[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 hSO(s  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of BDeX5/`U#  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of } +@H&}u  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear PyS~2)=B  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 epWO}@ b a  
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%fid=fopen('e21.dat','w'); 33{(IzL0  
N = 128;                       % Number of Fourier modes (Time domain sampling points) _m  *8f\  
M1 =3000;              % Total number of space steps Q UQ"2oC  
J =100;                % Steps between output of space (\Iz(N["G  
T =10;                  % length of time windows:T*T0 :< )"G&  
T0=0.1;                 % input pulse width O%g%*9  
MN1=0;                 % initial value for the space output location M%3\]&  
dt = T/N;                      % time step DRBRs-D  
n = [-N/2:1:N/2-1]';           % Index Vu%XoI)<KY  
t = n.*dt;   +EmT+$>J  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 >#q2KXh  
u20=u10.*0.0;                  % input to waveguide 2 j=%^CRum  
u1=u10; u2=u20;                 C^o9::ER  
U1 = u1;   @wy&Z  
U2 = u2;                       % Compute initial condition; save it in U b;N[_2  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. &?],uHB?d  
w=2*pi*n./T; Ag>E%N
  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T Xm|Uz`A;  
L=4;                           % length of evoluation to compare with S. Trillo's paper nTJ-1A7EP  
dz=L/M1;                       % space step, make sure nonlinear<0.05 n9;z=   
for m1 = 1:1:M1                                    % Start space evolution >d`XR"_e  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS =1JS6~CTLN  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; T,Bu5:@#  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform "funFvY  
   ca2 = fftshift(fft(u2)); B]`!L/  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation Y7vTs
eq  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   & *^FBJEa.  
   u2 = ifft(fftshift(c2));                        % Return to physical space sG/mmZHYzr  
   u1 = ifft(fftshift(c1)); "5KJ /7q!  
if rem(m1,J) == 0                                 % Save output every J steps. U5 `
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    U1 = [U1 u1];                                  % put solutions in U array $a.!X8sHB.  
    U2=[U2 u2]; +s*OZ6i [  
    MN1=[MN1 m1]; OX"^a$  
    z1=dz*MN1';                                    % output location ZfpV=DU  
  end NhI&
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end ,&DK*LT8U  
hg=abs(U1').*abs(U1');                             % for data write to excel +h64idM{U  
ha=[z1 hg];                                        % for data write to excel UBmD 3|Zo  
t1=[0 t']; jm-J_o;}z6  
hh=[t1' ha'];                                      % for data write to excel file 73-*
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%dlmwrite('aa',hh,'\t');                           % save data in the excel format )JO#Z(  
figure(1) Q^&oXM'x/i  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn ~*3obZ2>2  
figure(2) }~?B
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waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn #Ub"Ii  
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非线性超快脉冲耦合的数值方法的Matlab程序 4(VVEe  
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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。   u|!O
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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 di@4'$5#  
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%  This Matlab script file solves the nonlinear Schrodinger equations SIJ:[=5!7  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of =!axQ[)A  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear +E8Itb,  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 jV(\]g"/=  
egBjr?  
C=1;                           56;(mbW  
M1=120,                       % integer for amplitude 0_}^IiG  
M3=5000;                      % integer for length of coupler }(g`l)OX  
N = 512;                      % Number of Fourier modes (Time domain sampling points) yIm@m[B;  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. &1O!guq%  
T =40;                        % length of time:T*T0. RL|13CG OP  
dt = T/N;                     % time step [DW}z  
n = [-N/2:1:N/2-1]';          % Index /`M>3q[  
t = n.*dt;   T;cyU9  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. ]!u12^A{  
w=2*pi*n./T; hK!Z~  
g1=-i*ww./2; 4?#0fK  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; _(CuuP$`I  
g3=-i*ww./2; ?'xTSAn  
P1=0; @/S6P-4  
P2=0; N30w^W&  
P3=1; v&6=(k{E@R  
P=0; K!X>k

 
for m1=1:M1                 }E01B_T9z  
p=0.032*m1;                %input amplitude '~dE0ohWb  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 ~c e?xr|  
s1=s10; R&z)  
s20=0.*s10;                %input in waveguide 2 /UJ@e  
s30=0.*s10;                %input in waveguide 3 <OKzb3e  
s2=s20; PGT*4r21  
s3=s30; E$$pO.\  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   NDG3mCl  
%energy in waveguide 1 <O`yM2/pS  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   z3l=aAw8  
%energy in waveguide 2 $rB20!  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   o8!gV/oy  
%energy in waveguide 3 aR }|^ex  
for m3 = 1:1:M3                                    % Start space evolution cJEOwAN  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS _n.2'  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; traJub  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; X(D$
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   sca1 = fftshift(fft(s1));                       % Take Fourier transform F^5<o  
   sca2 = fftshift(fft(s2)); Yp8~wdm  
   sca3 = fftshift(fft(s3)); oB9t&yM  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   8\Y/?$on  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); cz8%p;F:  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); =AFTB<7-^  
   s3 = ifft(fftshift(sc3)); ~Rzn =>a  
   s2 = ifft(fftshift(sc2));                       % Return to physical space }$K2h*  
   s1 = ifft(fftshift(sc1)); UWdPB2x[  
end \bt+46y@]  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); ,hj5.;
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   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); )I80Nq  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); %G%##wv:  
   P1=[P1 p1/p10]; U @Il:\I  
   P2=[P2 p2/p10]; 7wt2|$Qz  
   P3=[P3 p3/p10]; cD-.thHO  
   P=[P p*p]; Luxo,Ve  
end 9N9dQ}[:g  
figure(1) \NYtxGV[Z  
plot(P,P1, P,P2, P,P3); 1Aq*|JSk(  
F+;{s(wx  
转自：http://blog.163.com/opto_wang/

谢谢哈~！~