[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 78&(>8@m  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of 21i?$ uU  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of fvnj:3RK  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear w6 0I;.hy  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 H:byCFN-  
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%fid=fopen('e21.dat','w'); YLs%u=e($  
N = 128;                       % Number of Fourier modes (Time domain sampling points) TpXbJ]o9  
M1 =3000;              % Total number of space steps uj#bK 7  
J =100;                % Steps between output of space O
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T =10;                  % length of time windows:T*T0 
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T0=0.1;                 % input pulse width VBV y3fnj  
MN1=0;                 % initial value for the space output location .:gZ*ks~  
dt = T/N;                      % time step 6$]@}O^V  
n = [-N/2:1:N/2-1]';           % Index n
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t = n.*dt;   B>sSl1opI  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 2\Bt~;EIx  
u20=u10.*0.0;                  % input to waveguide 2 1_$ybftS  
u1=u10; u2=u20;                 CqHCJ '  
U1 = u1;   trD-qi  
U2 = u2;                       % Compute initial condition; save it in U S9BwCKH  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. AmYqrmJ  
w=2*pi*n./T; rC )pCC  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T 5WJof`M  
L=4;                           % length of evoluation to compare with S. Trillo's paper k~ Z9og  
dz=L/M1;                       % space step, make sure nonlinear<0.05 nGb%mlb  
for m1 = 1:1:M1                                    % Start space evolution b {fZU?o  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS n?uVq6c  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; ;Z:zL^rvn  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform R%l6+Okr  
   ca2 = fftshift(fft(u2)); "Z xM,kI  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation 5-rG8  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   !F]7q]g  
   u2 = ifft(fftshift(c2));                        % Return to physical space |VC|@ Q  
   u1 = ifft(fftshift(c1)); G&
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if rem(m1,J) == 0                                 % Save output every J steps. m"3gTqG  
    U1 = [U1 u1];                                  % put solutions in U array 2e~ud9,  
    U2=[U2 u2]; 2Lravb3  
    MN1=[MN1 m1]; up`.#GWm  
    z1=dz*MN1';                                    % output location rqa?A}'  
  end j;%RV)e  
end )0F\[Jl}  
hg=abs(U1').*abs(U1');                             % for data write to excel MPSoRA: h  
ha=[z1 hg];                                        % for data write to excel t<sy7e='  
t1=[0 t']; "p,TYjT?R  
hh=[t1' ha'];                                      % for data write to excel file lJZ-*"9V  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format }~/u%vI@M5  
figure(1) }<G"w5.<  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn F"2rX&W  
figure(2) oEfy{54  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn `2}H
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非线性超快脉冲耦合的数值方法的Matlab程序 [+7Nu  
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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。   Um4$. BKD  
Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 R^t )~\d  
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%  This Matlab script file solves the nonlinear Schrodinger equations SU.9;I !  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of ur*a!U  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear wO\,?SI4  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 G3 h&nH,>  
e[5=?p@|  
C=1;                           ;4E(n  
M1=120,                       % integer for amplitude <<Zt.!hS  
M3=5000;                      % integer for length of coupler -s]  
N = 512;                      % Number of Fourier modes (Time domain sampling points) >LqW;/&S<  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. ">$.>sn{  
T =40;                        % length of time:T*T0. M{sn{  
dt = T/N;                     % time step L p(6K  
n = [-N/2:1:N/2-1]';          % Index (<.uvq61  
t = n.*dt;   s>d /9 b  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. iEe<+Eyns  
w=2*pi*n./T; ;0R|#9oX_  
g1=-i*ww./2; BbCt_z'  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; :Ng4? +@r  
g3=-i*ww./2; ry99R|/d1  
P1=0; Z:TW{:lrI  
P2=0; <OYy;s  
P3=1; _6Ex}`fyJ  
P=0; l8O
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for m1=1:M1                 gOk<pRcTb=  
p=0.032*m1;                %input amplitude K@0gBgN  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 ez2rCpA  
s1=s10; .JkcCEe{G  
s20=0.*s10;                %input in waveguide 2 PxqRb  
s30=0.*s10;                %input in waveguide 3 ~c;D@.e\  
s2=s20; u0& aw  
s3=s30; `#v(MK{9+V  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   $s[DT!8N  
%energy in waveguide 1 Muhq,>!U  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   SfHs,y6
 
%energy in waveguide 2 naQ0TN,  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   ]yR0"<W^xO  
%energy in waveguide 3 J}c`\4gD  
for m3 = 1:1:M3                                    % Start space evolution T3-8AUCK8?  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS {{3n">s}:  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; rXortK#\%  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; 83^|a5  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform l}#z#L2,`  
   sca2 = fftshift(fft(s2)); Y~R['u,  
   sca3 = fftshift(fft(s3)); n\U3f M>N  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   GpW
5)a  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); Obd};&6Q  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); U}r^M( s!  
   s3 = ifft(fftshift(sc3)); AX {~A:B  
   s2 = ifft(fftshift(sc2));                       % Return to physical space O@n1E'S/  
   s1 = ifft(fftshift(sc1)); y)5U*\b  
end @A-*XJNS":  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); d;Uzl1;  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); =Wb!j18]  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); LTSoo.dE  
   P1=[P1 p1/p10]; ]+ \]2`?  
   P2=[P2 p2/p10]; .:<-E%  
   P3=[P3 p3/p10]; I eQF+Xz  
   P=[P p*p]; ;k<n}shD  
end 9`3%o9V9Y  
figure(1) Cfz020u`g  
plot(P,P1, P,P2, P,P3); 319 &:  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~