| 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 |A/_Qe|s2 (IHBib " % This Matlab script file solves the coupled nonlinear Schrodinger equations of 5f@YrTO[@ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of n]c,0N % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear Eq;frnw>q % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 X&oy.Roo mf[79:90^ %fid=fopen('e21.dat','w'); /_\W*@ E N = 128; % Number of Fourier modes (Time domain sampling points) uOqDJM'RM M1 =3000; % Total number of space steps j=% -b] J =100; % Steps between output of space C\@YH] T =10; % length of time windows:T*T0 ,;pX.Ob U T0=0.1; % input pulse width QjN3j*@ MN1=0; % initial value for the space output location "hY^[@7 W dt = T/N; % time step V="f)'S$ n = [-N/2:1:N/2-1]'; % Index O|zmDp8a+ t = n.*dt; ^l9
*h u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10 TFNU+ u20=u10.*0.0; % input to waveguide 2 i1@g Hk u1=u10; u2=u20; 0M2+?aKif U1 = u1; bO%ck-om! U2 = u2; % Compute initial condition; save it in U Pm;*Jv% ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. <f{`}drp/ w=2*pi*n./T; 5MU@g*gj,C g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T >Nl~"J|]q L=4; % length of evoluation to compare with S. Trillo's paper \1D,Kx;Cb dz=L/M1; % space step, make sure nonlinear<0.05 2_v+q for m1 = 1:1:M1 % Start space evolution eG>Fn6G<g u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS sn`?Foh u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; HcS^3^Y ca1 = fftshift(fft(u1)); % Take Fourier transform ([o:_5/8I ca2 = fftshift(fft(u2)); 5{aQ4H>~tx c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation "E!p1 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift y+R$pzX u2 = ifft(fftshift(c2)); % Return to physical space #|E. y^IC u1 = ifft(fftshift(c1)); \ jdO,-( if rem(m1,J) == 0 % Save output every J steps. W?Abx U1 = [U1 u1]; % put solutions in U array &Sp:?I- U2=[U2 u2]; ~x|Sv4M MN1=[MN1 m1]; )W JI=jl z1=dz*MN1'; % output location 4>`w9 end ~2ei+#d!^ end [/j-d hg=abs(U1').*abs(U1'); % for data write to excel :u93yH6~8 ha=[z1 hg]; % for data write to excel c4W"CD;D t1=[0 t']; PP|xIAc hh=[t1' ha']; % for data write to excel file >m{-&1Tx %dlmwrite('aa',hh,'\t'); % save data in the excel format '-TFr NO;h figure(1) S]@iS[|? waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn v3#47F) figure(2) I@v.Hqg+7 waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn Yr0i9Qow sRI8znus 非线性超快脉冲耦合的数值方法的Matlab程序 vtjG&0GSK cu|q& 在研究脉冲在非线性耦合器中的演变时,我们需要求解非线性偏微分方程组。在如下的论文中,我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。 e$I:[> 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 :PkSX*E[q nwH|Hs riU 5|z[%x~f ueo3i1 % This Matlab script file solves the nonlinear Schrodinger equations #R|4(HlL % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of Y:BrAa[ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear l%/,Ef*3 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 X)5O@"4 ? ^S$w,
C=1; `XY[HK M1=120, % integer for amplitude +O6@)?pI M3=5000; % integer for length of coupler obGSc)?j N = 512; % Number of Fourier modes (Time domain sampling points) |9M
y>8k( dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05. 4}j}8y2)H T =40; % length of time:T*T0. .<hv&t
dt = T/N; % time step xSZw, n = [-N/2:1:N/2-1]'; % Index <h0ptCB t = n.*dt; roQIP%h! ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. #}?$mxME* w=2*pi*n./T; qIp`'.#m g1=-i*ww./2; > xw+2< g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
rR;Om1 -, g3=-i*ww./2; #y%Ao\~kG P1=0; ,oe4*b}O=. P2=0; H8U*oLlc P3=1; $E6uA}s P=0;
><^@1z.J for m1=1:M1 ?c*d
z{ p=0.032*m1; %input amplitude .quc i(D s10=p.*sech(p.*t); %input soliton pulse in waveguide 1 E>v~B;@ s1=s10; *x!5I$~J s20=0.*s10; %input in waveguide 2 A+&Va\|x s30=0.*s10; %input in waveguide 3 "zc!QHpSd s2=s20; q~lW s3=s30; o,I642R~ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1)))); yKJp37R %energy in waveguide 1 @"0qS:s]X p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1)))); ,"v% %energy in waveguide 2 =?hlgQ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1)))); 5E8PbV-l %energy in waveguide 3 ^&%?Q_] for m3 = 1:1:M3 % Start space evolution TB\CSXb s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS dl4.jLY s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; AS;{{^mM( s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; 5`Z#m:+u sca1 = fftshift(fft(s1)); % Take Fourier transform ;MD{p1w sca2 = fftshift(fft(s2)); `{":*V
sca3 = fftshift(fft(s3)); 'M{_S sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift )Ec;kr b+ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); nq;)!Wry sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); :OM>z4mQ s3 = ifft(fftshift(sc3)); /uVB[Tk^ s2 = ifft(fftshift(sc2)); % Return to physical space A{vG@Pwc: s1 = ifft(fftshift(sc1)); M?o`tWLhF end +Xk!)Ge5E* p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); rO~D{)Nu p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); 2ou?:5i p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); Z8W<RiR P1=[P1 p1/p10]; ~jaGf P2=[P2 p2/p10]; Ho/5e*X P3=[P3 p3/p10];
xMU) P=[P p*p]; QX4I+x~oo\ end JC-L80- figure(1) wP
i=+ plot(P,P1, P,P2, P,P3); n3w2& 2#^[`sFPO 转自:http://blog.163.com/opto_wang/
|
|