[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 m0Z7N5v)  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of 6UI>
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%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of Ws>i)6[  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear bs:QG1*.  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 vXf:~G]  
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%fid=fopen('e21.dat','w'); ^^ j/  
N = 128;                       % Number of Fourier modes (Time domain sampling points) fKYKW?g;)Z  
M1 =3000;              % Total number of space steps -eq=4N=s  
J =100;                % Steps between output of space xSOoIsL[  
T =10;                  % length of time windows:T*T0 u
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T0=0.1;                 % input pulse width s*+ZYPk  
MN1=0;                 % initial value for the space output location Z^+a*^w~{  
dt = T/N;                      % time step tnL."^%A2I  
n = [-N/2:1:N/2-1]';           % Index 4ac1m,Jlt  
t = n.*dt;   )rbc;{.  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 i;avwP<0  
u20=u10.*0.0;                  % input to waveguide 2 y&3TQ]f\  
u1=u10; u2=u20;                 :H3(w|T/  
U1 = u1;   .h!9wGi`  
U2 = u2;                       % Compute initial condition; save it in U ^Yr|K  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. /KP_Vc:g2_  
w=2*pi*n./T; rr)9Y][l}  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T 'ucGt  
L=4;                           % length of evoluation to compare with S. Trillo's paper 4)E|&)-fu8  
dz=L/M1;                       % space step, make sure nonlinear<0.05 tgfM:kzw  
for m1 = 1:1:M1                                    % Start space evolution iBS0rT_  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS L77E
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   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; }JH`'&3  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform @[0jFjK  
   ca2 = fftshift(fft(u2)); VlV)$z_  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation WRY~fM  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   gTuX *7w  
   u2 = ifft(fftshift(c2));                        % Return to physical space 6yp+h  
   u1 = ifft(fftshift(c1)); v2(U(Tt  
if rem(m1,J) == 0                                 % Save output every J steps. UXQb={  
    U1 = [U1 u1];                                  % put solutions in U array 9g4QVo|  
    U2=[U2 u2]; UMv"7~  
    MN1=[MN1 m1]; l&$*}yCK  
    z1=dz*MN1';                                    % output location 8`DO[Z  
  end KKV)DExv?  
end =;g=GcVK  
hg=abs(U1').*abs(U1');                             % for data write to excel rEg+i@~  
ha=[z1 hg];                                        % for data write to excel `M,Nd'5&|  
t1=[0 t']; V!H(;Tuuo  
hh=[t1' ha'];                                      % for data write to excel file phe"JNML  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format ujow?$&  
figure(1)
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waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn ( -xR7A  
figure(2) \N4d_fPj  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn M,ppCHy/$  
5nY9Ls(e  
非线性超快脉冲耦合的数值方法的Matlab程序 (}sDm~;s  
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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。   kz$(V(k<  
Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ~.iA`${y%  
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%  This Matlab script file solves the nonlinear Schrodinger equations 4Fh&V{`W  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of nD(w @c?  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear <( c
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%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 @pTD{OW?  
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C=1;                           jGJ.P
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M1=120,                       % integer for amplitude Jk%'mEGE  
M3=5000;                      % integer for length of coupler ?VU
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N = 512;                      % Number of Fourier modes (Time domain sampling points) "^Y6ctw  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. :EYu 4Y  
T =40;                        % length of time:T*T0. H\ {E%7^h-  
dt = T/N;                     % time step ;HR 6X  
n = [-N/2:1:N/2-1]';          % Index |X,$?ZDap  
t = n.*dt;   +SO2M|ru&  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. vU?b"n  
w=2*pi*n./T; z7| s%&  
g1=-i*ww./2; f<'n5}{RO0  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; j l}!T[5  
g3=-i*ww./2; G`9cd\^  
P1=0; '" ^ B&W  
P2=0; =U=e?AOG2  
P3=1; |if~i;VKL  
P=0; @X3 gBGY)  
for m1=1:M1                 bELIRM9  
p=0.032*m1;                %input amplitude '.=Wk^,Ua  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 aytq4Ts  
s1=s10; UY1JB^J$  
s20=0.*s10;                %input in waveguide 2 sM#!Xl;  
s30=0.*s10;                %input in waveguide 3 w
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s2=s20; Rrh<mo(yj#  
s3=s30; AD~~e% s=  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   3Gc ,I:\  
%energy in waveguide 1 ^fFtI?.6jI  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   mrK,Ql  
%energy in waveguide 2 O
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p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   pESB Il  
%energy in waveguide 3 Uzan7A  
for m3 = 1:1:M3                                    % Start space evolution z0\;m{TH  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS e} sc]MTM  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; EC^Ev|PB\u  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; 7(yXsVq  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform L2[Ei|9_  
   sca2 = fftshift(fft(s2)); FE0qw1{qQ  
   sca3 = fftshift(fft(s3)); )j{WeG7L  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   `G_(xN7O  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); sN6 0o 7.  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); IyrZez  
   s3 = ifft(fftshift(sc3)); w{_e"N  
   s2 = ifft(fftshift(sc2));                       % Return to physical space 2$o2.$i81  
   s1 = ifft(fftshift(sc1)); _#/!s]$d#  
end ipx@pNW;"  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); 8O"x;3I9  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); f28gE7Y\a  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); ZAI1p+  
   P1=[P1 p1/p10]; *,O :>Z5I  
   P2=[P2 p2/p10]; FBR$,j;Y  
   P3=[P3 p3/p10]; zF[3%qZE:T  
   P=[P p*p]; a)I=U[  
end WE+sFaKq-  
figure(1) ;FV~q{  
plot(P,P1, P,P2, P,P3); :6 Hxxh  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~