| 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 F>*{e \^jjK,OK % This Matlab script file solves the coupled nonlinear Schrodinger equations of ;+a2\j+ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of *r;xw % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear fN@{y+6 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 V43TO {?Od{d9 %fid=fopen('e21.dat','w'); =_l)gx+Y+y N = 128; % Number of Fourier modes (Time domain sampling points) |#k@U6`SG M1 =3000; % Total number of space steps \Wr,<Y J =100; % Steps between output of space => qTNh*' T =10; % length of time windows:T*T0 qw<HY$3= T0=0.1; % input pulse width 7\Co`J>p2 MN1=0; % initial value for the space output location [KSH~:h:NR dt = T/N; % time step TkRmV6'w n = [-N/2:1:N/2-1]'; % Index d`mD!)j t = n.*dt; $#e1SS32 u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10 -U>y u20=u10.*0.0; % input to waveguide 2 E;9>ePd@ u1=u10; u2=u20; ZIDbqQu U1 = u1; Or8kp/d U2 = u2; % Compute initial condition; save it in U Rb EKP(uw ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. ;'0=T0\ w=2*pi*n./T; .1#kDM g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T 0OnV0SIL L=4; % length of evoluation to compare with S. Trillo's paper H>XFz(LWh dz=L/M1; % space step, make sure nonlinear<0.05 Qs%B'9") for m1 = 1:1:M1 % Start space evolution 2}vNSQvG u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS tlQC6Fb# u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; ,$N#Us(Wa ca1 = fftshift(fft(u1)); % Take Fourier transform Z+4D.bA ca2 = fftshift(fft(u2)); o:~LF6A- c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation 2%]Z
Kd c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift 4t*so~ u2 = ifft(fftshift(c2)); % Return to physical space * ?]~
# u1 = ifft(fftshift(c1)); O$D?A2eI if rem(m1,J) == 0 % Save output every J steps. Ls}7VKl' U1 = [U1 u1]; % put solutions in U array u -3:k U2=[U2 u2]; -DjJ",h( $ MN1=[MN1 m1]; UE.4qY_7 z1=dz*MN1'; % output location _MuZ4tc end 5)UQWnd5 end }r%X`i| hg=abs(U1').*abs(U1'); % for data write to excel
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(,.' ha=[z1 hg]; % for data write to excel Z"y=sDO{ t1=[0 t']; BUsV|e\ hh=[t1' ha']; % for data write to excel file fQdK]rLj %dlmwrite('aa',hh,'\t'); % save data in the excel format tU:EN;H figure(1) S6g<M5^R waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn +?dl`!rE figure(2) %JyXbv3m, waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn Y`BRh9Sa %IY``r)j 非线性超快脉冲耦合的数值方法的Matlab程序 (Un_!) m@Rtlb 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。 =0
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 ;j%BK(5 k[kju%i4 Vsnuy8~k :O= \<t % This Matlab script file solves the nonlinear Schrodinger equations }`\/f % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of x@KZ] % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear V[nQQxWp= % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 p B;3bc yuhnYR\`m C=1; .(CP. d M1=120, % integer for amplitude =
ieag7! M3=5000; % integer for length of coupler D5,P)[ N = 512; % Number of Fourier modes (Time domain sampling points) x@Hd^xH` dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05. )#iq4@)|g T =40; % length of time:T*T0. S* *oA 6 dt = T/N; % time step N!2Rl n = [-N/2:1:N/2-1]'; % Index VQ#3#Hj t = n.*dt; O1'm@
q) ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. \Ae9\Jp8M w=2*pi*n./T; hC <O`|lF g1=-i*ww./2; tptN6Isuh g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; \ZU1Jb1c g3=-i*ww./2; Q'O[R+YT , P1=0; QPtGdd P2=0; cWyW~Ek P3=1; ^vilgg~ P=0; !> }.~[M for m1=1:M1 3&&9_`r&_ p=0.032*m1; %input amplitude ={>Lrig:l s10=p.*sech(p.*t); %input soliton pulse in waveguide 1 X;v$5UKU s1=s10; Vv1|51B s20=0.*s10; %input in waveguide 2
Q6'x\ s30=0.*s10; %input in waveguide 3 UFAL1c<V s2=s20; \;u@ " s3=s30; ,Uhb p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1)))); _j?e~w&0b %energy in waveguide 1 1K,1X(0rL8 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1)))); A+J*e %energy in waveguide 2 UhA"nt0 p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1)))); VA*y|Q6 %energy in waveguide 3 ,<BbpIQ2o for m3 = 1:1:M3 % Start space evolution xj5;: g#! s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS Sf5X3,Uw s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; ^V$Ajt s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; I$N8tn+E sca1 = fftshift(fft(s1)); % Take Fourier transform X3'H
`/ sca2 = fftshift(fft(s2)); ]I3!fEAWR sca3 = fftshift(fft(s3)); J:&[59 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift EnOU?D sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); MUfG?r\t sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); mKo C.J s3 = ifft(fftshift(sc3)); EBz}|GY; s2 = ifft(fftshift(sc2)); % Return to physical space 9z)5Mdf1j s1 = ifft(fftshift(sc1)); *HEuorl end r'QnX;99T p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); EdZ\1'&/9 p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); g~(E>6Y p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); oy<WsbnS P1=[P1 p1/p10]; ^&y$Wd]6 P2=[P2 p2/p10]; 34\(7JO P3=[P3 p3/p10]; }!IL]0q P=[P p*p]; ,^#yo6- end pPd#N'\* figure(1) 5j~$Mj` plot(P,P1, P,P2, P,P3); P#=`2a#G Yn8= 转自:http://blog.163.com/opto_wang/
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