| 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 7!2
HNg Rf[V)x % This Matlab script file solves the coupled nonlinear Schrodinger equations of Dl;d33 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of {K7YTLWY % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 6f]r Q9 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ESDB[
O+`x v$$]Gv( %fid=fopen('e21.dat','w'); H+cNX\, N = 128; % Number of Fourier modes (Time domain sampling points) 8sw,k M1 =3000; % Total number of space steps 5()Fvae{k J =100; % Steps between output of space 7U:=~7GH T =10; % length of time windows:T*T0 W(&6 T0=0.1; % input pulse width ?q%b*Ek MN1=0; % initial value for the space output location ^g!B.ll` dt = T/N; % time step D@vMAW n = [-N/2:1:N/2-1]'; % Index
lfy7w| t = n.*dt; Vm!i u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10 4MX7=!E u20=u10.*0.0; % input to waveguide 2 %D^bahf u1=u10; u2=u20; wOHEv^, U1 = u1; k!E"wJkpz U2 = u2; % Compute initial condition; save it in U 3Xdn62[& ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. #AncOo w=2*pi*n./T; o=9' g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T QHQj/)J8 L=4; % length of evoluation to compare with S. Trillo's paper V.,bwPb{9 dz=L/M1; % space step, make sure nonlinear<0.05 aJ2H.E for m1 = 1:1:M1 % Start space evolution /2h][zrZ[. u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS BW71 s u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; u33zceE8 ca1 = fftshift(fft(u1)); % Take Fourier transform 5<N~3
1z ca2 = fftshift(fft(u2)); @+dHF0aXd c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation WEVl9]b'e+ c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift X')S;KW u2 = ifft(fftshift(c2)); % Return to physical space 8_iHVc;< u1 = ifft(fftshift(c1)); SOI)/u if rem(m1,J) == 0 % Save output every J steps. e\~l!f'z U1 = [U1 u1]; % put solutions in U array sV'v*
1| U2=[U2 u2]; VR v02m5 MN1=[MN1 m1]; n2E4!L|q z1=dz*MN1'; % output location l"L+e! B~ end j i##$xC end #PH#2/[ hg=abs(U1').*abs(U1'); % for data write to excel yiO31uQt ha=[z1 hg]; % for data write to excel M c@GH t1=[0 t']; I{<;;;a hh=[t1' ha']; % for data write to excel file -aN":?8(G %dlmwrite('aa',hh,'\t'); % save data in the excel format >
Z++^YVE figure(1) lWlUWhLnP waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn ^^
j/ figure(2) `5<1EGJsD waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn R.UumBM eE,;K1 非线性超快脉冲耦合的数值方法的Matlab程序 LJ
l1v O=`o'%K< 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。 pVz pN8! 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 (uT^Nn9L= )"-fHW+fy z'e1"Y. zf7rF} % This Matlab script file solves the nonlinear Schrodinger equations c85O_J % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of X{'wWWZC % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear kDg{>mf % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 =N;$0Y(g xiJz`KD& C=1; c&A]pLn+x M1=120, % integer for amplitude 8L{$v~ + M3=5000; % integer for length of coupler W60Q3 N = 512; % Number of Fourier modes (Time domain sampling points) J5-rp| dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05. $~TfL{$ T =40; % length of time:T*T0. taixBNv dt = T/N; % time step
Q_v\1"c n = [-N/2:1:N/2-1]'; % Index B%y! aQep t = n.*dt; F*X%N_n ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. ?.~]mvOR w=2*pi*n./T; # a.\P.{L g1=-i*ww./2; CHg]U l g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; 9g4QVo| g3=-i*ww./2; UMv"7~ P1=0; l&$*}yCK P2=0; 8`DO[Z P3=1; $Llvp bl P=0; I=K[SY,]9 for m1=1:M1 +=Yk-nJ p=0.032*m1; %input amplitude (}6wAfGo s10=p.*sech(p.*t); %input soliton pulse in waveguide 1 i@Vs4E[b s1=s10;
srvYAAE s20=0.*s10; %input in waveguide 2 N]V/83_ s30=0.*s10; %input in waveguide 3 %OuX`w= s2=s20; m^5s>hUl s3=s30; _>;&-e p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1)))); FBcm;cjH %energy in waveguide 1 N: A3kp p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1)))); 7<fL[2- %energy in waveguide 2 {$3j/b p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1)))); k RQ~hRT6 %energy in waveguide 3 9y;y7i{>? for m3 = 1:1:M3 % Start space evolution j,Pwket s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS z( *]'Y s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; t2Ip\>;9f s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; 4Fh&V{`W sca1 = fftshift(fft(s1)); % Take Fourier transform vT&j{2U7XW sca2 = fftshift(fft(s2)); w<v1N sca3 = fftshift(fft(s3)); <&KLo>B^ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift qjJ{+Rz2 sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); u0wn=Dg sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); 2\DTJ`Y, s3 = ifft(fftshift(sc3)); 4n#YDZ s2 = ifft(fftshift(sc2)); % Return to physical space ~v^%ze s1 = ifft(fftshift(sc1)); jC#`PA3m= end `Fz\wPd p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); / *AJ+K._ p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); v/]Qq p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); te4F"SEf P1=[P1 p1/p10]; ]Jja P2=[P2 p2/p10]; _E3U.mV P3=[P3 p3/p10]; LG"c8Vv&)~ P=[P p*p]; |)m*EME end U LV)0SB figure(1) 44Q6vb? plot(P,P1, P,P2, P,P3); 'y'T'2N3 #4Dn@Gqh.Y 转自:http://blog.163.com/opto_wang/
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