[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 $jDD0
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of @#J H=-06  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of R7y
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%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear e1Dj0s?i~K  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 1gO//fdI  
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%fid=fopen('e21.dat','w'); ;%lJD"yF  
N = 128;                       % Number of Fourier modes (Time domain sampling points) FxMMxY,*%  
M1 =3000;              % Total number of space steps Z7ZWf'o  
J =100;                % Steps between output of space zbdOCfA;  
T =10;                  % length of time windows:T*T0 7Co3P@@  
T0=0.1;                 % input pulse width c lq <$-  
MN1=0;                 % initial value for the space output location 1j8/4:  
dt = T/N;                      % time step ">rsA&hN-  
n = [-N/2:1:N/2-1]';           % Index :Fq2x_IUE  
t = n.*dt;   d;IJ0xB+by  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 vQE` c@^{  
u20=u10.*0.0;                  % input to waveguide 2
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u1=u10; u2=u20;                 WIhIEU7/  
U1 = u1;   #zh6=.,7  
U2 = u2;                       % Compute initial condition; save it in U * N2#{eF&]  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. HE4`9$kVLr  
w=2*pi*n./T; *(>F'>F1"  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T s2kGU^]y  
L=4;                           % length of evoluation to compare with S. Trillo's paper noWRYS%  
dz=L/M1;                       % space step, make sure nonlinear<0.05 99=[>Ck)G  
for m1 = 1:1:M1                                    % Start space evolution K7YT0cG  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS aA!@;rR<yU  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; eU<]h>2  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform &C!g(fS  
   ca2 = fftshift(fft(u2)); UzP@{?  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation .CB"@.7  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   S8rW'}XJ=H  
   u2 = ifft(fftshift(c2));                        % Return to physical space ~`a#h#  
   u1 = ifft(fftshift(c1)); i|::vl  
if rem(m1,J) == 0                                 % Save output every J steps. Uj y6vgU;  
    U1 = [U1 u1];                                  % put solutions in U array $NH`Iu9t  
    U2=[U2 u2]; 0$Qn
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    MN1=[MN1 m1]; W\ZV0T;<]  
    z1=dz*MN1';                                    % output location H"kc^G+(R"  
  end P W0q71  
end uk>q\j  
hg=abs(U1').*abs(U1');                             % for data write to excel X}ey0
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ha=[z1 hg];                                        % for data write to excel bs4fyb  
t1=[0 t']; 5+#?7J1  
hh=[t1' ha'];                                      % for data write to excel file g%KGF)+H  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format
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figure(1) \ZmFH8=|f  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn Q7OnhGA  
figure(2) rZwf%}  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn tOp:e KN  
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非线性超快脉冲耦合的数值方法的Matlab程序 QmDhZ04f  
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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。   kfG65aa>_  
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 gXJ19zB+  
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%  This Matlab script file solves the nonlinear Schrodinger equations d[qEP6B  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of UlLM<33_)  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear nATfmUN L  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 %^)JaEUC  
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C=1;                           !Barc,kA  
M1=120,                       % integer for amplitude ~L Bq5a  
M3=5000;                      % integer for length of coupler vb80J<4  
N = 512;                      % Number of Fourier modes (Time domain sampling points) 2rE~V.)%  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. E?;T:7.%  
T =40;                        % length of time:T*T0. GYy!
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dt = T/N;                     % time step is_dPc  
n = [-N/2:1:N/2-1]';          % Index #xJGuYdv  
t = n.*dt;   cxF?&0[mY  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. )b:~kuHi  
w=2*pi*n./T; V+@%(x@D_  
g1=-i*ww./2; WEY97_@  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; Q,`2DHhK  
g3=-i*ww./2; osgS?=8  
P1=0; _|5FrN  
P2=0; S<bz7 k9  
P3=1; GwIfGixqH  
P=0; c<t3y7  
for m1=1:M1                 ]oWZ{#r2  
p=0.032*m1;                %input amplitude <PuB3PEvV  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 spoWdRM2  
s1=s10; 9OO_Hp#|9  
s20=0.*s10;                %input in waveguide 2 $'mB8 S  
s30=0.*s10;                %input in waveguide 3 KE)D =P  
s2=s20; B$[%pm`'2  
s3=s30;
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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))));   /B#lju!  
%energy in waveguide 1 O|7{%5h  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   zL!~,B8C  
%energy in waveguide 2 ^J}$y7  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   h/+I-],RF  
%energy in waveguide 3 +hvIJv ?  
for m3 = 1:1:M3                                    % Start space evolution 6/WK((Fd  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS 0)]C&;}_M  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; MnrGD>M@|  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; 1b]PCNz  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform ]OCJ~Zw  
   sca2 = fftshift(fft(s2)); +]~w ?^h  
   sca3 = fftshift(fft(s3)); ~RLx;  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   oJ;O>J@c  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); kI[O{<kQ  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); P@S;>t{TD  
   s3 = ifft(fftshift(sc3)); cPBy(5^  
   s2 = ifft(fftshift(sc2));                       % Return to physical space `J7L
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   s1 = ifft(fftshift(sc1)); LXfeXWw?,  
end /5'<w(  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); _Ag/gu2-?  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); -$MC  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); bZlLivi  
   P1=[P1 p1/p10]; 0jZ{?  
   P2=[P2 p2/p10]; j{w,<Wt>  
   P3=[P3 p3/p10]; SUi1*S  
   P=[P p*p]; !DUg"o3G>  
end Jc#)T;#6  
figure(1) Xgth|C}k  
plot(P,P1, P,P2, P,P3); /$.vHt5nt  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~