[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 4d G-  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of &o@5%Rz2/  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of 9`xFZMd31A  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear >;v0zE  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 NRSse"  
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%fid=fopen('e21.dat','w'); ~4MjJKzA  
N = 128;                       % Number of Fourier modes (Time domain sampling points) "n }fEVJ,  
M1 =3000;              % Total number of space steps ]a#]3(o]}  
J =100;                % Steps between output of space tcEf ~|3  
T =10;                  % length of time windows:T*T0 hX%v`8  
T0=0.1;                 % input pulse width ddDJXk)!0  
MN1=0;                 % initial value for the space output location Az9J{
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dt = T/N;                      % time step ;}~Bv
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n = [-N/2:1:N/2-1]';           % Index K)UOx#xe1  
t = n.*dt;   &W+G{W{3  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 Ko|xEz=  
u20=u10.*0.0;                  % input to waveguide 2 P=[x!}.I  
u1=u10; u2=u20;                  jnzz~:  
U1 = u1;   w9<FX>@  
U2 = u2;                       % Compute initial condition; save it in U OCO,-
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ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. t0H=NUP8  
w=2*pi*n./T; +1jqCW  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T h$ iyclX  
L=4;                           % length of evoluation to compare with S. Trillo's paper _8pkejg  
dz=L/M1;                       % space step, make sure nonlinear<0.05 TL{pc=eBo  
for m1 = 1:1:M1                                    % Start space evolution lkWeQ)V  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS 7TPLVa=hO  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; *2 $m>N  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform "rDzrz  
   ca2 = fftshift(fft(u2)); [I<'E LX  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation q\y#  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   T>Rf?%o  
   u2 = ifft(fftshift(c2));                        % Return to physical space 1qKxg  
   u1 = ifft(fftshift(c1)); sFM>gG  
if rem(m1,J) == 0                                 % Save output every J steps. S%s|P=u  
    U1 = [U1 u1];                                  % put solutions in U array 'A(-MTd%  
    U2=[U2 u2]; m\Fb ,  
    MN1=[MN1 m1]; Ldj^O9p(  
    z1=dz*MN1';                                    % output location &R FM d=  
  end us,,W(q  
end C\2>7  
hg=abs(U1').*abs(U1');                             % for data write to excel xiOrk  
ha=[z1 hg];                                        % for data write to excel 2td|8vDA  
t1=[0 t']; =
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hh=[t1' ha'];                                      % for data write to excel file VmH_0IM^6  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format aco}pXz  
figure(1) lyH X#]  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn }Oh'YX#[  
figure(2) 9c5G6n0  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn =']};  
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非线性超快脉冲耦合的数值方法的Matlab程序 19w,'}CGk  
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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。   J(&M<<%  
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 ny_ kr`$42  
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%  This Matlab script file solves the nonlinear Schrodinger equations ':2*+
 
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of . I&)MZ>n  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear g9weJ6@}M  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ]^6y NtLK  
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C=1;                           JU=\]E@8c  
M1=120,                       % integer for amplitude zTBi{KrZ  
M3=5000;                      % integer for length of coupler {Fp`l\,  
N = 512;                      % Number of Fourier modes (Time domain sampling points) Vh.;p.!e  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. ;$tv8%_L[  
T =40;                        % length of time:T*T0. !%RJC,X  
dt = T/N;                     % time step u388Wj   
n = [-N/2:1:N/2-1]';          % Index L3=YlX`UL  
t = n.*dt;   LY88;*:S  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. zr;Y1Xt4  
w=2*pi*n./T; 71<PEawL  
g1=-i*ww./2; lfpt:5a9&  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; Eagmafu  
g3=-i*ww./2; tp0!,ne*  
P1=0; <;,S"e  
P2=0; N}x/&e  
P3=1; &b@!DAwAJ  
P=0; qvfAG
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for m1=1:M1                 3e!Yu.q:  
p=0.032*m1;                %input amplitude Puth8$  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 [>M*_1F  
s1=s10; dj
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s20=0.*s10;                %input in waveguide 2 WP%{{zR$  
s30=0.*s10;                %input in waveguide 3 ahi57r[  
s2=s20; [;IDTo!<>  
s3=s30; X\3
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p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   kTiPZZI  
%energy in waveguide 1 =4M.QA@lI!  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   rMXOwkE  
%energy in waveguide 2 ej"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))));   }KaCf,O  
%energy in waveguide 3 ]g8i>,G  
for m3 = 1:1:M3                                    % Start space evolution B )1<`nJA  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS z7t'6Fy9'  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; @^:7UI_  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; 5;K-,"UQ  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform BudWbZ5>Ep  
   sca2 = fftshift(fft(s2)); JW%/^'  
   sca3 = fftshift(fft(s3)); u.pKK  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   5}d/8tS  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); HV$9b~(  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); lEyG9Xvi  
   s3 = ifft(fftshift(sc3)); q(jkit~`A  
   s2 = ifft(fftshift(sc2));                       % Return to physical space 9#EHXgz  
   s1 = ifft(fftshift(sc1)); az\<sWb#  
end P
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   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); I4o=6ts  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); B.Zm$JZ:  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); [ n0##/  
   P1=[P1 p1/p10]; fOK+DT~  
   P2=[P2 p2/p10]; e$ XY\{  
   P3=[P3 p3/p10]; !0!U01SWa  
   P=[P p*p]; ,{uW8L  
end "J8;4p  
figure(1) ySixYt  
plot(P,P1, P,P2, P,P3); #4P3xa  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~