| 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 !=PH5jTY 7<*0fy5n n % This Matlab script file solves the coupled nonlinear Schrodinger equations of h@\-]zN{ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of li
v=q % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear &M<"Fmn % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 tpEy-"D& U~)5 { %fid=fopen('e21.dat','w'); "igA^^?X1N N = 128; % Number of Fourier modes (Time domain sampling points) w8R7Ksn( M1 =3000; % Total number of space steps ZS4dW_*[ J =100; % Steps between output of space
{U$XHG T =10; % length of time windows:T*T0 =0]K(p, T0=0.1; % input pulse width bGL} nPo MN1=0; % initial value for the space output location *?d\Zcj85[ dt = T/N; % time step d~r A`!s7` n = [-N/2:1:N/2-1]'; % Index cW_wIy\]& t = n.*dt; =X^a u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10 F-rhxJd u20=u10.*0.0; % input to waveguide 2 u"(NN9s u1=u10; u2=u20; :Ae#+([V U1 = u1; Hv/5) U2 = u2; % Compute initial condition; save it in U kP+,x H)1 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. ^67}&O^1 , w=2*pi*n./T; 9
@ < g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T B>>_t2IU L=4; % length of evoluation to compare with S. Trillo's paper NJgu`@YoI dz=L/M1; % space step, make sure nonlinear<0.05 IqFcrU$4 for m1 = 1:1:M1 % Start space evolution 2t_g\Q u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS Zv!XNc!"$y u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; Q"D ca1 = fftshift(fft(u1)); % Take Fourier transform NQ;X|$!zH ca2 = fftshift(fft(u2)); +aL c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation 89^g$ ac c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift Qs
za,09 u2 = ifft(fftshift(c2)); % Return to physical space fX 1%I u1 = ifft(fftshift(c1)); O50<h O]l if rem(m1,J) == 0 % Save output every J steps. 9xz@2b@ U1 = [U1 u1]; % put solutions in U array ^pd7nr~Y U2=[U2 u2]; MnqT?Cc4$j MN1=[MN1 m1]; b way+lh z1=dz*MN1'; % output location No6-i{HZ end P ?f${t+ end :%J;[bS+ hg=abs(U1').*abs(U1'); % for data write to excel ;YY<KuT ha=[z1 hg]; % for data write to excel i6k6l% t1=[0 t']; oF>`> hh=[t1' ha']; % for data write to excel file A :KZyd"Z %dlmwrite('aa',hh,'\t'); % save data in the excel format xtD(tiqh.; figure(1) B
E8_.> waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn WwTl|wgvyI figure(2) HQ9tvSc waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn 0+op|bdj `r-Jy{!y4 非线性超快脉冲耦合的数值方法的Matlab程序 F7O*%y.'; 8)?&eE' 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。 "Y L^j~A 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 e,p*R?Y{[ !`H{jwH u28$V]
PkyX,mr#1 % This Matlab script file solves the nonlinear Schrodinger equations ~Yg)8 % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of 9#P~cW? % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear S-o)d % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 "1^tVw| y[.lfW?) C=1; -ak.wwx\ M1=120, % integer for amplitude X9|*`h < M3=5000; % integer for length of coupler X41Qkf{ N = 512; % Number of Fourier modes (Time domain sampling points) //|B?4kk dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05. 2;"vF9WMm T =40; % length of time:T*T0. 7L&,Na dt = T/N; % time step 9y&;6V.' n = [-N/2:1:N/2-1]'; % Index DFQ`(1Q t = n.*dt; Q njK<}M9 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. YYFS
({ w=2*pi*n./T; _F[a2PE2+ g1=-i*ww./2; ww7nQ}H5( g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; AN:s%w2 g3=-i*ww./2; lJ= EP.T P1=0; =dHdq D P2=0; nTo?~=b P3=1; 2>^(&95M P=0; Ew{*)r)m for m1=1:M1 $$.q6 p=0.032*m1; %input amplitude ^&86VBP s10=p.*sech(p.*t); %input soliton pulse in waveguide 1 h_P[B s1=s10; ;}f {o^ ]' s20=0.*s10; %input in waveguide 2 5<`83;R9 s30=0.*s10; %input in waveguide 3 ktynIN s2=s20; iR9duP+ s3=s30; iOhX\@& p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1)))); k3t]lGp %energy in waveguide 1 J`0dF<<{[y p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1)))); [Q8Wy/o
Q %energy in waveguide 2 +{=U!}3| p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1)))); m?yztm~u %energy in waveguide 3 r`sKe
& for m3 = 1:1:M3 % Start space evolution ~Azj Y 8 s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS _u6NaB s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; rp<~=X s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; D`[@7$t sca1 = fftshift(fft(s1)); % Take Fourier transform :}fA98S sca2 = fftshift(fft(s2)); R"HV|Dm|m sca3 = fftshift(fft(s3)); cE`qfz sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift CfS;F sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); U_'M9g{,< sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); q]pHD})O s3 = ifft(fftshift(sc3)); .p=J_%K}0x s2 = ifft(fftshift(sc2)); % Return to physical space &g90q s1 = ifft(fftshift(sc1)); _i7yyt;h end A#?Cts,M p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); P8h|2,c% p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); ^Tj{}<yT p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); &$2d=q8mh P1=[P1 p1/p10]; `?[,1 P2=[P2 p2/p10]; %wru) P3=[P3 p3/p10]; 6
F 39' P=[P p*p]; _]ZlGq!L end ct=K.m@E%X figure(1) ,d lq2 plot(P,P1, P,P2, P,P3); CF-tod PWp=}f.y 转自:http://blog.163.com/opto_wang/
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