| 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 rQEi/ HmExfW
% This Matlab script file solves the coupled nonlinear Schrodinger equations of zBt`L,^ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of D#7_TKX % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear T;!ukGoFP % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 90s;/y( RxZm/:yuJ. %fid=fopen('e21.dat','w'); 1s`)yu^`v N = 128; % Number of Fourier modes (Time domain sampling points) JzMZB"Z? M1 =3000; % Total number of space steps @8nLQh^ J =100; % Steps between output of space >+
]R4 T =10; % length of time windows:T*T0 B:-U`CHHQ T0=0.1; % input pulse width \2Og>{"U MN1=0; % initial value for the space output location uuSR%KK]| dt = T/N; % time step Y}LLOj@L n = [-N/2:1:N/2-1]'; % Index @Y
UY9+D& t = n.*dt; :p<kQ4
u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10 't(}Rq@ u20=u10.*0.0; % input to waveguide 2 5g``30:o u1=u10; u2=u20; 'j,oIqx U1 = u1; d(fPECv( U2 = u2; % Compute initial condition; save it in U qO-C%p
[5 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. o\ngR\> w=2*pi*n./T; R-pH Quu3 g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T '@TI48 J+ L=4; % length of evoluation to compare with S. Trillo's paper qL|
5-(P dz=L/M1; % space step, make sure nonlinear<0.05 JI"/N`-?;b for m1 = 1:1:M1 % Start space evolution ~uI**{ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS tAqA^f*{ u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; #JA}LA"l ca1 = fftshift(fft(u1)); % Take Fourier transform zF5q=9 4$ ca2 = fftshift(fft(u2)); ja[OcR-tX c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation 1")FWN_K/T c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift mG)8U{L u2 = ifft(fftshift(c2)); % Return to physical space Di*]ab u1 = ifft(fftshift(c1)); bD35JG^&i if rem(m1,J) == 0 % Save output every J steps. pkX v.D` U1 = [U1 u1]; % put solutions in U array 6&89~W{
U2=[U2 u2]; A&?}w_|9 MN1=[MN1 m1]; GQN98Y+h z1=dz*MN1'; % output location +z\\VD end Lt1U+o[ot end 4\M8BRuE hg=abs(U1').*abs(U1'); % for data write to excel n]+. ha=[z1 hg]; % for data write to excel BhKO_wQ?:J t1=[0 t']; +YTx
hh=[t1' ha']; % for data write to excel file ^7u X$ %dlmwrite('aa',hh,'\t'); % save data in the excel format <cYp~e%xIw figure(1) a3q\<"| waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn JO2xT#V figure(2) Is13: waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn AD]e0_E Dl%?OG< 非线性超快脉冲耦合的数值方法的Matlab程序 u4YM^* S. k oM]S+1 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。 2FGx _Y 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 s~^*+kq rvic%bsk a/~29gW8E\ B{p4G`$i1 % This Matlab script file solves the nonlinear Schrodinger equations *Bs^NU. % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
EX:{EmaT % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear !z MDP/V % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 #{x5L^v>] 3 > |uF C=1; vM`7s[oAK M1=120, % integer for amplitude >AG^fUArH M3=5000; % integer for length of coupler (/K5! qh N = 512; % Number of Fourier modes (Time domain sampling points) @EHIp{0. dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05. asr=m{C" T =40; % length of time:T*T0. vX+.e1m dt = T/N; % time step WL l_'2h n = [-N/2:1:N/2-1]'; % Index &~#iIk~% t = n.*dt; :a.0hes ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. mc
ZGg;3 w=2*pi*n./T; /b#q*x-b g1=-i*ww./2; txq~+'A:+ g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; rB%y6P B g3=-i*ww./2; 5Z{_m;I. P1=0; R"+wih P2=0; 6NX3"i0eT P3=1; \D?:J3H*] P=0; +TN^NE for m1=1:M1 %/T7Z;d p=0.032*m1; %input amplitude =i>\2J%'R s10=p.*sech(p.*t); %input soliton pulse in waveguide 1 sTkkM9 s1=s10; l~J*' m2 s20=0.*s10; %input in waveguide 2 \9)#l#m s30=0.*s10; %input in waveguide 3 L-\ =J s2=s20; Zu21L3 s3=s30; 5&!'^! p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1)))); #cU^U#;= r %energy in waveguide 1 C>X|VP|C p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1)))); k4{:9zL1#? %energy in waveguide 2 YEv
Lhh p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1)))); S~)w\(r %energy in waveguide 3 5mgHlsDzu for m3 = 1:1:M3 % Start space evolution Ei5 wel6! s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS mS%4gx~~_n s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; r_U>VT^E: s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; Izo! rC sca1 = fftshift(fft(s1)); % Take Fourier transform cin2>3Z$ sca2 = fftshift(fft(s2)); CzVmNy)kl sca3 = fftshift(fft(s3)); -M4p\6)Ge sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift +E5=$` sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); ?6P.b6m}0 sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); a1c1k} s3 = ifft(fftshift(sc3)); W7=V{}b+ s2 = ifft(fftshift(sc2)); % Return to physical space cozXb$bBY s1 = ifft(fftshift(sc1)); E0 l_-- end gR Nv-^ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); ~R]35Cp-# p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); )TJS4? p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); 8=;k" P1=[P1 p1/p10]; WE6\dhJ< P2=[P2 p2/p10]; 4=[7Em?oLb P3=[P3 p3/p10]; t'1Y@e P=[P p*p]; {fDTSr?/ end E(^0B(JF figure(1) H?` g!cX plot(P,P1, P,P2, P,P3); aeP[+ I9 edvFQ#,d 转自:http://blog.163.com/opto_wang/
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