| 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 9"1=um= ~e,K % This Matlab script file solves the coupled nonlinear Schrodinger equations of V_v+i c^ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of 2fc+PE % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear yJqDB$0 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 6rG7/ Yu&\a?]\2 %fid=fopen('e21.dat','w'); P&5vVA6K7 N = 128; % Number of Fourier modes (Time domain sampling points) R*LPwJuv M1 =3000; % Total number of space steps _3f/lG?&- J =100; % Steps between output of space F/A)2 H_ T =10; % length of time windows:T*T0 WRAv>s9 T0=0.1; % input pulse width ^dxy%*Z/ MN1=0; % initial value for the space output location T?u*ey~Tv dt = T/N; % time step +U<Ae^V n = [-N/2:1:N/2-1]'; % Index DX3jE p2 t = n.*dt; MfLus40;n u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10 aG@GJ@w u20=u10.*0.0; % input to waveguide 2 l`0JL7 u1=u10; u2=u20; G~*R6x2g U1 = u1; 436SIh U2 = u2; % Compute initial condition; save it in U r`u 9MJ* ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. 5HvYy
*B/ w=2*pi*n./T; {EU]\Mp0j g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T Mwj7*pxUh L=4; % length of evoluation to compare with S. Trillo's paper p<@+0Uw2 dz=L/M1; % space step, make sure nonlinear<0.05 aM8z_j!!u for m1 = 1:1:M1 % Start space evolution l`JKQk u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS <_bGV u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; K~5(j{Kb8 ca1 = fftshift(fft(u1)); % Take Fourier transform )5;|mV ca2 = fftshift(fft(u2)); ?PB}2*R c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation dwzk+@]8 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift u8y('\( u2 = ifft(fftshift(c2)); % Return to physical space a5@lWpQsV u1 = ifft(fftshift(c1)); "bO]AG if rem(m1,J) == 0 % Save output every J steps.
_ @|_`5W U1 = [U1 u1]; % put solutions in U array 0b,{4DOD U2=[U2 u2]; Gn10)Uf8X MN1=[MN1 m1]; Rg~[X5 z1=dz*MN1'; % output location *(*XNd|| end bV@5B#] 2R end i2Gh!5]f hg=abs(U1').*abs(U1'); % for data write to excel hM(Hq4ed, ha=[z1 hg]; % for data write to excel \WVY@eB t1=[0 t']; n^epC>a" b hh=[t1' ha']; % for data write to excel file $:D hK %dlmwrite('aa',hh,'\t'); % save data in the excel format rIH+X2x figure(1) I)G.tJZ
e waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn G&0JK ,Y figure(2) hA"z0Fszh waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn #xrE^Txh (W`=`]! 非线性超快脉冲耦合的数值方法的Matlab程序 ve=1y) lCK:5$
z0 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。 A)^A2xZQ 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 !P _'n N%?8Bm~dP YH!` uU(Lh l)1ySX&BU % This Matlab script file solves the nonlinear Schrodinger equations ,rQPs % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of >Gxu8,_; % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear /lvH p
% pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ;\+A6(GX{ ga91#NWgK C=1; C?b_E M1=120, % integer for amplitude Tq >?.bq9 M3=5000; % integer for length of coupler \6Hu&WHy N = 512; % Number of Fourier modes (Time domain sampling points) %G~%:uJ5 dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05. en gh3TZC T =40; % length of time:T*T0. zd[cp@ dt = T/N; % time step ~E7=c3:" n = [-N/2:1:N/2-1]'; % Index O7I|<H/gVE t = n.*dt; P1QGfp0-J ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. ^`!EpO>k9 w=2*pi*n./T; #EU x1II g1=-i*ww./2; Ibl==Irk g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; uI[lrMQYa g3=-i*ww./2; -U_<: P1=0; })r[qsv P2=0; @AkD-}^[ P3=1; 30/( P=0; Rs%6O|u7 for m1=1:M1 kv3jbSKCT p=0.032*m1; %input amplitude )u'(" s10=p.*sech(p.*t); %input soliton pulse in waveguide 1 8/E?3a_g- s1=s10; -{fbZk&A s20=0.*s10; %input in waveguide 2 7":0CU%% s30=0.*s10; %input in waveguide 3 =zW.~(c{ s2=s20; o%tvwv s3=s30; +#y[sKa p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1)))); $
V"7UA22 %energy in waveguide 1 ;HaG-c</ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1)))); *tT}y(M %energy in waveguide 2 nZM|8 p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1)))); Iih~rWJ %energy in waveguide 3 &wZ:$lK#o for m3 = 1:1:M3 % Start space evolution 5lC "10 s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS ~?{@0,$ s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; TNV# s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; Mzx y'UV sca1 = fftshift(fft(s1)); % Take Fourier transform hzc2 c.gcF sca2 = fftshift(fft(s2)); u37@9 sca3 = fftshift(fft(s3)); b-+iL sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift =lG5Kc{B sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); rT
~qoA\ sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); ,*V{gpC7 s3 = ifft(fftshift(sc3)); g=:C/>g s2 = ifft(fftshift(sc2)); % Return to physical space IXf@YV s1 = ifft(fftshift(sc1)); <H~ (iQ end 3u8H F- p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); o^},L? p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); A_@#V)D2 p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
p_QL{gn P1=[P1 p1/p10]; '5eW"HGU]` P2=[P2 p2/p10]; fF8g3|p: P3=[P3 p3/p10]; eW+z@\d9Gz P=[P p*p]; u U>Bun
end ([ xYOxcp5 figure(1) jfHVXu^M plot(P,P1, P,P2, P,P3); 8\t~*@" m`-{ V<(M 转自:http://blog.163.com/opto_wang/
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