| 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 jK^Q5iD .9NYa |+0 % This Matlab script file solves the coupled nonlinear Schrodinger equations of l+nT$IPF % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of WuuF&0?8C % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
B\54e Tn % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 %T6
sm s$gR;su)g %fid=fopen('e21.dat','w'); )JrG`CvdU N = 128; % Number of Fourier modes (Time domain sampling points) ;kDUQw M1 =3000; % Total number of space steps Lv&9s J =100; % Steps between output of space 9Bao~(j/k T =10; % length of time windows:T*T0 Y_zMj`HE T0=0.1; % input pulse width XCyU)[wY MN1=0; % initial value for the space output location xlcL;e&^P dt = T/N; % time step &+5ij;AD n = [-N/2:1:N/2-1]'; % Index zC,c9b t = n.*dt; W1Vy5V|M u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10 $c{fPFe- u20=u10.*0.0; % input to waveguide 2 Xj9\:M- u1=u10; u2=u20; +)hxYLk&I U1 = u1; 0%<OwA2d U2 = u2; % Compute initial condition; save it in U ({3Ap{Q} ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. hmkm^2 w=2*pi*n./T; N7u|<
0[ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T NkV81? L=4; % length of evoluation to compare with S. Trillo's paper XL[Dmu& dz=L/M1; % space step, make sure nonlinear<0.05 h! Bg}B~ for m1 = 1:1:M1 % Start space evolution ds2%i
u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS S]&:R)#@ u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; ?W>`skQ ca1 = fftshift(fft(u1)); % Take Fourier transform M5a&eO ca2 = fftshift(fft(u2)); jM}(?^@ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation {/j gB"9 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift |}? H$d u2 = ifft(fftshift(c2)); % Return to physical space %M3L<2 u1 = ifft(fftshift(c1)); &,P; 7 R if rem(m1,J) == 0 % Save output every J steps. .07"I7 U1 = [U1 u1]; % put solutions in U array _N {4Rs0 U2=[U2 u2]; [D+,I1u2h MN1=[MN1 m1]; 8_VGB0~3i z1=dz*MN1'; % output location $1$0M end jddhX]>I end aGd
wuD hg=abs(U1').*abs(U1'); % for data write to excel ~N%+ZXh&E ha=[z1 hg]; % for data write to excel -{}h6r t1=[0 t']; O{EPq' x hh=[t1' ha']; % for data write to excel file dF[|9%) %dlmwrite('aa',hh,'\t'); % save data in the excel format jGi{:} `lB figure(1) ,5V6=pr$ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn +_L]d6
figure(2) 80=LT-%# waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn xG;;ykh.] l$Vy\CfK3n 非线性超快脉冲耦合的数值方法的Matlab程序 qm"SN<2S* ?nPG#Z|% 在研究脉冲在非线性耦合器中的演变时,我们需要求解非线性偏微分方程组。在如下的论文中,我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。 !?>QN'p.b Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 8_E(.]U _Vl~'+ e 'A>?aUq]: t7xJ$^p[|K % This Matlab script file solves the nonlinear Schrodinger equations dl"=ZI
'^ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of ttdY]+Fj % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear {i+
o'Lw % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 !u'xdV+bf gD51N()s, C=1; u]Q}jqiq" M1=120, % integer for amplitude S6}_N/;6~ M3=5000; % integer for length of coupler 064k;|>D N = 512; % Number of Fourier modes (Time domain sampling points) tfe]=_U dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05. U3C"o|
T =40; % length of time:T*T0. w\MWr+4 dt = T/N; % time step g^Hf^%3xP n = [-N/2:1:N/2-1]'; % Index B~^*@5#0| t = n.*dt; >|c?ZqW ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. Ka6u*:/ w=2*pi*n./T; $#-rOi / g1=-i*ww./2; ImG8v[Q
E g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; Q=8YAiCu g3=-i*ww./2; *RxJ8.G P1=0; =%<,
^2o P2=0; n?nzm "g P3=1; 6}m `_d? P=0; "0uM%*2 for m1=1:M1 O Bcz'f~ p=0.032*m1; %input amplitude SzIzQR93& s10=p.*sech(p.*t); %input soliton pulse in waveguide 1 @I-,5F|r s1=s10; {ZrlbDQX s20=0.*s10; %input in waveguide 2 Yb^e7Eug s30=0.*s10; %input in waveguide 3 #2s}s<Sc; s2=s20; ;-8.~Sm s3=s30; JH{/0x#+ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1)))); zt:
!hM/Vt %energy in waveguide 1 tVO}{[U} p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1)))); 4~3
n
=T* %energy in waveguide 2 G"`
}"T0} p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1)))); u.|%@ %energy in waveguide 3 ~CT]&({ for m3 = 1:1:M3 % Start space evolution +Eh.PWEe s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS nKzm.D gt_ s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; z?<B@\~ s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; =]]1x_GB sca1 = fftshift(fft(s1)); % Take Fourier transform 4VZI]3K, sca2 = fftshift(fft(s2)); l99Lxgx= sca3 = fftshift(fft(s3)); ij!d-eM/b sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift _\KFMe=PV sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); )M.s<Y sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); gy%.+!4>v` s3 = ifft(fftshift(sc3)); =TDKU s2 = ifft(fftshift(sc2)); % Return to physical space ']TWWwj$ s1 = ifft(fftshift(sc1)); eJTU'aX* end &muBSQ- p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); 6`O,mpPu4G p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); 8 7(t<3V& p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); WI4<2u; P1=[P1 p1/p10]; w.w{L=p:<" P2=[P2 p2/p10]; L4Zt4Yuw P3=[P3 p3/p10]; I{OizBom P=[P p*p]; ~*7$aj end QZ l#^-on figure(1) g}v](Q plot(P,P1, P,P2, P,P3); Ny2
Z
<TW udqrHR5 转自:http://blog.163.com/opto_wang/
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