[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 <KX#;v!I  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of =j-{Mxb3  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of 3&f{lsLAC  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear KW\`&ki  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 \&0NH=*^  
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%fid=fopen('e21.dat','w'); Dlp::U*N'  
N = 128;                       % Number of Fourier modes (Time domain sampling points) pP&~S<[  
M1 =3000;              % Total number of space steps mMH0 o  
J =100;                % Steps between output of space ~7g6o^A>  
T =10;                  % length of time windows:T*T0 Y!zlte|P  
T0=0.1;                 % input pulse width |EunDb[Y  
MN1=0;                 % initial value for the space output location &/p9+gd  
dt = T/N;                      % time step l]gfT&  
n = [-N/2:1:N/2-1]';           % Index ]h
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t = n.*dt;   GU`2I/R  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 D@e:Fu1\R  
u20=u10.*0.0;                  % input to waveguide 2 ifUgj8i_  
u1=u10; u2=u20;                 cqDnZ`|6  
U1 = u1;   7Jbr
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U2 = u2;                       % Compute initial condition; save it in U 4[D@[kAs  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. +FI]0r  
w=2*pi*n./T; nM#\4Q[}Jh  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T %"D-1&%zY  
L=4;                           % length of evoluation to compare with S. Trillo's paper qW*)]s)z  
dz=L/M1;                       % space step, make sure nonlinear<0.05 Jh1fM`kB5K  
for m1 = 1:1:M1                                    % Start space evolution \oyr[so(i  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS y$rp1||lH  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; c{[WOrA~#  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform f`cO5lP/:)  
   ca2 = fftshift(fft(u2)); *"ws
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   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation "Z <1Msz  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   /OEj]DNY  
   u2 = ifft(fftshift(c2));                        % Return to physical space S:wmm}XQ  
   u1 = ifft(fftshift(c1)); t+t&eg  
if rem(m1,J) == 0                                 % Save output every J steps. A#}IbcZ|b  
    U1 = [U1 u1];                                  % put solutions in U array :|bPr_&U$  
    U2=[U2 u2]; gU:j
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    MN1=[MN1 m1]; Onao'sjY  
    z1=dz*MN1';                                    % output location yd$y\pN=<  
  end pnWDsC~)  
end pV_2JXM~@  
hg=abs(U1').*abs(U1');                             % for data write to excel ==&=3  
ha=[z1 hg];                                        % for data write to excel ;-59#S&?tB  
t1=[0 t']; ~~&M&Fe  
hh=[t1' ha'];                                      % for data write to excel file +u7mw<A 8  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format R"jX9~3Ln  
figure(1) d4/ZOj+%  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn 0oD?4gn  
figure(2) BO^e.iB/  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn ].eGsh2  
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非线性超快脉冲耦合的数值方法的Matlab程序 Q/':<QY  
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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。   |X>:"?4t  
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 /J^yOR9  
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%  This Matlab script file solves the nonlinear Schrodinger equations 4q2aVm  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of BQsy)H`4E  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear YkTEAI|i  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 h-V5&em"_  
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C=1;                           mAz'
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M1=120,                       % integer for amplitude >>p3#~/  
M3=5000;                      % integer for length of coupler X=lOwPvP  
N = 512;                      % Number of Fourier modes (Time domain sampling points) Zx@{nVoYe~  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. R
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T =40;                        % length of time:T*T0. R4{2+q=0  
dt = T/N;                     % time step ) b?HK SqI  
n = [-N/2:1:N/2-1]';          % Index L0}"H .  
t = n.*dt;   WL<Cj_N_{H  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. wT;D<rqe`  
w=2*pi*n./T; ?_IRO|  
g1=-i*ww./2; }{s<!b  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; 7^=O^!sa  
g3=-i*ww./2; 6#v"+V  
P1=0; t68h$u  
P2=0; $Ad 5hkz  
P3=1; 7cH[}v`pn  
P=0; xI$B",?(  
for m1=1:M1                 .Gw;]s3  
p=0.032*m1;                %input amplitude $5l8V  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 lCDXFy(E  
s1=s10; M(xd:Fa?  
s20=0.*s10;                %input in waveguide 2 5F$W^N  
s30=0.*s10;                %input in waveguide 3 :Fm)<VN"  
s2=s20; lj(}{O  
s3=s30; :`25@<*u  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   \)pk/  
%energy in waveguide 1 52=?! JM  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   lIz"mk  
%energy in waveguide 2 1-4W4"#  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   *22}b.)  
%energy in waveguide 3 J"# o #~  
for m3 = 1:1:M3                                    % Start space evolution |\J8:b>}  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS UT%^!@u  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; h5>JBLawQP  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; m z) O  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform &^92z:?  
   sca2 = fftshift(fft(s2)); 4g
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   sca3 = fftshift(fft(s3)); Y;G+jC8   
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   Vv#|%^0  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); ND77(I$3s  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); })%WL;~  
   s3 = ifft(fftshift(sc3)); t[|^[%i  
   s2 = ifft(fftshift(sc2));                       % Return to physical space blEs!/A`  
   s1 = ifft(fftshift(sc1)); L> > %  
end F<VoPqHq  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); =y.?=`"  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); sz9C':`W  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); ,SNN[a  
   P1=[P1 p1/p10]; #**vIwX-Q  
   P2=[P2 p2/p10]; 8K=sx@l  
   P3=[P3 p3/p10]; '#L.w6<B  
   P=[P p*p]; -AWL :<  
end LR|LP)I  
figure(1) :A9G>qg  
plot(P,P1, P,P2, P,P3); hi^@969  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~