| tianmen |
2011-06-12 18:33 |
求解光孤子或超短脉冲耦合方程的Matlab程序
计算脉冲在非线性耦合器中演化的Matlab 程序 yj4+5`|f .NtbL./=| % This Matlab script file solves the coupled nonlinear Schrodinger equations of ~Lc066bLeq % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of {3N'D2N % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear Hw#d_P: % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 9qS"uj 0%!rx{f#\ %fid=fopen('e21.dat','w'); -v6M< N = 128; % Number of Fourier modes (Time domain sampling points) P0`Mdk371 M1 =3000; % Total number of space steps JG{j)O|L J =100; % Steps between output of space L
8{\r$ T =10; % length of time windows:T*T0 g$.
\ T0=0.1; % input pulse width qj cp65^ MN1=0; % initial value for the space output location NEa>\K<\ dt = T/N; % time step oK{ V7 n = [-N/2:1:N/2-1]'; % Index hHqh{:q{v t = n.*dt; /?';
nGq u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10 EGl^!.' u20=u10.*0.0; % input to waveguide 2 fDx9iHGv u1=u10; u2=u20; !n6wWl U1 = u1; 5U_H>oD U2 = u2; % Compute initial condition; save it in U h*u`X>!! ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. LJoGpr8 w=2*pi*n./T; u&wiGwF[ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T Zo>]rKeV L=4; % length of evoluation to compare with S. Trillo's paper pLv$\MiZ dz=L/M1; % space step, make sure nonlinear<0.05 =IAsH85Q for m1 = 1:1:M1 % Start space evolution Gycm,Cy u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS +2 Af&~T u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; Z$J#| ca1 = fftshift(fft(u1)); % Take Fourier transform XD"_Iq! ca2 = fftshift(fft(u2)); 9W5onn c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation o:V|:*1Q c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift |p$spQ u2 = ifft(fftshift(c2)); % Return to physical space qC'{;ko u1 = ifft(fftshift(c1)); a#T]*(Yq) if rem(m1,J) == 0 % Save output every J steps. Fd*8N8Pi U1 = [U1 u1]; % put solutions in U array !nAX$i~ U2=[U2 u2]; {}:ToIp MN1=[MN1 m1]; gk`zA z1=dz*MN1'; % output location I@\OaUGr+ end %/updw#{B end Le%ZV%, hg=abs(U1').*abs(U1'); % for data write to excel pKi& [ ha=[z1 hg]; % for data write to excel T6ENtp t1=[0 t']; iX3HtIBj' hh=[t1' ha']; % for data write to excel file RoAlf+&Qb %dlmwrite('aa',hh,'\t'); % save data in the excel format ytNO*XoR figure(1) =_0UD{"_0 waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn =/\:>+p^.y figure(2) -\#0]F:- waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn /r_~:3F <id}<H 非线性超快脉冲耦合的数值方法的Matlab程序 ,-z9 #t fA89|NTSUh 在研究脉冲在非线性耦合器中的演变时,我们需要求解非线性偏微分方程组。在如下的论文中,我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。 U!Ek' Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 N!`e}Z6S d|4}obCt 2h%z ("3/ ~Ch+5A; % This Matlab script file solves the nonlinear Schrodinger equations 2U-3Q]/I} % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of @Vu(XG % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 8mQmi` % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 bu51$s?B jbR0%X2 C=1; yV^s,P1 M1=120, % integer for amplitude n9s iX M3=5000; % integer for length of coupler >$ 2V%}; N = 512; % Number of Fourier modes (Time domain sampling points) V%Sy"IG dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05. VWO9=A*Y| T =40; % length of time:T*T0. VcoOeAKL dt = T/N; % time step ;V<fB/S.=+ n = [-N/2:1:N/2-1]'; % Index ":_vK}5 t = n.*dt; _/O25% l ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. W2.qhY 5 w=2*pi*n./T; R"K#7{p9 g1=-i*ww./2; +o9":dl g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; Y/7 $1k g3=-i*ww./2; im @h -A]0 P1=0; \m1~jMz*>k P2=0; "U7qo}`I P3=1; ciMzf$+G$ P=0; E4hLtc^
+ for m1=1:M1 7NJhRz`_ p=0.032*m1; %input amplitude ?Ae ven s10=p.*sech(p.*t); %input soliton pulse in waveguide 1 `hb%+-lj+ s1=s10; o*J3C> s20=0.*s10; %input in waveguide 2 ) Yd?m0m* s30=0.*s10; %input in waveguide 3 F8apH{&t s2=s20; &-;5*
lg)0 s3=s30; ,{c?ym w? p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1)))); 5L!y-3 %energy in waveguide 1 v;)..X30 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1)))); 4t)/ %energy in waveguide 2 |6<p(i7 p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1)))); &%-73nYw %energy in waveguide 3 8w.YYo8` for m3 = 1:1:M3 % Start space evolution C9t4#" s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS [Vma^B$7Vj s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; Sy
'Dp9!| s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
>FkWH7 sca1 = fftshift(fft(s1)); % Take Fourier transform K>{T_) { sca2 = fftshift(fft(s2)); Ih"XV sca3 = fftshift(fft(s3)); CvD"sHVq% sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift ~sXcnxLz sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); }+sT4'Ah> sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); )vSRHE s3 = ifft(fftshift(sc3)); E@b(1@ s2 = ifft(fftshift(sc2)); % Return to physical space hq #?kN s1 = ifft(fftshift(sc1)); @< | |