[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 Ea?.HRxl  
#J_i 5KmXJ  
%  This Matlab script file solves the coupled nonlinear Schrodinger equations of *_wBV M=2  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of 67?5Cv  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 566Qikw2  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 v'tk:Hm1  
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%fid=fopen('e21.dat','w'); z^.0eP8\j  
N = 128;                       % Number of Fourier modes (Time domain sampling points) s=4.Ovd
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M1 =3000;              % Total number of space steps CgC wM=!r  
J =100;                % Steps between output of space |sz9l/,lG  
T =10;                  % length of time windows:T*T0 |{T2|iJI  
T0=0.1;                 % input pulse width 8vK&d>  
MN1=0;                 % initial value for the space output location k7*q.20  
dt = T/N;                      % time step bSfQH4F  
n = [-N/2:1:N/2-1]';           % Index 5FxU=M1gF  
t = n.*dt;   \ 714Pyy  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 at!?"
u  
u20=u10.*0.0;                  % input to waveguide 2 3 6 ;hg#  
u1=u10; u2=u20;                 -wB AFr  
U1 = u1;   "T|\  
U2 = u2;                       % Compute initial condition; save it in U 9&cZIP  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. \BL9}5y  
w=2*pi*n./T; <=Qk^Y2k  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T jxvVp*-=<j  
L=4;                           % length of evoluation to compare with S. Trillo's paper 5oS\uX|  
dz=L/M1;                       % space step, make sure nonlinear<0.05 eAMT72_  
for m1 = 1:1:M1                                    % Start space evolution 32yNEP{  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS "|if<
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   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; KXJHb{?  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform kN)ev?pQ[  
   ca2 = fftshift(fft(u2)); (&(f`c@I  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation JFZ p^{  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   iweP3u##  
   u2 = ifft(fftshift(c2));                        % Return to physical space 0*)79Sz  
   u1 = ifft(fftshift(c1)); fvDwg  
if rem(m1,J) == 0                                 % Save output every J steps. rzu^br9X  
    U1 = [U1 u1];                                  % put solutions in U array T (qu~}  
    U2=[U2 u2]; 9!LAAE`  
    MN1=[MN1 m1]; \IKr+wlN8  
    z1=dz*MN1';                                    % output location 7F.,Xvw&@  
  end :"4~VDu  
end kbY@Y,:w  
hg=abs(U1').*abs(U1');                             % for data write to excel VZ8L9h<{"  
ha=[z1 hg];                                        % for data write to excel jkq+j^  
t1=[0 t']; $dR%8@.H  
hh=[t1' ha'];                                      % for data write to excel file 9L}
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%dlmwrite('aa',hh,'\t');                           % save data in the excel format k;sUDmrO  
figure(1) YdFCYSiS  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn {8' 5  
figure(2) -LyIu#  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn {-xnBx  
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非线性超快脉冲耦合的数值方法的Matlab程序 nV,a|V5Xm  
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在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   F<$&G'% H  
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 V+^\SiM  
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%  This Matlab script file solves the nonlinear Schrodinger equations L|<Mtw  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of Oe$C5KA>LW  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear STI8[e7{  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 %^S1 fUwT  
LE;c+(CAU  
C=1;                           ,0~=9dR  
M1=120,                       % integer for amplitude W;=ZQ5Lw  
M3=5000;                      % integer for length of coupler (~jOtUyT  
N = 512;                      % Number of Fourier modes (Time domain sampling points) Z1Wra-g  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. 1n^xVk-G  
T =40;                        % length of time:T*T0. V|7 cdX#H  
dt = T/N;                     % time step FW2} 9#R  
n = [-N/2:1:N/2-1]';          % Index  KLX>QR@  
t = n.*dt;   s[hD9$VB>  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. ;/v^@  
w=2*pi*n./T; m\(a{x  
g1=-i*ww./2; TtzB[F  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; kW"N~Xw)  
g3=-i*ww./2; ,D8Tca\v  
P1=0; #u~8Txt  
P2=0; '>Z Ou3>  
P3=1; %EuSP0  
P=0; ~Y{K^:wN^  
for m1=1:M1                 uB\A8zC  
p=0.032*m1;                %input amplitude Ae"B]Cxb_X  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 PH6uP]  
s1=s10; y0xte&  
s20=0.*s10;                %input in waveguide 2 8qT/1b  
s30=0.*s10;                %input in waveguide 3 j:0z/gHp$  
s2=s20; }u :sh >2  
s3=s30; {J[0U
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p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   *p"%cas  
%energy in waveguide 1 37VSE@Z+  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   Z',pQ{rD  
%energy in waveguide 2 K#>B'>A\  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   d2pVO]l YZ  
%energy in waveguide 3 .mMM]*e[0  
for m3 = 1:1:M3                                    % Start space evolution L!\I>a5C0G  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS 8{AzB8xp  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; ).\%a h  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; RJ`F2b sYN  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform "_lSw3  
   sca2 = fftshift(fft(s2)); Kg56.$  
   sca3 = fftshift(fft(s3)); 4g|}]K1s  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift    0y?bwxkc  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); YQ]W<0(  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); \j4TDCs_[  
   s3 = ifft(fftshift(sc3)); &U:;jlST9  
   s2 = ifft(fftshift(sc2));                       % Return to physical space /)j:Y:5  
   s1 = ifft(fftshift(sc1)); LKhUqW  
end T{Av[>M  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); W_%Dg]l   
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); Gx!Y 4Q}-  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); XLB7 E  
   P1=[P1 p1/p10]; 0y*8;7-|r)  
   P2=[P2 p2/p10]; 8RB\P:6h  
   P3=[P3 p3/p10]; "5=Gu1  
   P=[P p*p]; d4~!d>{n|c  
end />H9T[3=  
figure(1) _G@)Bj^*  
plot(P,P1, P,P2, P,P3); *5u0`k^j  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~