| 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 q)Cwc[H z[+Sb; % This Matlab script file solves the coupled nonlinear Schrodinger equations of 8"yZS)09
% soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of +sFpIiJg % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear v$~$_K % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 r<c&;* o9]i
{e>L %fid=fopen('e21.dat','w'); (C.<H6]= N = 128; % Number of Fourier modes (Time domain sampling points) "X,*VQl: M1 =3000; % Total number of space steps l?)!^}Qc J =100; % Steps between output of space UAe8Ct=YJ T =10; % length of time windows:T*T0 +sT S1t T0=0.1; % input pulse width ?4cj"i MN1=0; % initial value for the space output location P"%f8C~r dt = T/N; % time step PWk\#dJN& n = [-N/2:1:N/2-1]'; % Index oe<DP7e t = n.*dt; PnZC
I!Mw u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10 W[<ZI>mf u20=u10.*0.0; % input to waveguide 2 l!mx,O` u1=u10; u2=u20; _"[Ls?tRX U1 = u1; 2;ju/9x U2 = u2; % Compute initial condition; save it in U yS1i$[JV ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. W5,&*mo w=2*pi*n./T; r1[c+Hy g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T C`qE ,2. L=4; % length of evoluation to compare with S. Trillo's paper aUk]wiwIR9 dz=L/M1; % space step, make sure nonlinear<0.05 XNJ3.w:R for m1 = 1:1:M1 % Start space evolution 53WCF[ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS X^Fc^U8 u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; i
?PgYk&} ca1 = fftshift(fft(u1)); % Take Fourier transform s;cGf+ ca2 = fftshift(fft(u2)); *Gul|Lp$<I c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation 1YNw= c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift (0E<Fz
V u2 = ifft(fftshift(c2)); % Return to physical space 1pAcaJzf u1 = ifft(fftshift(c1)); otX/sg.B* if rem(m1,J) == 0 % Save output every J steps. xVk5% U1 = [U1 u1]; % put solutions in U array }0,dG4Oo= U2=[U2 u2]; XK&G `cJ[ MN1=[MN1 m1]; foUB/&Ee z1=dz*MN1'; % output location 28qlp>U end 8SA"
bH: end #>6Jsnv1 hg=abs(U1').*abs(U1'); % for data write to excel 0D Lw ha=[z1 hg]; % for data write to excel RM;Uq>l t1=[0 t']; P$Q,t2$A hh=[t1' ha']; % for data write to excel file }N&?8s= %dlmwrite('aa',hh,'\t'); % save data in the excel format vXm'ARj
figure(1) G*_qqb{B waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn 60 %VG figure(2) C_Z/7x*>d waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn Y"L |D,ex #p
;O3E@ 非线性超快脉冲耦合的数值方法的Matlab程序 n?U^vK_ OG9 '[o`8 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。 U\(71= 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
WSgO(y w' E(9gV '{-Ic?F<P @]!9;?so % This Matlab script file solves the nonlinear Schrodinger equations {Fqwr>e % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of *d`KD64 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear $01csj % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 TF9A4 W,"Re,`H C=1; n
=WH=:& M1=120, % integer for amplitude \d*ts(/a* M3=5000; % integer for length of coupler 4jSYR#Hqp` N = 512; % Number of Fourier modes (Time domain sampling points) r.lHlHl dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05. A{e>7Z72 T =40; % length of time:T*T0. XhA tf@n dt = T/N; % time step \B^NdG5Y n = [-N/2:1:N/2-1]'; % Index C1+f\A|9FP t = n.*dt; +u&[ j/ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. uq;yR[w" w=2*pi*n./T; y+Hz(}4 g1=-i*ww./2; 9g\;L:' g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; $s4.Aj g3=-i*ww./2; J?EDz, P1=0; ANNVE}, P2=0; I$MlIz$l v P3=1; 8N+T=c P=0; bLSc=f& for m1=1:M1 jijwHL p=0.032*m1; %input amplitude zvVo-{6 s10=p.*sech(p.*t); %input soliton pulse in waveguide 1 w$Fg0JS s1=s10; Rj4C-X4= s20=0.*s10; %input in waveguide 2 YYT#{>& s30=0.*s10; %input in waveguide 3 <_ENC>NP s2=s20; TEh.?
s3=s30; !\$V?*p7 p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1)))); !/!ga)Y %energy in waveguide 1 -7]j[{?w p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1)))); }i,r{Y]s] %energy in waveguide 2 JXMH7 p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1)))); zj(V\y&H %energy in waveguide 3 %1$#fxR for m3 = 1:1:M3 % Start space evolution 7~F~ 'V s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS Sb> &m s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; IRwtM'%0 s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; =JW-EQ6[T sca1 = fftshift(fft(s1)); % Take Fourier transform d$n31F sca2 = fftshift(fft(s2));
)UM^#<- sca3 = fftshift(fft(s3)); _Z!@#y@j sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift 2aX*|DGpw sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); EwX{i}j_V sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); yW(|auq s3 = ifft(fftshift(sc3)); n=bdV(?4 s2 = ifft(fftshift(sc2)); % Return to physical space KbtV> s1 = ifft(fftshift(sc1)); W7
dSx end \Dy|}LE p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); #CaPj:>[ p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); pmvd%X\f p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); -YAtM-VL P1=[P1 p1/p10]; 5QLK P2=[P2 p2/p10]; gK9d `5 P3=[P3 p3/p10]; Qj;{Z*l%+ P=[P p*p]; ,aLwOmO end aY#?QjL figure(1) 1kKfFpN plot(P,P1, P,P2, P,P3); %^HE^ & ~^V&n`*7D 转自:http://blog.163.com/opto_wang/
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