[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 (C)p9-,  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of AkiDL=;w  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of {+b7sA3
 
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 9-m=*|p  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 Oa>Ppldeg  
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%fid=fopen('e21.dat','w'); 7Fsay+a  
N = 128;                       % Number of Fourier modes (Time domain sampling points) dUdT7ixo  
M1 =3000;              % Total number of space steps hK|Ul]qI  
J =100;                % Steps between output of space 6D_D';o  
T =10;                  % length of time windows:T*T0 @`Su0W+.  
T0=0.1;                 % input pulse width k$}fWR  
MN1=0;                 % initial value for the space output location w@fi{H(R  
dt = T/N;                      % time step Fv`,3aNB  
n = [-N/2:1:N/2-1]';           % Index `~q<N  
t = n.*dt;   vY`s'%WV  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 ;YL i{  
u20=u10.*0.0;                  % input to waveguide 2 lqpp)Cq  
u1=u10; u2=u20;                 jb!i$/%w  
U1 = u1;   El"Q'(:/U  
U2 = u2;                       % Compute initial condition; save it in U '@P^0+B!(.  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. +X]vl=0  
w=2*pi*n./T; ENY+^7  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T -d:Jta!}{  
L=4;                           % length of evoluation to compare with S. Trillo's paper "U"Z 3*  
dz=L/M1;                       % space step, make sure nonlinear<0.05  %D "I  
for m1 = 1:1:M1                                    % Start space evolution Dv`c<+q(#  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS D^;Uq8NDKq  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; ^_
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   ca1 = fftshift(fft(u1));                        % Take Fourier transform q'MZ R'<@  
   ca2 = fftshift(fft(u2)); "g8M
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   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation b>JDH1)  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   |$_sX9\`?|  
   u2 = ifft(fftshift(c2));                        % Return to physical space ]e@Oiq  
   u1 = ifft(fftshift(c1)); $L]lHji  
if rem(m1,J) == 0                                 % Save output every J steps. DM>eVS3}  
    U1 = [U1 u1];                                  % put solutions in U array S|+o-[e8O  
    U2=[U2 u2]; FaJ&GOM,  
    MN1=[MN1 m1]; 5l*&>C[(i  
    z1=dz*MN1';                                    % output location nzeX[*  
  end jRV/A!4  
end q>
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hg=abs(U1').*abs(U1');                             % for data write to excel :*\Pn!r  
ha=[z1 hg];                                        % for data write to excel _:27]K:  
t1=[0 t']; @f_+=}|dc  
hh=[t1' ha'];                                      % for data write to excel file /&94 eC  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format 6)Lk-D  
figure(1) "snw4if  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn 1|wL\I  
figure(2) 6!FQzFCZq  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn ~&bq0(  
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非线性超快脉冲耦合的数值方法的Matlab程序 *;*r8[U}q  
h'F=YF$o  
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。   Tnm.A?  
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 83q6Sv  
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%  This Matlab script file solves the nonlinear Schrodinger equations CeC6hGR5  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of }`~+]9<  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear sON|w86B  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 @<&m|qtMsz  
%bfQ$a:  
C=1;                           ~Jz6O U*z  
M1=120,                       % integer for amplitude N?"]  
M3=5000;                      % integer for length of coupler w+CA1q<  
N = 512;                      % Number of Fourier modes (Time domain sampling points) kW&TJP+5*  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. +; AZ+w]ZF  
T =40;                        % length of time:T*T0. :20W\P<O!A  
dt = T/N;                     % time step Jg|XH L)  
n = [-N/2:1:N/2-1]';          % Index ,01"SWE  
t = n.*dt;   0:Ol7  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. 9-*uPK]m9  
w=2*pi*n./T; oM
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g1=-i*ww./2; 0KOgw*>_  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; p=}Nn(  
g3=-i*ww./2; @J`"[%U  
P1=0; ,nDaqQ-C!!  
P2=0; 6V01F8&w  
P3=1; SI-Ops~e  
P=0; R/z=p_6p7`  
for m1=1:M1                 @6T/Tdz  
p=0.032*m1;                %input amplitude !d0kV,F:  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 ;MdlwQ$`  
s1=s10; FQ5U$x.[P  
s20=0.*s10;                %input in waveguide 2 Z>5b;8  
s30=0.*s10;                %input in waveguide 3 ~FG]wNgS  
s2=s20; v z '&%(  
s3=s30; [K0(RDV)%  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   '16b2n+F@#  
%energy in waveguide 1 fS78>*K  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   'AH0ww_)n  
%energy in waveguide 2 @r/nF5  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   ^,T(mKS  
%energy in waveguide 3 HRfYl,S,  
for m3 = 1:1:M3                                    % Start space evolution _>X+ZlpU
:  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS eV?2LtT#5  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; 2!=f hN
 
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; O[JL+g4  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform I(BQ34q  
   sca2 = fftshift(fft(s2)); 4u})+2W  
   sca3 = fftshift(fft(s3)); {[?(9u7R  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   (M.&^w;`,  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); %aVq+kC h  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); i6Emhji  
   s3 = ifft(fftshift(sc3)); \n|EM@=eE  
   s2 = ifft(fftshift(sc2));                       % Return to physical space PBTnIU  
   s1 = ifft(fftshift(sc1)); JYbL?N  
end ou{2@"  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); V{3x!+q  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); ok\vQs(a  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); z/@slT  
   P1=[P1 p1/p10]; 6fEqqUeV  
   P2=[P2 p2/p10]; 1ztG;\  
   P3=[P3 p3/p10]; >V8-i`  
   P=[P p*p]; u^8{Z;mm  
end =R$u[~Xl2X  
figure(1) )W _v:?A9  
plot(P,P1, P,P2, P,P3); Tq
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~