[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 CqFk(Td9-D  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of ^L?2y/  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of 1Y+g^Z;G  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear l~(A(1  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 oU`{6 ~;  
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%fid=fopen('e21.dat','w'); u,~/oTgO  
N = 128;                       % Number of Fourier modes (Time domain sampling points) (baBi9<P=  
M1 =3000;              % Total number of space steps vCX
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J =100;                % Steps between output of space 5.M82rR;~  
T =10;                  % length of time windows:T*T0 Gov]^?^D-  
T0=0.1;                 % input pulse width !FA[ ]d4  
MN1=0;                 % initial value for the space output location 9 `+RmX;m  
dt = T/N;                      % time step ~8 S2BV3@  
n = [-N/2:1:N/2-1]';           % Index 4ux^K:z  
t = n.*dt;   <rI8O;\H  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10
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u20=u10.*0.0;                  % input to waveguide 2 |\BxKwS^  
u1=u10; u2=u20;                 vX;~m7+  
U1 = u1;   bDtb"V8e  
U2 = u2;                       % Compute initial condition; save it in U Wj INY  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. }}b &IA#  
w=2*pi*n./T; Um%$TGw5  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T Eg+z(m$M  
L=4;                           % length of evoluation to compare with S. Trillo's paper HRg< f= oz  
dz=L/M1;                       % space step, make sure nonlinear<0.05 NTV@
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for m1 = 1:1:M1                                    % Start space evolution CNM
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   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS n?mV(?N  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; |V-)3#c  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform >(He,o@M  
   ca2 = fftshift(fft(u2)); zvOSQxGQ  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation }rA _4%  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   |C`.m
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   u2 = ifft(fftshift(c2));                        % Return to physical space kO}QOL4  
   u1 = ifft(fftshift(c1)); k#"}oI{< 6  
if rem(m1,J) == 0                                 % Save output every J steps. v|IG G'r  
    U1 = [U1 u1];                                  % put solutions in U array
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    U2=[U2 u2]; K<E|29t^k  
    MN1=[MN1 m1]; ana?;NvC  
    z1=dz*MN1';                                    % output location 0eFvcH:qG  
  end Nhrh>x[wJ  
end m{?uR.O  
hg=abs(U1').*abs(U1');                             % for data write to excel 2)T.Ci cx  
ha=[z1 hg];                                        % for data write to excel fI }v}L^  
t1=[0 t']; :9]"4ktoJ  
hh=[t1' ha'];                                      % for data write to excel file Z(c2F]  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format 9{&oVt~Y$  
figure(1) <G60R^o  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn <sor;;T  
figure(2) J_7&nIH7  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn Bhf4 /$  
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非线性超快脉冲耦合的数值方法的Matlab程序 i1^#TC$x  
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在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   R4AKp1Y  
Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 {w52]5l  
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%  This Matlab script file solves the nonlinear Schrodinger equations JXAH/N&i  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of I%tJLdL  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear )^]1j$N=3  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 uTvck6  
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C=1;                           Rd:wMy$  
M1=120,                       % integer for amplitude dU.H9\p  
M3=5000;                      % integer for length of coupler g1(`a`M  
N = 512;                      % Number of Fourier modes (Time domain sampling points) fl*>m,  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. Ja%(kq[v  
T =40;                        % length of time:T*T0. V[fcP;
  
dt = T/N;                     % time step {hi'LA-4@  
n = [-N/2:1:N/2-1]';          % Index 0Q5fX}  
t = n.*dt;   =x-@-\m  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. $[M5Vv  
w=2*pi*n./T; 57rH`UFXH  
g1=-i*ww./2; tish%Qnpd  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; DcX,o*ec!  
g3=-i*ww./2; 'Ej&zh  
P1=0; >*e,+ok  
P2=0; f{ER]U  
P3=1; c~v(bK  
P=0; e
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for m1=1:M1                 X~>2iL  
p=0.032*m1;                %input amplitude yQdoy^d/4  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 BjAmM*k  
s1=s10; Y4,LXuQ
 
s20=0.*s10;                %input in waveguide 2 :uQ~?amM  
s30=0.*s10;                %input in waveguide 3 ? yek\X  
s2=s20; xAJuIR1Hi  
s3=s30; ![hVTZ,hyZ  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   PNG!q}(c  
%energy in waveguide 1 NTy0NH  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   IrTMZG  
%energy in waveguide 2 Ika(ip#]=  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   Jwe9L^gL  
%energy in waveguide 3 M
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for m3 = 1:1:M3                                    % Start space evolution nEbJ,#>Z  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS ?nV& :~eY  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; pipqXe  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; 6U[bAp  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform 9,>u,  
   sca2 = fftshift(fft(s2)); \K%A}gnHe  
   sca3 = fftshift(fft(s3)); 0PT\/imgN  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   >Qold7 M  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); 5$Da\?Fpn  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); q8[I` V{  
   s3 = ifft(fftshift(sc3)); mIm.+U`a2  
   s2 = ifft(fftshift(sc2));                       % Return to physical space HZEDr}RN  
   s1 = ifft(fftshift(sc1)); *Rj(~Q/t  
end _|} GhdYE  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); <
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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)))); #azD&6`  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); Kfk/pYMDq  
   P1=[P1 p1/p10]; u
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   P2=[P2 p2/p10]; tC4 7P[b  
   P3=[P3 p3/p10]; 2}8xY:|@(U  
   P=[P p*p]; ,/6 aA7(  
end -9> oB  
figure(1) _7Rp.)[&  
plot(P,P1, P,P2, P,P3); 3|9 U`@  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~