[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 Y=i_2R2e2  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of .]0:`Y,;  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of -UWyBM3c@  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear cJ>^@pd{  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 yjOZed;M  
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%fid=fopen('e21.dat','w'); ~<}?pDA}~  
N = 128;                       % Number of Fourier modes (Time domain sampling points) vl!o^_70(  
M1 =3000;              % Total number of space steps tR.>d  
J =100;                % Steps between output of space aI;fNy/K  
T =10;                  % length of time windows:T*T0 +f}w+  
T0=0.1;                 % input pulse width 1]W8A.ZS  
MN1=0;                 % initial value for the space output location J[UTn'M8]  
dt = T/N;                      % time step S#
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n = [-N/2:1:N/2-1]';           % Index 3*F|`js"  
t = n.*dt;   &?I3xzvK  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 |}: 
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u20=u10.*0.0;                  % input to waveguide 2 {qm5H7sL  
u1=u10; u2=u20;                 djn<Oc`  
U1 = u1;   7H)tF
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U2 = u2;                       % Compute initial condition; save it in U ivSpi?   
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. Snq0OxS[v  
w=2*pi*n./T; o9v.]tb  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T 2h)*  
L=4;                           % length of evoluation to compare with S. Trillo's paper {M23a _t\  
dz=L/M1;                       % space step, make sure nonlinear<0.05 A&d_!u>  
for m1 = 1:1:M1                                    % Start space evolution 1`1Jn*|TI  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS H:t2;Z'  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; BOl*. t  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform Q@s G6iz  
   ca2 = fftshift(fft(u2)); m[w~h\FS  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation 'h>l_A
 
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   [
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   u2 = ifft(fftshift(c2));                        % Return to physical space }]pOR&o  
   u1 = ifft(fftshift(c1)); cr!sq.)s  
if rem(m1,J) == 0                                 % Save output every J steps. $wcV~'fM  
    U1 = [U1 u1];                                  % put solutions in U array r3Yf
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    U2=[U2 u2]; 2bf#L?5g/  
    MN1=[MN1 m1]; "9RW<+  
    z1=dz*MN1';                                    % output location 5(DnE?}vo  
  end `J}FSUn\  
end bR=TGL&  
hg=abs(U1').*abs(U1');                             % for data write to excel K&&YxX~3  
ha=[z1 hg];                                        % for data write to excel  P!/:yWd  
t1=[0 t']; PkK#HD  
hh=[t1' ha'];                                      % for data write to excel file 602=qb  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format AVp"<Uv  
figure(1) E;r~8^9)  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn &RlYw#*1.  
figure(2) \qbEC.-K  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn 6}_J;g\|  
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非线性超快脉冲耦合的数值方法的Matlab程序 0[s<!k9=  
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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。   ^p~3H  
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 sv*xO7D.  
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Wp=:|J  
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%  This Matlab script file solves the nonlinear Schrodinger equations -vS7%Fbr  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of 68!=`49r>  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear IUy5=Sl  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 v
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C=1;                           .7H*F9  
M1=120,                       % integer for amplitude G]I^zd&P  
M3=5000;                      % integer for length of coupler c6HH%|  
N = 512;                      % Number of Fourier modes (Time domain sampling points) ;4(FS  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. ,,(BW7(  
T =40;                        % length of time:T*T0. "\kr;X'  
dt = T/N;                     % time step E2|c;{c  
n = [-N/2:1:N/2-1]';          % Index YwF\  
t = n.*dt;   _lG\_6oJ,  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. jF%l\$)/  
w=2*pi*n./T; +|Qe/
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g1=-i*ww./2; -MeO|HWm  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; tP/R9Ezp  
g3=-i*ww./2; FuO'%3;c  
P1=0; (
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P2=0; xwrleB  
P3=1; 2ZFp(e^%  
P=0; 96CC5  
for m1=1:M1                 t/:]\|]WB  
p=0.032*m1;                %input amplitude _qhYG1t  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 ht^xcc  
s1=s10; V: ivnx*  
s20=0.*s10;                %input in waveguide 2 lmr:PX  
s30=0.*s10;                %input in waveguide 3
btU:=6  
s2=s20; `@i!'h  
s3=s30; 8Vqh1<
 
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   r1X\$&  
%energy in waveguide 1 :S{
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p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   XDq*nA8#5B  
%energy in waveguide 2 /bv4/P  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   ]+i~Cbj  
%energy in waveguide 3 hlTM<E  
for m3 = 1:1:M3                                    % Start space evolution C9FQo7  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS eI*o9k$Qs  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; g"L$}#iTsl  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; +tPqU6  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform [P746b_\e  
   sca2 = fftshift(fft(s2)); E14Dq#L  
   sca3 = fftshift(fft(s3)); bT{iei]?  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   69u"/7X  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); m%km@G$  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); GFBku^pi  
   s3 = ifft(fftshift(sc3)); + %07J6  
   s2 = ifft(fftshift(sc2));                       % Return to physical space 2N:|BO>  
   s1 = ifft(fftshift(sc1)); <Xr{1M D  
end P ||:?3IH  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); JA~v:ec  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); ')>&:~  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); |\MgE.N  
   P1=[P1 p1/p10]; P>3 ;M'KsO  
   P2=[P2 p2/p10]; G\ht)7SGgf  
   P3=[P3 p3/p10]; ?ydqmj2[F  
   P=[P p*p]; O o+pi$W  
end s!j[Ovtx  
figure(1) UL.x*@o  
plot(P,P1, P,P2, P,P3); f?A1=lm~  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~