% o_  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format ht2 f-EKf{  
figure(1) C2CYIo k$&  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn %)BwE  
figure(2) mXQl;  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn A*rZQh b[  
S@9w'upd  
非线性超快脉冲耦合的数值方法的Matlab程序 KbXbT  
@bc[ eas  
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。   Sjw2 j#Q  
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 8mk}nex  
S&5Q~}{,  
 AQB1gzE  
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%  This Matlab script file solves the nonlinear Schrodinger equations P#w}3^  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of @YEw^J~  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear /_ $~rW  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 o G (0i  
J"/ JRn  
C=1;                           #DQX<:u  
M1=120,                       % integer for amplitude 17WNJ  
M3=5000;                      % integer for length of coupler E}]I%fi  
N = 512;                      % Number of Fourier modes (Time domain sampling points) I~d#p ]>  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. Ko1AaX(I'+  
T =40;                        % length of time:T*T0. 8FB\0LA!g  
dt = T/N;                     % time step kyy0&L  
n = [-N/2:1:N/2-1]';          % Index >Y,/dyT Zm  
t = n.*dt;   _L?v6MTj  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. C<r(-qO{5  
w=2*pi*n./T; ` %FIgE^  
g1=-i*ww./2; xIS\4]F?r  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; >W>##vK  
g3=-i*ww./2; /d{glOk  
P1=0; T r SN00  
P2=0; 70'} f  
P3=1; q,<n,0)K  
P=0; zWF 5m )-  
for m1=1:M1                 AeNyZ[40T  
p=0.032*m1;                %input amplitude WpXODkQL  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 2q`)GCES~  
s1=s10; bHhC56[M  
s20=0.*s10;                %input in waveguide 2 B0-4 ZT  
s30=0.*s10;                %input in waveguide 3 o,*folL  
s2=s20; 0t5Q9#RY  
s3=s30; RnMBGxa  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   ~bQFk?ZN+  
%energy in waveguide 1 <bEN8b  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   g0^~J2sDd  
%energy in waveguide 2 *\=2KIF'  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   u~' m7  
%energy in waveguide 3 XX]5T`D  
for m3 = 1:1:M3                                    % Start space evolution M[:O(  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS YH /S2D  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; AzHIp^  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; YWt"|  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform el <<D  
   sca2 = fftshift(fft(s2)); /2g)Z!&+L  
   sca3 = fftshift(fft(s3)); [<#<:h &\  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   B6tcKh9d,  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); E[)7tr  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); qT4I Y$h  
   s3 = ifft(fftshift(sc3)); 8gVxiFjo  
   s2 = ifft(fftshift(sc2));                       % Return to physical space J{nyo1A  
   s1 = ifft(fftshift(sc1)); pr0@sri@  
end h]J&A  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); !A'`uf4u  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); GN htnB  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); WmT}t  
   P1=[P1 p1/p10]; 8w{#R{w  
   P2=[P2 p2/p10]; n:5O9,umZ  
   P3=[P3 p3/p10]; Z$OF|ZZQ  
   P=[P p*p]; q|47;bK'  
end Gt\K Ln  
figure(1) :GwSs'$O  
plot(P,P1, P,P2, P,P3); *_4n2<W$  
xJ[k#?T'  
转自:http://blog.163.com/opto_wang/
ciomplj 2014-06-22 22:57
谢谢哈~!~
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