| 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 )c+k_;t'+
bq NP#C % This Matlab script file solves the coupled nonlinear Schrodinger equations of 2"X~ju % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of D"^'.DL@wG % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear Xb,T{.3@ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 to`mnp9Z ]Lm'RlV %fid=fopen('e21.dat','w'); y`So&:1 N = 128; % Number of Fourier modes (Time domain sampling points) ~KPv7WfG M1 =3000; % Total number of space steps VD[pZ2;4 J =100; % Steps between output of space $(rc/h0/E T =10; % length of time windows:T*T0 v@n_F T0=0.1; % input pulse width <#*.}w~ MN1=0; % initial value for the space output location sJU`u'w dt = T/N; % time step Q4Q pn n = [-N/2:1:N/2-1]'; % Index 9:8|)a(1 t = n.*dt; x+7*ADKb u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10 cbYK5fj"T u20=u10.*0.0; % input to waveguide 2 (>7>3 u1=u10; u2=u20; nB] Ia? U1 = u1; 5jZiJw( U2 = u2; % Compute initial condition; save it in U PVYyE3`UB ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. 5k$vlC#[H w=2*pi*n./T; r,;\/^ u* g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T o35fifM` L=4; % length of evoluation to compare with S. Trillo's paper NBOCt)C;H dz=L/M1; % space step, make sure nonlinear<0.05 8@eOTzm for m1 = 1:1:M1 % Start space evolution :NE/Ddgc' u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS }r3~rG<D71 u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; tJU-<{8 ca1 = fftshift(fft(u1)); % Take Fourier transform ^ R~~L ca2 = fftshift(fft(u2)); GBQn_(b9I c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
rLv;Y c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift ,;jGJr u2 = ifft(fftshift(c2)); % Return to physical space sn{tra u1 = ifft(fftshift(c1)); {HrZ4xQnpV if rem(m1,J) == 0 % Save output every J steps. 3WUH~l{UJ U1 = [U1 u1]; % put solutions in U array |5MbAqjzC U2=[U2 u2]; ;Gd~YGW^# MN1=[MN1 m1]; :L:&t,X z1=dz*MN1'; % output location :dwt1> end OZ(dpV9.S end $NG++N hg=abs(U1').*abs(U1'); % for data write to excel +ts0^;QO2{ ha=[z1 hg]; % for data write to excel |.U)ll(c t1=[0 t']; s\3q!A?S3 hh=[t1' ha']; % for data write to excel file .%}+R|g %dlmwrite('aa',hh,'\t'); % save data in the excel format 5v
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Oq figure(1) n7! H:{L waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn tef^ShF] figure(2) Nneo{j waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn (f#b7O-Wn r>t1 _b+nu 非线性超快脉冲耦合的数值方法的Matlab程序 'i|rjW( E6A/SVp 在研究脉冲在非线性耦合器中的演变时,我们需要求解非线性偏微分方程组。在如下的论文中,我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。 ]A+o>#n}x Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ELD!{bMT |i7a@'0) 55DE\<r U[\Vj_?(I % This Matlab script file solves the nonlinear Schrodinger equations h~}.G{" % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of "484n/D % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear uGVy6, % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 QP(BZJC 9A$m$ C=1; v"O5u%P M1=120, % integer for amplitude (<c7<_-H M3=5000; % integer for length of coupler ,kM)7!]N N = 512; % Number of Fourier modes (Time domain sampling points) osP\DiQ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05. >U!*y4 T =40; % length of time:T*T0. cP>o+-) dt = T/N; % time step md Gwh7/3 n = [-N/2:1:N/2-1]'; % Index &^.57] t = n.*dt; nk=$B(h ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. N{Qxq>6 G w=2*pi*n./T; U5r}6D!) g1=-i*ww./2; G}zZQy g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; 9Kv|>#zff g3=-i*ww./2; _aS;!6b8W P1=0; -ysn&d\rV P2=0; +9A\HQ|22 P3=1; ]uh3R{a/ P=0; `BXS)xj for m1=1:M1 R9o- `Wz p=0.032*m1; %input amplitude 7/IlL s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
``K#}3 s1=s10; W;_E 4 s20=0.*s10; %input in waveguide 2 ,_
2x{0w:> s30=0.*s10; %input in waveguide 3 MgMD\ s2=s20; 42C<1@>zO s3=s30; `ldz`yu6++ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1)))); V"KS[>>f %energy in waveguide 1 8Cx^0 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1)))); }
p:%[ %energy in waveguide 2 j;~%lg=) p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1)))); 5FeFN) %energy in waveguide 3 ?&+9WJ<M for m3 = 1:1:M3 % Start space evolution mI1H! s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS Jh/ E@}' s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; ?h8{xa5b s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; Lxl_"kG sca1 = fftshift(fft(s1)); % Take Fourier transform &2.u%[gO[q sca2 = fftshift(fft(s2)); $)~ sca3 = fftshift(fft(s3)); /F/;G*n sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift wIvo"|% sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); ?}P5p^6 sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); 'Prxocxq s3 = ifft(fftshift(sc3)); 0#p/A^\#7M s2 = ifft(fftshift(sc2)); % Return to physical space s][24)99 s1 = ifft(fftshift(sc1)); |UUdz_i!: end oYM3Rgxf9Q p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); 4"?^UBr p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); 9WG{p[ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); 9)dfL?x8V{ P1=[P1 p1/p10]; UK[v6".^h P2=[P2 p2/p10]; 6QQfQ, P3=[P3 p3/p10]; ;3'NMk P=[P p*p]; |AZW9 end |UnUG figure(1) Q4]4@96Aj plot(P,P1, P,P2, P,P3); V4w=/e_ n$L51#' 转自:http://blog.163.com/opto_wang/
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