| 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 f*U3s N^y I(!i"b9 % This Matlab script file solves the coupled nonlinear Schrodinger equations of }}L :6^ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of 1P i_V % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear NH+?7rf8 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 VrDSN &[QvMh %fid=fopen('e21.dat','w'); gD`|N@W$5 N = 128; % Number of Fourier modes (Time domain sampling points) ?Vg251-H M1 =3000; % Total number of space steps =GH>-*qp J =100; % Steps between output of space ZYf0FC=- T =10; % length of time windows:T*T0 n$]78\C T0=0.1; % input pulse width zY_?$9l0 MN1=0; % initial value for the space output location X+6`]] dt = T/N; % time step oN3DM; n = [-N/2:1:N/2-1]'; % Index ob= ]( t = n.*dt; [{R^!Az&b< u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10 MPa F u20=u10.*0.0; % input to waveguide 2 rf@Cz%xDD u1=u10; u2=u20; :@x_& b U1 = u1; :'hc&wk` U2 = u2; % Compute initial condition; save it in U p ~LTu<*S ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. jTSN`R9@ w=2*pi*n./T; 47<fg&T g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T M{(g"ha L=4; % length of evoluation to compare with S. Trillo's paper (}!xO?NA( dz=L/M1; % space step, make sure nonlinear<0.05 v*Dz4K# for m1 = 1:1:M1 % Start space evolution }.ZT?p\ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS st4WjX_Q u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; D^m`&asC ca1 = fftshift(fft(u1)); % Take Fourier transform zeqwmV= ca2 = fftshift(fft(u2)); 8D]&wBR: c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation =qWcw7!" c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift | XGj97#M u2 = ifft(fftshift(c2)); % Return to physical space =\ek;d0Tqb u1 = ifft(fftshift(c1)); PH1jN?OEwZ if rem(m1,J) == 0 % Save output every J steps. .
.5s2 U1 = [U1 u1]; % put solutions in U array J=l\t7w U2=[U2 u2]; D*_Z"q_B MN1=[MN1 m1]; )(/Bw&$ z1=dz*MN1'; % output location &mPR[{ end 7=wPd4
end {9c_T!c hg=abs(U1').*abs(U1'); % for data write to excel >2^|r8l5 ha=[z1 hg]; % for data write to excel lWyg_YO@ t1=[0 t']; Efa3{
7>{ hh=[t1' ha']; % for data write to excel file 8
*Y(wqH %dlmwrite('aa',hh,'\t'); % save data in the excel format hy}n&h figure(1) w3>.d(Q waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn j>I.d+ figure(2) K%@#a}kRb waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn }Q1m ^ZD0rp(l 非线性超快脉冲耦合的数值方法的Matlab程序 zI&). m\"X%Y# 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。 |h 3`z 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 (GJX[$@ IAFj_VWC0 knABlU Y-
tK % This Matlab script file solves the nonlinear Schrodinger equations Fu*Qci1Z % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of a
IgV"3 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear +*=?0 \ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 s g6e%
5 @ sG5Do C=1; Lv<)Dur0K M1=120, % integer for amplitude lj+}5ySG/ M3=5000; % integer for length of coupler m'"Ra- N = 512; % Number of Fourier modes (Time domain sampling points) G_5E#{u dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05. rCn"{.rI T =40; % length of time:T*T0. M^?=!!US^ dt = T/N; % time step e=4k|8 G n = [-N/2:1:N/2-1]'; % Index V?C_PMa t = n.*dt; c
6$n: ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. 0qk.NPMB0 w=2*pi*n./T; nH(Hk%~ g1=-i*ww./2; L~} 2&w g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; TM$Ek^fQ. g3=-i*ww./2; I3D#wXW P1=0; ba"a!#wA P2=0; F<^93a9 P3=1; lITZ|u P=0; *3W e5 for m1=1:M1 x1ID6kI[{* p=0.032*m1; %input amplitude
g+iV0bbT s10=p.*sech(p.*t); %input soliton pulse in waveguide 1 )gq( s1=s10; C},$(2>0+ s20=0.*s10; %input in waveguide 2 @5-+>\Hd^t s30=0.*s10; %input in waveguide 3 dj0`Q:VZ s2=s20; k<3_!?3 s3=s30; 3tTz$$-# p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1)))); yYvv;E %energy in waveguide 1 TAu*lL(F p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1)))); SY}iU@xo %energy in waveguide 2 ^2PQ75V@. p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1)))); v1j]&3O %energy in waveguide 3 XU#nqvS` . for m3 = 1:1:M3 % Start space evolution S-:7P.#Q s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS (d C<N3 s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; ^Y:Q%?uB/ s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; D{,B[5 sca1 = fftshift(fft(s1)); % Take Fourier transform r4xq%hy sca2 = fftshift(fft(s2)); OQA3 ~\Vu sca3 = fftshift(fft(s3)); Hvq< _&2 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift | We @p sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); 6zLz<p? sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); 4[!&L:tR s3 = ifft(fftshift(sc3)); 7}r!%<^ s2 = ifft(fftshift(sc2)); % Return to physical space ++13m*fA s1 = ifft(fftshift(sc1)); J 6S end k-
sbZL p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); <!zItFMD[m p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); |"P5%k#6^> p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); @ec QVk P1=[P1 p1/p10]; %'* |N[ P2=[P2 p2/p10]; 3MjMN %{P P3=[P3 p3/p10]; 5Kv=;o=U P=[P p*p]; (>0d+ KT end M14_w, figure(1) =QyO$:t plot(P,P1, P,P2, P,P3); !4jS=Lhe> FZA8@J|Q4 转自:http://blog.163.com/opto_wang/
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