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 P}.yEta fxtYo,;$ % This Matlab script file solves the coupled nonlinear Schrodinger equations of Zo}\gg3 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of Bcd0 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 8+g|>{Vov % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 '%eaK_+7 U#FJ8CD&u %fid=fopen('e21.dat','w'); Q%AS;(d N = 128; % Number of Fourier modes (Time domain sampling points) F_M~!]<na M1 =3000; % Total number of space steps HPd+Bd J =100; % Steps between output of space Tg{dIh.Q~O T =10; % length of time windows:T*T0 !,-qn)b T0=0.1; % input pulse width u6bB5(s`& MN1=0; % initial value for the space output location 4%c7#AX[T dt = T/N; % time step u[6`Jr~ n = [-N/2:1:N/2-1]'; % Index .@/z-OgXg t = n.*dt; 46.q anh u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10 B#Oc8`1Y u20=u10.*0.0; % input to waveguide 2 t6,M u1=u10; u2=u20; NNREt:+kr
U1 = u1; /S=;DxZ,r U2 = u2; % Compute initial condition; save it in U NGb!7Mu9 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. !tFU9Zt w=2*pi*n./T; WSpg(\Cs g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T RZ,<D I L=4; % length of evoluation to compare with S. Trillo's paper ~:RDw<PWp dz=L/M1; % space step, make sure nonlinear<0.05 o`y*yucHI for m1 = 1:1:M1 % Start space evolution e&a[k u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS [2H(yLw O u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; W<Vzd4hR ca1 = fftshift(fft(u1)); % Take Fourier transform )1tnZ=& ca2 = fftshift(fft(u2)); WY.\<$7 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
"ppb%= c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift ,*}g
r u2 = ifft(fftshift(c2)); % Return to physical space %Cbc@=k u1 = ifft(fftshift(c1)); VkP:%-*#v if rem(m1,J) == 0 % Save output every J steps. C6=;(=?C U1 = [U1 u1]; % put solutions in U array (=&bo p U2=[U2 u2]; !^"!fuoNC MN1=[MN1 m1]; U*+!w@
. z1=dz*MN1'; % output location DGuUI}|) end F#37Qv end yfw>y=/p hg=abs(U1').*abs(U1'); % for data write to excel IkXKt8`YVA ha=[z1 hg]; % for data write to excel %RD7=Z-z t1=[0 t']; H|Fqc=qp hh=[t1' ha']; % for data write to excel file a518N*]j %dlmwrite('aa',hh,'\t'); % save data in the excel format =x.v*W]F` figure(1) Z?!:=x>7m waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn LXEu^F~{u# figure(2) !&:W1Jkp( waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn z?) RF[ d\<aJOi+- 非线性超快脉冲耦合的数值方法的Matlab程序 +q,n}@y= A
=Az[ 在研究脉冲在非线性耦合器中的演变时,我们需要求解非线性偏微分方程组。在如下的论文中,我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。 X|n[9h:% Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ws(}K+y_ D!E 9@*Lf )+{omQ7v ; dHOH\,: % This Matlab script file solves the nonlinear Schrodinger equations rxK[CDM, % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of [,?A$Z*Z| % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear j]F3[gpc % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 wk
<~Y 3u xbH!:R; C=1; xp;8p94 M1=120, % integer for amplitude :x5o3xE M3=5000; % integer for length of coupler c68$pgG N = 512; % Number of Fourier modes (Time domain sampling points) % |Gzht\ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05. 7/$Z7J!k T =40; % length of time:T*T0. hE`%1j2( dt = T/N; % time step 8 P y_Y> n = [-N/2:1:N/2-1]'; % Index jE5
9h t = n.*dt; p){RSq ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. 5}^08Xl w=2*pi*n./T; n_NG~/x g1=-i*ww./2; ?;7>`F6ld g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; bzL;)H4Eo g3=-i*ww./2; iW%0pLn P1=0; +q?0A^C> P2=0; ^WYG?/{4 P3=1; v@1Jhns P=0; .?)oiPW# for m1=1:M1 7Z :l;%]K p=0.032*m1; %input amplitude !F s)"? s10=p.*sech(p.*t); %input soliton pulse in waveguide 1 IG@&l0ARL s1=s10; M@ZpgAfq s20=0.*s10; %input in waveguide 2 M#<fh:> s30=0.*s10; %input in waveguide 3 E6\~/=X=% s2=s20; 8}b[Q/h! s3=s30; @{GxQzo p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1)))); *1]k&#s %energy in waveguide 1 3\~fe/z'I p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1)))); eeR@p$4i %energy in waveguide 2 t-m,~Io W p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1)))); F&j|Y>m %energy in waveguide 3 ba:^zO^ for m3 = 1:1:M3 % Start space evolution &IY_z0= s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS EF{'J8AQ s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; h/~BUg' s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; 90k|u'ikOp sca1 = fftshift(fft(s1)); % Take Fourier transform ~g|0uO}. sca2 = fftshift(fft(s2)); #EK8Qe_ sca3 = fftshift(fft(s3)); 4T\/wyq0 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift }n8;A;axi sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); $ =a$z" sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); \(t>(4s_~ s3 = ifft(fftshift(sc3)); i_^NbC s2 = ifft(fftshift(sc2)); % Return to physical space 9uoj3Rh< s1 = ifft(fftshift(sc1)); Gl:T end UC$+&&rO p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); "lb!m9F{ p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); "<R
2oo)^ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); VQ}3r)ch P1=[P1 p1/p10]; qnV9TeU) P2=[P2 p2/p10]; nECf2>Yp v P3=[P3 p3/p10]; wA&)y>n- P=[P p*p]; BkqW>[\5xm end %+J*oFwQu figure(1) .[s82c]]6 plot(P,P1, P,P2, P,P3); Av4E?@R .Q@'O b` 转自:http://blog.163.com/opto_wang/
|
|