[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 frB~ajXK  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of 1;O%8sp&  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of n/ ]<Bc?  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear .Z[Bz7  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 6 <&jY  
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%fid=fopen('e21.dat','w'); ){ywk  
N = 128;                       % Number of Fourier modes (Time domain sampling points) }6YD5?4  
M1 =3000;              % Total number of space steps RZwjc<T  
J =100;                % Steps between output of space 3awh>1N2W  
T =10;                  % length of time windows:T*T0 ~nul[>z  
T0=0.1;                 % input pulse width r?^[o  
MN1=0;                 % initial value for the space output location gWlv;oq  
dt = T/N;                      % time step V4c$V]7  
n = [-N/2:1:N/2-1]';           % Index \_H-TbU8  
t = n.*dt;   0UV5}/2rP  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 RPH]@  
u20=u10.*0.0;                  % input to waveguide 2 l5?fF6#j  
u1=u10; u2=u20;                 ,{4G@:Fm  
U1 = u1;   ?|Q[QP  
U2 = u2;                       % Compute initial condition; save it in U #9HQW:
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ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. if|j)h&  
w=2*pi*n./T; "S#}iYp  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T [=Qv?am  
L=4;                           % length of evoluation to compare with S. Trillo's paper Y\CR*om!W  
dz=L/M1;                       % space step, make sure nonlinear<0.05 0I|IL]JL  
for m1 = 1:1:M1                                    % Start space evolution kzZdYiC  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS P<Wtv;Z1Z  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; ;W ZA  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform %O9kq  
   ca2 = fftshift(fft(u2)); \\<waU''  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation TDvUiJm  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   m(~5X0  
   u2 = ifft(fftshift(c2));                        % Return to physical space }zA kUt  
   u1 = ifft(fftshift(c1)); #X~{p4Lr  
if rem(m1,J) == 0                                 % Save output every J steps. jt({@;sU[<  
    U1 = [U1 u1];                                  % put solutions in U array RPb/U8  
    U2=[U2 u2]; z:m`  
    MN1=[MN1 m1]; a[Q\8<  
    z1=dz*MN1';                                    % output location `R}q&|o7<  
  end `O:ecPD4M  
end %by8i1
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hg=abs(U1').*abs(U1');                             % for data write to excel iw`,\V&  
ha=[z1 hg];                                        % for data write to excel P=Au~2X  
t1=[0 t']; z]P=>w  
hh=[t1' ha'];                                      % for data write to excel file -,;r %7T  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format u!NY@$Wc  
figure(1) ~d+.w%Z`  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn yrp;G_  
figure(2) 1e Wl:S}  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn AsBep  
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非线性超快脉冲耦合的数值方法的Matlab程序 6fP"I_c  
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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。   2(_+PQ6C=  
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 p&Os5zw;|  
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%  This Matlab script file solves the nonlinear Schrodinger equations UODbT&&  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of }sbh|#  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear Idq&0<I  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ^h q?E2-  
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C=1;                           0+a-l[!p  
M1=120,                       % integer for amplitude 7d44i  
M3=5000;                      % integer for length of coupler SGuR
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N = 512;                      % Number of Fourier modes (Time domain sampling points) OxGS{zs  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. 3~Qvp )~  
T =40;                        % length of time:T*T0. z_)`='&n  
dt = T/N;                     % time step XkG:1H;Q%  
n = [-N/2:1:N/2-1]';          % Index O'<5PwhG  
t = n.*dt;   oCl $ 0x  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. 3J^"$qfSn  
w=2*pi*n./T; -k$
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g1=-i*ww./2; ){XaO;k<]  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; [M:ag_rm+f  
g3=-i*ww./2; 1qEpQ
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P1=0; S4r-s;U-v/  
P2=0; \Lp|S:u  
P3=1; >8I?YT.  
P=0; ~EYsUC#B_  
for m1=1:M1                 !B&OK&*  
p=0.032*m1;                %input amplitude 7Wd}H Z  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 QD<GXPu?N  
s1=s10; *]L(,_:"  
s20=0.*s10;                %input in waveguide 2 .7h:/d Y:  
s30=0.*s10;                %input in waveguide 3 Ya%-/u  
s2=s20; : h"Bf@3  
s3=s30; *bi!iz5F  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   oWJ0>)  
%energy in waveguide 1 9n(.v}  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   0j=xWC  
%energy in waveguide 2 Gr1WBYK  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   K,ccM[hu|  
%energy in waveguide 3 j_3X 1w)k  
for m3 = 1:1:M3                                    % Start space evolution y:C=Ni&,"  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS gpIq4Q<  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; l ~b  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; NuL.l__W  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform 3RwDIk?>%  
   sca2 = fftshift(fft(s2)); 2Hh5gD|>  
   sca3 = fftshift(fft(s3)); 7GY3_`  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   ?+Q?K30:  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); E< 57d,3l  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); !Vtj:2PQL  
   s3 = ifft(fftshift(sc3)); <)f1skJsP  
   s2 = ifft(fftshift(sc2));                       % Return to physical space 3lkz:]SsE  
   s1 = ifft(fftshift(sc1)); OoG Nij  
end u$vA9g4  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); m1d*Lt>F@  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); HDV@d^]-  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); g>@T5&1q*  
   P1=[P1 p1/p10]; _m;H$N~I#  
   P2=[P2 p2/p10]; nIckI!U#D  
   P3=[P3 p3/p10]; K!L0|WH%!  
   P=[P p*p]; | Ns-l (l  
end ,aA%,C.0U
 
figure(1) :1O49g3R  
plot(P,P1, P,P2, P,P3); `$fKS24u  
PP]Z~ne0X  
转自：http://blog.163.com/opto_wang/

谢谢哈~！~