[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 &IsPqO  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of :o~]d  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of q$`>[&I~)  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear )t:8;;W@Ir  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 a1QW0d  
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%fid=fopen('e21.dat','w'); F ^m;xy  
N = 128;                       % Number of Fourier modes (Time domain sampling points) ZXIz.GFy+  
M1 =3000;              % Total number of space steps TQ%F\@"  
J =100;                % Steps between output of space t8.
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T =10;                  % length of time windows:T*T0 jz>b>;  
T0=0.1;                 % input pulse width Mp[2Auf  
MN1=0;                 % initial value for the space output location @~&^1%37)  
dt = T/N;                      % time step o!c~"  
n = [-N/2:1:N/2-1]';           % Index Pmd5P:n*,  
t = n.*dt;   >McEuoZx9  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 lg{/5gQG  
u20=u10.*0.0;                  % input to waveguide 2 x0%@u^BF  
u1=u10; u2=u20;                 3BF3$_u)o  
U1 = u1;   |8)\8b|VuC  
U2 = u2;                       % Compute initial condition; save it in U SO<9?uk.  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. (rq(y$N  
w=2*pi*n./T; j6L(U~%  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T l|;]"&|_]c  
L=4;                           % length of evoluation to compare with S. Trillo's paper >Nx4 +|  
dz=L/M1;                       % space step, make sure nonlinear<0.05 r$x;
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for m1 = 1:1:M1                                    % Start space evolution jw0wR\1  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS A!}Ps"Z  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; 9kbczL^Y  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform }'n]C|gZ  
   ca2 = fftshift(fft(u2)); x,fL656t  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation 0Fsa&<{6?  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   GLMpWD`Wo  
   u2 = ifft(fftshift(c2));                        % Return to physical space Y_~otoSoY  
   u1 = ifft(fftshift(c1)); E@AV?@<sc  
if rem(m1,J) == 0                                 % Save output every J steps. aY6F4,7/B  
    U1 = [U1 u1];                                  % put solutions in U array 2zuQeFsK  
    U2=[U2 u2]; @3S:W2k  
    MN1=[MN1 m1]; iqN?'8  
    z1=dz*MN1';                                    % output location /Ba/gq0j  
  end I8YCXh  
end .>LJ(Sx9b  
hg=abs(U1').*abs(U1');                             % for data write to excel cIP%t pTW.  
ha=[z1 hg];                                        % for data write to excel kdhwnO  
t1=[0 t']; vI,T1%llu  
hh=[t1' ha'];                                      % for data write to excel file @Qp#Tg<'  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format aP"
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figure(1) Jje!*?&8X  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn vF/wV'Kk  
figure(2) =hY/Yr%P  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn 9n"MNedqH  
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非线性超快脉冲耦合的数值方法的Matlab程序 oY7jj=z#T  
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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。   v2="j  
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 jdx T662q  
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%  This Matlab script file solves the nonlinear Schrodinger equations ntW1 )H'o  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of \)ZC
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%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 77ztDQDtM  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 nlaW$b{=  
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C=1;                           cS Qb3}a\  
M1=120,                       % integer for amplitude xV=Tmu6l  
M3=5000;                      % integer for length of coupler
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N = 512;                      % Number of Fourier modes (Time domain sampling points) hVui.]  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. Ys&)5j-  
T =40;                        % length of time:T*T0. yT~x7,  
dt = T/N;                     % time step :\y' ?d- Q  
n = [-N/2:1:N/2-1]';          % Index s'$2 }K  
t = n.*dt;   %.onO0})  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. \k^ojzJ  
w=2*pi*n./T; 8;#yXlf  
g1=-i*ww./2; ?-)v{4{s  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; I0!]J{  
g3=-i*ww./2; !
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P1=0; sRqecG(n  
P2=0; vTTXeS-b  
P3=1; ia_lP  
P=0; 2U(q
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for m1=1:M1                 Lj3Pp$h  
p=0.032*m1;                %input amplitude 
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s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 PC|ul{[*}  
s1=s10; 1aCpeD4|)  
s20=0.*s10;                %input in waveguide 2 `*U$pg  
s30=0.*s10;                %input in waveguide 3 W|y;Kxy  
s2=s20; 0G0(g,3p  
s3=s30; gga}mqMv=  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   jL'`M%8O  
%energy in waveguide 1 S4'<kF0z  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   9
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%energy in waveguide 2 +C[g>c}d  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   d325Cw?  
%energy in waveguide 3 $2RSYI`py  
for m3 = 1:1:M3                                    % Start space evolution _x|.\j  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS 9y<h.T
 
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; JodD6;P  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; _A])q  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform &/WE{W  
   sca2 = fftshift(fft(s2)); C,GZ  
   sca3 = fftshift(fft(s3)); n.z,-H17  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   DfP-(Lm)  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); 7D4tuXUq2  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); Ak8Y?#"wz  
   s3 = ifft(fftshift(sc3)); RZ;s_16GQ  
   s2 = ifft(fftshift(sc2));                       % Return to physical space v"Ax'()  
   s1 = ifft(fftshift(sc1)); v(!:HK0oeT  
end [[zNAq)"  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); 4e#$-V   
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); !?/:p.  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); 7 )rL<+  
   P1=[P1 p1/p10]; T~(Sc'8  
   P2=[P2 p2/p10]; X8R`C0   
   P3=[P3 p3/p10]; ,&qC R sw  
   P=[P p*p]; &i.sSqSI5  
end 3 yy5 l!fv  
figure(1) ;i'[c`  
plot(P,P1, P,P2, P,P3); I.GoY[u_%  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~