[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 VRYj&s'@  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of R 2uo ZA,  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of zV\\T(R)  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 3_W1)vd{
 
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 2*6b{}yJH  
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%fid=fopen('e21.dat','w'); cn$E?&-
 
N = 128;                       % Number of Fourier modes (Time domain sampling points) 1!"0fZh9U  
M1 =3000;              % Total number of space steps !5Ko^:+Y  
J =100;                % Steps between output of space /s3AZ j9  
T =10;                  % length of time windows:T*T0 Iaf"j
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T0=0.1;                 % input pulse width sO~:e?F  
MN1=0;                 % initial value for the space output location +53 Tf  
dt = T/N;                      % time step #`5{?2gS9  
n = [-N/2:1:N/2-1]';           % Index hPhNDmL#3  
t = n.*dt;   3jIi$X06  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 #pbPaRJL(  
u20=u10.*0.0;                  % input to waveguide 2 P agzp%m  
u1=u10; u2=u20;                 k=2]@K$%  
U1 = u1;   bv`gjR  
U2 = u2;                       % Compute initial condition; save it in U CUgXpU*  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. XUmL8  
w=2*pi*n./T; *ktM<N58  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T xQX,1NbH5  
L=4;                           % length of evoluation to compare with S. Trillo's paper .%7#o
 
dz=L/M1;                       % space step, make sure nonlinear<0.05 )cnB>Qul  
for m1 = 1:1:M1                                    % Start space evolution Z 55i
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   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS [vkz<sL"  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; ,vEwck#  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform Ml` f+$  
   ca2 = fftshift(fft(u2)); 7pDov@K<{  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation TJ3CXyRq  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   =.,]}  
   u2 = ifft(fftshift(c2));                        % Return to physical space 77
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   u1 = ifft(fftshift(c1)); ?y82S*sb#  
if rem(m1,J) == 0                                 % Save output every J steps. cQ~}qE>I  
    U1 = [U1 u1];                                  % put solutions in U array +!IIt {u  
    U2=[U2 u2]; %"~\Pu*>  
    MN1=[MN1 m1]; U7d%*g  
    z1=dz*MN1';                                    % output location GUJ[2/V~A  
  end ((wG K|d  
end i.Iiwe0G  
hg=abs(U1').*abs(U1');                             % for data write to excel F|q-ZlpW-  
ha=[z1 hg];                                        % for data write to excel |?6r
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t1=[0 t']; _Z'j%/-4@D  
hh=[t1' ha'];                                      % for data write to excel file Hzs]\%"  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format O;c;>x_dA  
figure(1) 0UeDM*  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn @EH:4~  
figure(2) Kl<qp7o0  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn s0"S;{_#  
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非线性超快脉冲耦合的数值方法的Matlab程序 m`!C|?hu  
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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。   57e'a&}e  
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 =s`\W7/;{-  
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%  This Matlab script file solves the nonlinear Schrodinger equations -M}#-qwf  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of U2z1HIs  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear kxt@t#  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 +L1%mVq]y  
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C=1;                           Jr m<ut  
M1=120,                       % integer for amplitude u9rlNmf$  
M3=5000;                      % integer for length of coupler \tTZN  
N = 512;                      % Number of Fourier modes (Time domain sampling points) BsiHVr  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. Wf/Gt\?  
T =40;                        % length of time:T*T0. &gxRw l  
dt = T/N;                     % time step #4"(M9kf  
n = [-N/2:1:N/2-1]';          % Index @O9.~6  
t = n.*dt;   GFasGHAw  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. ;rWgt!l  
w=2*pi*n./T; 4VINu9\V  
g1=-i*ww./2; Iih~W&  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; @'`!2[2'?  
g3=-i*ww./2; }N^.4HOS8  
P1=0; mY?^]3-_  
P2=0; {Y-<#U~iH  
P3=1; o %s
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P=0; /,dcr*  
for m1=1:M1                 rLO1Sv  
p=0.032*m1;                %input amplitude <R
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s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 /n;-f%dL  
s1=s10; T X.YTU  
s20=0.*s10;                %input in waveguide 2 ?_q e 2R.  
s30=0.*s10;                %input in waveguide 3 X[b=25Ct  
s2=s20; E>f+E8?  
s3=s30; ?{l}35Q.@  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   WGFp<R  
%energy in waveguide 1 W]MKc&R  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   ^6s<  
%energy in waveguide 2 |Fz/9+I  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   f<WP<!N%  
%energy in waveguide 3 3jQy"9f  
for m3 = 1:1:M3                                    % Start space evolution ve[` 0  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS uu L
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   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; >2tQ')%DJ  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; FWI<_KZO  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform 1o\P7PLe  
   sca2 = fftshift(fft(s2)); >aXyi3B  
   sca3 = fftshift(fft(s3)); U 2am1}  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   8enlF\I8g  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); (`PgvBL:  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);  4b]/2H  
   s3 = ifft(fftshift(sc3)); i356m9j  
   s2 = ifft(fftshift(sc2));                       % Return to physical space {/`iZzPg  
   s1 = ifft(fftshift(sc1)); mne4uW
 
end S0().2#  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); U_ n1QU  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); 9r.Os  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); }&A!h  
   P1=[P1 p1/p10]; i"mN0%  
   P2=[P2 p2/p10]; KDr?<"2L  
   P3=[P3 p3/p10]; nNJU@<|{*  
   P=[P p*p]; @\0U`*]^)  
end a@:(L"Or  
figure(1) ZHT_o\  
plot(P,P1, P,P2, P,P3); -d]-R?mQ  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~