| 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 uSn<]OrZo` `]l*H3+hg % This Matlab script file solves the coupled nonlinear Schrodinger equations of 9A9yZl t % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of -JB~yO?0 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear a2`|6M; % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 N'e3< @G>Q(a*, %fid=fopen('e21.dat','w'); !&8HA N = 128; % Number of Fourier modes (Time domain sampling points) i slg5 M1 =3000; % Total number of space steps j= Ebk;6p J =100; % Steps between output of space !S}4b T =10; % length of time windows:T*T0 q8e34Ly7 T0=0.1; % input pulse width |c5r&oM&m MN1=0; % initial value for the space output location 9)]asY dt = T/N; % time step b#z{["%Zp n = [-N/2:1:N/2-1]'; % Index -H(\[{3{V t = n.*dt; ojQjx|Q} u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10 dw
e$, 9 u20=u10.*0.0; % input to waveguide 2 u'Ua ++a\ u1=u10; u2=u20; eZ[O:W vk: U1 = u1; f6-OR]R5 U2 = u2; % Compute initial condition; save it in U y72=d?]W ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. HOrD20 w=2*pi*n./T; auV<=1<zJ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T F8%.-.l) L=4; % length of evoluation to compare with S. Trillo's paper 7Eett)4 dz=L/M1; % space step, make sure nonlinear<0.05 f)/5%W7n} for m1 = 1:1:M1 % Start space evolution b63 tjqk u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS #:n:3]t u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; b )mU9 ca1 = fftshift(fft(u1)); % Take Fourier transform W.t` ca2 = fftshift(fft(u2)); ct#3*] c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation w-M,@[G c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift h1'j1uI u2 = ifft(fftshift(c2)); % Return to physical space }Kc03Ue`%e u1 = ifft(fftshift(c1)); S>s{t=AY~ if rem(m1,J) == 0 % Save output every J steps. %uWq)D4r U1 = [U1 u1]; % put solutions in U array U4hFPK< U2=[U2 u2]; hs m%o\ MN1=[MN1 m1]; ZdjmZx%% z1=dz*MN1'; % output location &6mXsx$ end ndU<,{r end 0pu=, hg=abs(U1').*abs(U1'); % for data write to excel 0j)D[K ha=[z1 hg]; % for data write to excel chr^>%Q_ t1=[0 t']; vw/L|b7G hh=[t1' ha']; % for data write to excel file W<AxctId %dlmwrite('aa',hh,'\t'); % save data in the excel format vUU)zZB~ figure(1) }JePEmj waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn !.nyIA( figure(2) sF`ELrR \ waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn p#eai Anu`F%OzB 非线性超快脉冲耦合的数值方法的Matlab程序 .+ w#n<
1:+f@# 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。 %kRQ9I". 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 O!7v&$]1 ,xeJf6es 97%S{_2m/ x&SG gl % This Matlab script file solves the nonlinear Schrodinger equations .7|kxJq % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of *Fe % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 3+j!{tJ
z2 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ~T_4M Jbrjt/OG#I C=1; uGxh}'& M1=120, % integer for amplitude u\9t+wi}< M3=5000; % integer for length of coupler 6ofi8(n[ N = 512; % Number of Fourier modes (Time domain sampling points) NQx`u"= dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05. AD , T =40; % length of time:T*T0. <lBY dt = T/N; % time step ?Thh7#7LM n = [-N/2:1:N/2-1]'; % Index ]N\J~Gm t = n.*dt; )S;pYVVAl ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. ah(lH5r w=2*pi*n./T; dP0%<Q| g1=-i*ww./2; ,a&&y0, g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; :Rq>a@Rp g3=-i*ww./2; C{r Sq P1=0; j6NK7Li P2=0; 8 )W{C> P3=1; {O4y Y=G P=0; rk$$gXg9/ for m1=1:M1 .D~ZE94@ p=0.032*m1; %input amplitude aWe?n; s10=p.*sech(p.*t); %input soliton pulse in waveguide 1 1I{^]]qw s1=s10; e95x,|.-_ s20=0.*s10; %input in waveguide 2 ,'KQF C s30=0.*s10; %input in waveguide 3 |V 3AA s2=s20; V@QWJZ" s3=s30; am$-1+iX p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1)))); 'k?%39 %energy in waveguide 1 \,b@^W6e> p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1)))); COF_a% %energy in waveguide 2 tdl Y p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1)))); ]Ywj@-*q %energy in waveguide 3 U',9t for m3 = 1:1:M3 % Start space evolution /:YJ2AARY s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS nMniHB' s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; wcdD i[E>i s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; w
A0$d sca1 = fftshift(fft(s1)); % Take Fourier transform >8pmClVvmR sca2 = fftshift(fft(s2)); -W^jmwM sca3 = fftshift(fft(s3)); jP]I>Tq sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift X/5\L.g2 sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); 3(Y#*f| sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); [%8t~zg s3 = ifft(fftshift(sc3)); !yo/ F&6 s2 = ifft(fftshift(sc2)); % Return to physical space %,l+?fF s1 = ifft(fftshift(sc1)); 8op,;Z7Y end
~s
:Ml p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); @dy<=bh~ p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); zjzW;bo( d p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); y?t2@f]!XK P1=[P1 p1/p10]; x"n!nT%Z P2=[P2 p2/p10]; %|6t\[gn P3=[P3 p3/p10]; yEaim~ P=[P p*p]; 63J_u-o end 5eZ8$-&([ figure(1) |Ew~3-u! plot(P,P1, P,P2, P,P3); k,~I>qg M!{;:m28X! 转自:http://blog.163.com/opto_wang/
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