[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 H8A=]Gq  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of $xK(bc'{  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of :Tdl84  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear +:3p*x%1H  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 yHnN7&  
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%fid=fopen('e21.dat','w'); 'e*:eBoyb  
N = 128;                       % Number of Fourier modes (Time domain sampling points) 1>
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M1 =3000;              % Total number of space steps M5`wfF,j  
J =100;                % Steps between output of space vpP8'f.  
T =10;                  % length of time windows:T*T0 7!A3PDAe  
T0=0.1;                 % input pulse width CA3`Ee+rD  
MN1=0;                 % initial value for the space output location @5\/L6SRfL  
dt = T/N;                      % time step _Kv;hR>  
n = [-N/2:1:N/2-1]';           % Index 1Ba.'~:  
t = n.*dt;   {W%/?d9m  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 cHUj6'neO  
u20=u10.*0.0;                  % input to waveguide 2 )%bY2 pk  
u1=u10; u2=u20;                 QuBaG
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U1 = u1;   GC)xQZU)s  
U2 = u2;                       % Compute initial condition; save it in U zJTSg  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1.  V/t-  
w=2*pi*n./T; ]64?S0p1c!  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T fH 0&Wc3yC  
L=4;                           % length of evoluation to compare with S. Trillo's paper 0kL tL!3  
dz=L/M1;                       % space step, make sure nonlinear<0.05 WO+_|*&  
for m1 = 1:1:M1                                    % Start space evolution V]|P>>`v9p  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS 2rqYm6  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; ktiC*|fd  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform 9m}c2:p  
   ca2 = fftshift(fft(u2)); qViolmDz  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation fHacVjJ  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   =aR
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   u2 = ifft(fftshift(c2));                        % Return to physical space /;9]LC.g  
   u1 = ifft(fftshift(c1)); 3k* U/*  
if rem(m1,J) == 0                                 % Save output every J steps. }tPI#[cfK  
    U1 = [U1 u1];                                  % put solutions in U array gro@+^DmT  
    U2=[U2 u2]; YCu9dBeVS  
    MN1=[MN1 m1]; ZJ}|t  
    z1=dz*MN1';                                    % output location sRSy++FRF  
  end }zqYn`ffD  
end bS*oFm@u  
hg=abs(U1').*abs(U1');                             % for data write to excel h7[PU^m  
ha=[z1 hg];                                        % for data write to excel Ks.kn7<l  
t1=[0 t']; =xPBolxm5U  
hh=[t1' ha'];                                      % for data write to excel file psAdYEGk!  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format 3QD##Wr^  
figure(1) `KJBQK  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn ^ ,yh38
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figure(2) ns9a+QQ  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn r?wE;gH  
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非线性超快脉冲耦合的数值方法的Matlab程序 ewv[nJD$  
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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。   TkV*^j5
 
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 .RxAYf|  
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%  This Matlab script file solves the nonlinear Schrodinger equations R{A$hnhW6  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of MYF6tZ*  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear yXL]uh#b  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 06~HVv  
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C=1;                           o;2QZ"v  
M1=120,                       % integer for amplitude H| 1O>p&  
M3=5000;                      % integer for length of coupler &[4lP~  
N = 512;                      % Number of Fourier modes (Time domain sampling points) J,]U"+;H  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. k-a3oLCR,  
T =40;                        % length of time:T*T0. l*z.20^P  
dt = T/N;                     % time step RE}$(T=  
n = [-N/2:1:N/2-1]';          % Index 'hl4cHk14  
t = n.*dt;   WZJ}HHePr  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. <X1^w  
w=2*pi*n./T; #jNN?,ZK  
g1=-i*ww./2; #iAEcC0k5  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; V+2C!)f(  
g3=-i*ww./2; 298@&_  
P1=0; ]M5w!O!  
P2=0; W
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P3=1; O6$d@r;EK]  
P=0; &p#$}tm  
for m1=1:M1                 ]EZiPW-uy  
p=0.032*m1;                %input amplitude dy^zOqc  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 O5eTkKUc  
s1=s10; f/6,b&l,  
s20=0.*s10;                %input in waveguide 2 5T4!'4n  
s30=0.*s10;                %input in waveguide 3 1y($h<  
s2=s20; amH..D7_>  
s3=s30; xf]_@T;  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));    +*aZ9g  
%energy in waveguide 1 ;VAHgIpx;  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   hbg:}R=B<  
%energy in waveguide 2 I>(\B|\6  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   a2'f#[as
 
%energy in waveguide 3 ,aBo
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for m3 = 1:1:M3                                    % Start space evolution &?xZHr`  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS oe{K0.`  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; .V Cfh+*J#  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; O^,%V{]6\  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform w`$M}oX(  
   sca2 = fftshift(fft(s2)); ^$I8ga  
   sca3 = fftshift(fft(s3)); _pS|bqF  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   aX$Q}mgb  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); MQ{.%  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); efu'PfZ`&  
   s3 = ifft(fftshift(sc3)); M'D l_dx-  
   s2 = ifft(fftshift(sc2));                       % Return to physical space z[`OYwsW  
   s1 = ifft(fftshift(sc1)); t+?m<h6w;l  
end nPU=n[t8O  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); ~l@ h  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); U'(@?]2<G  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); qXw^y  
   P1=[P1 p1/p10]; ~d072qUos  
   P2=[P2 p2/p10]; 6,q}1-  
   P3=[P3 p3/p10]; $)O=3dNbo  
   P=[P p*p]; yHk}'YP  
end .h7`Q{  
figure(1) b&j}f  
plot(P,P1, P,P2, P,P3); muJR~
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~