| 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 s`,g4ce` 6=Q6J % This Matlab script file solves the coupled nonlinear Schrodinger equations of %O[1yZh
\ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of <]oPr1 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear t^6ams$ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 d= vD Pf WyQ8}]1b %fid=fopen('e21.dat','w'); jL3
*m N = 128; % Number of Fourier modes (Time domain sampling points) K'"s9b8 M1 =3000; % Total number of space steps Z!'kN\z J =100; % Steps between output of space $OGMw+$C^ T =10; % length of time windows:T*T0 U/v)6:j)4R T0=0.1; % input pulse width "J}B
lB MN1=0; % initial value for the space output location 91a);d dt = T/N; % time step 0@u{(m n = [-N/2:1:N/2-1]'; % Index b=W kRj t = n.*dt; Zcc7
7dRA u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10 Bv*VNfUm u20=u10.*0.0; % input to waveguide 2 vu*{+YpH u1=u10; u2=u20; w+\RSqz/ U1 = u1; 9/&1lFKJ U2 = u2; % Compute initial condition; save it in U ?"}U?m= ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. V0#E7u`4 w=2*pi*n./T; '}>8+vU` g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T 3_eg'EP.E L=4; % length of evoluation to compare with S. Trillo's paper Tn3C0 dz=L/M1; % space step, make sure nonlinear<0.05 j~;y~Cx? for m1 = 1:1:M1 % Start space evolution !+UXu]kA u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS iztF u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; .rDao]K ca1 = fftshift(fft(u1)); % Take Fourier transform )kKeA ca2 = fftshift(fft(u2)); McdK!V c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation ^b.fci{1m c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift &XhxkN$8 u2 = ifft(fftshift(c2)); % Return to physical space VWCC(YRU|$ u1 = ifft(fftshift(c1)); h=NXU9n%' if rem(m1,J) == 0 % Save output every J steps. -/7@ A U1 = [U1 u1]; % put solutions in U array <`A!9+ U2=[U2 u2]; FklO#+<: MN1=[MN1 m1]; 8L@@UUjr z1=dz*MN1'; % output location {+9t!' end sJg3WN end IeIv k55 hg=abs(U1').*abs(U1'); % for data write to excel "(+aWvb ha=[z1 hg]; % for data write to excel /cZcfCW t1=[0 t']; yW"}%)
d hh=[t1' ha']; % for data write to excel file ^#7&R" %dlmwrite('aa',hh,'\t'); % save data in the excel format d _=44( - figure(1) GL&rT& waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn 7tY~8gQel figure(2) )B5U0iIi waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn R*vfp?x H[r6 4~Sth 非线性超快脉冲耦合的数值方法的Matlab程序 =G rg pl 1CEoe 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。 f5nAD 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 \5)
ZI'q ,=}+.ax -r{]9v2j u,@x7a,z % This Matlab script file solves the nonlinear Schrodinger equations %U97{y % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of kr]_?B(r % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear V}G;oz&>) % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 d[ce3':z vmtmiN8;d C=1; 4-xg+*() M1=120, % integer for amplitude a'\fS7aE0l M3=5000; % integer for length of coupler Vao3D8 N = 512; % Number of Fourier modes (Time domain sampling points) D_I_=0qNd dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05. d8f S79 T =40; % length of time:T*T0. -EU~
%/=m+ dt = T/N; % time step tpKQ$)ed n = [-N/2:1:N/2-1]'; % Index ?eR^\-e t = n.*dt; YccD^w[`B ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. C5#$NV99p w=2*pi*n./T; ?~~,?Uxw! g1=-i*ww./2; rP&.`m88n g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; \OF"hPq g3=-i*ww./2; 0OVxx>p/x P1=0; ezk:XDi4 P2=0; 4*+)D8 P3=1; I [v~nY~l` P=0; hKp-" for m1=1:M1 ,tOc+3Qz$ p=0.032*m1; %input amplitude 6q^.Pg-Y s10=p.*sech(p.*t); %input soliton pulse in waveguide 1 .n|
M5X s1=s10; ,W;2A0A?X s20=0.*s10; %input in waveguide 2 -M?s<R[& s30=0.*s10; %input in waveguide 3 32):&X"AIh s2=s20; EXbhyg s3=s30; ,N5-(W p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1)))); Z <tJ+ %energy in waveguide 1 <UO'&?G p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1)))); E.rfS$<1 %energy in waveguide 2 Ha/-v?E p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1)))); T$9tO{ %energy in waveguide 3 q \\52:\ for m3 = 1:1:M3 % Start space evolution UR.l*+<W7 s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS A!!W\Jt s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; rc]`PV s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; HA(G q sca1 = fftshift(fft(s1)); % Take Fourier transform "zBYhZr sca2 = fftshift(fft(s2)); w#`E;fN' sca3 = fftshift(fft(s3)); IH'&W sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift ZZ{:f+=?$ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); b\9}zmG[u sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); ,Tc598D s3 = ifft(fftshift(sc3)); FOd)zU*L2 s2 = ifft(fftshift(sc2)); % Return to physical space !BW6l)=L s1 = ifft(fftshift(sc1)); go$zi5{h# end *4F6U p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); 2p|[yZ p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); JN-wToOF p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); |\/Y<_)JD P1=[P1 p1/p10]; =;^#5dpt$ P2=[P2 p2/p10]; 1-60gI1) P3=[P3 p3/p10]; ^<O=<tN\ P=[P p*p]; pElAY3 end D^9r#& figure(1) WfE,U=e* plot(P,P1, P,P2, P,P3); 8yV?l7 %JC-%TRWK 转自:http://blog.163.com/opto_wang/
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