[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 ZW|VAn'>  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of 'zhw]L;'g  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of ^6 sT$set  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear <ArP_! `3  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 !j.jvI%e;  
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%fid=fopen('e21.dat','w'); P'6(HT>F?  
N = 128;                       % Number of Fourier modes (Time domain sampling points) /< CjBW:
 
M1 =3000;              % Total number of space steps GcPhT  
J =100;                % Steps between output of space (N\Zz*PLz  
T =10;                  % length of time windows:T*T0 /Iu._2  
T0=0.1;                 % input pulse width cnOk  
MN1=0;                 % initial value for the space output location jsvD[\P  
dt = T/N;                      % time step Lay+)S.ta[  
n = [-N/2:1:N/2-1]';           % Index ~4iIG}Y<  
t = n.*dt;   ]-aeoa#  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 $|YIr7?R  
u20=u10.*0.0;                  % input to waveguide 2 uOrv
mb  
u1=u10; u2=u20;                 7o+!Gts]  
U1 = u1;   %?EOD=e=  
U2 = u2;                       % Compute initial condition; save it in U "ppT<8Qi'  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1.
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w=2*pi*n./T; D4r5wc%  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T 'g
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L=4;                           % length of evoluation to compare with S. Trillo's paper
G?]E6R  
dz=L/M1;                       % space step, make sure nonlinear<0.05 $0Y&r]'  
for m1 = 1:1:M1                                    % Start space evolution %zyMWC  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS $
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   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; 5b[:B~J  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform V|.aud=7z  
   ca2 = fftshift(fft(u2)); [,a O*7N  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation rQ'tab.,]  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   ^>ca*g  
   u2 = ifft(fftshift(c2));                        % Return to physical space !DCJ2h%E[_  
   u1 = ifft(fftshift(c1)); bhSpSul  
if rem(m1,J) == 0                                 % Save output every J steps. <5(8LMF  
    U1 = [U1 u1];                                  % put solutions in U array lq_W;L  
    U2=[U2 u2]; =D4E
PfQn1  
    MN1=[MN1 m1]; y+?tUSPP  
    z1=dz*MN1';                                    % output location 2`vCQV  
  end "=<lPi  
end 9,'5~+7  
hg=abs(U1').*abs(U1');                             % for data write to excel ?4Z0)%6  
ha=[z1 hg];                                        % for data write to excel h{sW$WA  
t1=[0 t']; %~ecrQ;  
hh=[t1' ha'];                                      % for data write to excel file q'2PG@  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format -H`G6oMOO  
figure(1) $_Qo  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn 1qUdj[Bj  
figure(2) 2>O2#53ls0  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn =,[46 ;q  
i:kWO7aP  
非线性超快脉冲耦合的数值方法的Matlab程序 P+3G*M=}  
0 \LkJ*i  
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。   4'54  
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 uU.9*B=H9  
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:/vB,JC  
%  This Matlab script file solves the nonlinear Schrodinger equations ,0
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%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of yK?~XV:  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear AD?DIE(v  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 |7`Vw Z  
R~w(]  
C=1;                           p!aeL}g`  
M1=120,                       % integer for amplitude X=\#n-*  
M3=5000;                      % integer for length of coupler }h_Op7.5D  
N = 512;                      % Number of Fourier modes (Time domain sampling points) t48(GKF  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. $xu?zd"  
T =40;                        % length of time:T*T0. #]eXI $HP  
dt = T/N;                     % time step +zs6$OI]V  
n = [-N/2:1:N/2-1]';          % Index `FJnR~d  
t = n.*dt;   Xq>e]#gR  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. iY|YEi8  
w=2*pi*n./T; \;7DS:d@  
g1=-i*ww./2; b7AuKY{L  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; U*&ZQw  
g3=-i*ww./2; 50DPzn  
P1=0; X^|oY]D  
P2=0; o@>c[knJ  
P3=1; U[A*A^$c}  
P=0; }uHc7gTBF7  
for m1=1:M1                 ==XP}w)m  
p=0.032*m1;                %input amplitude ^CK)q2K>[  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 [BQw$8+n_  
s1=s10; CMBW]b|  
s20=0.*s10;                %input in waveguide 2 owMH  
s30=0.*s10;                %input in waveguide 3 <,E*,&0W  
s2=s20; z}Z`kq+C  
s3=s30; g Go  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   s3+O
=5  
%energy in waveguide 1 {-Y_8@&  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   <;6])  
%energy in waveguide 2 L\Jl'r|  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   @^` <iTK&p  
%energy in waveguide 3 z'qV
EHc)  
for m3 = 1:1:M3                                    % Start space evolution y2+a2  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS :>X7(&j8  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; h+74W0 $  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; _"sRL}-Z  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform M)J*Df0@  
   sca2 = fftshift(fft(s2)); W1@;94Sb~  
   sca3 = fftshift(fft(s3)); 6gKOpa  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   wFJK!9KA8  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); Agi1r]W  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); EORRSP,$2  
   s3 = ifft(fftshift(sc3)); zJnVO$A'  
   s2 = ifft(fftshift(sc2));                       % Return to physical space Un/fP1  
   s1 = ifft(fftshift(sc1)); 0&.lS
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end I)Lb"  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); wi9|  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); og\XLJ}_  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); U2AGH2emw  
   P1=[P1 p1/p10]; t3GK{X  
   P2=[P2 p2/p10]; Pu^~]^W)  
   P3=[P3 p3/p10]; *(`.h\+  
   P=[P p*p]; iCK$ o_`?  
end &tgvE6/V  
figure(1) f oVD+\~Y  
plot(P,P1, P,P2, P,P3); ^97ZH)Ww  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~