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 |t*(]U2O0 zF6R\w % This Matlab script file solves the coupled nonlinear Schrodinger equations of :@)UI, % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of k@U8K(:x % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear Mg;%];2Nt % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 sHD8#t^{ W)3?T&` %fid=fopen('e21.dat','w'); !!Z#'Wq N = 128; % Number of Fourier modes (Time domain sampling points) }#'wy M1 =3000; % Total number of space steps )orVI5ti J =100; % Steps between output of space |m7U^ T =10; % length of time windows:T*T0 ~K}iVX T0=0.1; % input pulse width OQMkpX-dH MN1=0; % initial value for the space output location Y-\hV6v6 dt = T/N; % time step C( 8i0(1 n = [-N/2:1:N/2-1]'; % Index exw~SvT3 t = n.*dt; [G2@[CtY1 u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10 1oD,E!+^d u20=u10.*0.0; % input to waveguide 2 nmZz`P9g u1=u10; u2=u20; s. I%[kada U1 = u1; ntbl0Sk U2 = u2; % Compute initial condition; save it in U xF:
O6KL ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. V(_OyxeC{2 w=2*pi*n./T; |D+"+w/ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T z<aB GG L=4; % length of evoluation to compare with S. Trillo's paper $Llv6<B dz=L/M1; % space step, make sure nonlinear<0.05 Qd;P?W6 for m1 = 1:1:M1 % Start space evolution >p#` %S u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS "s!!\/^9C u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; 1O@
qpNm ca1 = fftshift(fft(u1)); % Take Fourier transform 4k/B=%l ca2 = fftshift(fft(u2)); n%zW6} c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation nVkx Q?2 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift 0Jz H dz u2 = ifft(fftshift(c2)); % Return to physical space %@
UH,Ew u1 = ifft(fftshift(c1)); |U{9Yy6p if rem(m1,J) == 0 % Save output every J steps. li'h&!|] U1 = [U1 u1]; % put solutions in U array A>WMPe:sSS U2=[U2 u2]; 4?Pdld MN1=[MN1 m1]; [8|Y2Z\N z1=dz*MN1'; % output location r09gB#K4 end %@tKcQ end ' i5 VU4?K hg=abs(U1').*abs(U1'); % for data write to excel {hQ0=rv< ha=[z1 hg]; % for data write to excel j6v|D>I t1=[0 t']; K"u-nroHW hh=[t1' ha']; % for data write to excel file !v/5G_pr %dlmwrite('aa',hh,'\t'); % save data in the excel format 8G$ %DZ $ figure(1) X[/>{rK waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn d: D`rpcC figure(2) 3FRz&FS:j waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn "fK`F/ Xi$( U8J_ 非线性超快脉冲耦合的数值方法的Matlab程序 MMlryn||1 V]I@&*O~r 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。 s~e<Pr?yu 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 $A~UA 8B#;ffkmN a&:1W83 Gk_%WY* % This Matlab script file solves the nonlinear Schrodinger equations J{>9ctN % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of <Sds5 d % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear MKVz'-`u % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 x/~qyX8vo g4b-~1[S C=1; ^(z7?T M1=120, % integer for amplitude 1Q_ C M3=5000; % integer for length of coupler EWOS6Yg7 N = 512; % Number of Fourier modes (Time domain sampling points) >,c$e' h dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05. eu=G[> T =40; % length of time:T*T0. ZEY="pf dt = T/N; % time step -& Qm"-?: n = [-N/2:1:N/2-1]'; % Index WgHl.
:R t = n.*dt; HI iMq'H^ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. +*u'vt? w=2*pi*n./T; {g8uMt\4 g1=-i*ww./2; 0IZaf%zYc g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; ;+v5li g3=-i*ww./2; Pdgn9 P1=0; bVfFhfh* P2=0; V11(EZJ/j P3=1; vW6
a=j8 P=0; ]U[y3 for m1=1:M1 Xjb 4dip p=0.032*m1; %input amplitude Xae0xs s10=p.*sech(p.*t); %input soliton pulse in waveguide 1 b"D? @dGB, s1=s10; JFAmND;+ s20=0.*s10; %input in waveguide 2 w+A:]SU s30=0.*s10; %input in waveguide 3 pypW s2=s20; /#mq*kNIM6 s3=s30; B$A`thQp p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1)))); H~Z$ pk% %energy in waveguide 1 :~uvxiF p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1)))); j^4KczJl %energy in waveguide 2 F;
upb5 p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1)))); )"( ojh %energy in waveguide 3 '8%pEl^ for m3 = 1:1:M3 % Start space evolution ku2gFO s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS oJ\)-qSf s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; TcB^Sctf s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; $qz(9M(m# sca1 = fftshift(fft(s1)); % Take Fourier transform b5!\"v4c sca2 = fftshift(fft(s2)); T,'{0q sca3 = fftshift(fft(s3)); c}XuzgSY sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift FEOr'H<3x sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); P:~Xaz\F sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); }s*H|z s3 = ifft(fftshift(sc3)); w$5~'Cbi s2 = ifft(fftshift(sc2)); % Return to physical space hbZ]DRg s1 = ifft(fftshift(sc1)); ^pI&f{q end
ywQ>T+ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); 4}i2j p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); x"N{5 p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); "zN2+X"& P1=[P1 p1/p10]; _:RQ9x' P2=[P2 p2/p10]; ^{ Kj{M22 P3=[P3 p3/p10]; Vgh;w-a P=[P p*p]; OO7sj@ end V)pn)no'V figure(1) N3M:|D plot(P,P1, P,P2, P,P3); Cx
N]fo |)%]MK$; 转自:http://blog.163.com/opto_wang/
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