| 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 iB{O"l@w
hV_0f_Og % This Matlab script file solves the coupled nonlinear Schrodinger equations of 7u0!Q\ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of \=1k29O % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear [@Y?'={qE % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 V*LpO8= O]`CSTv'_ %fid=fopen('e21.dat','w'); '\P6NszY~ N = 128; % Number of Fourier modes (Time domain sampling points) ^,@Rd\q M1 =3000; % Total number of space steps 7h,SX]4Q J =100; % Steps between output of space 4k}u`8 a T =10; % length of time windows:T*T0 BoXQBcG]w T0=0.1; % input pulse width VcA87*pel MN1=0; % initial value for the space output location ]QRhTz dt = T/N; % time step ^~?VD n = [-N/2:1:N/2-1]'; % Index .pK_j~}P t = n.*dt; q8`JRmt)H u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10 \ c9EE- u20=u10.*0.0; % input to waveguide 2 MYDAS- u1=u10; u2=u20; :(N3s9:vz U1 = u1; "4zTP!Ow U2 = u2; % Compute initial condition; save it in U nTyKZ(#u ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. X^7bOFWE w=2*pi*n./T; }hhDJ_I5M g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T Kb#py6 L=4; % length of evoluation to compare with S. Trillo's paper >^{}Hjt dz=L/M1; % space step, make sure nonlinear<0.05 uveTx for m1 = 1:1:M1 % Start space evolution fU8 &fo%ER u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS YOd0dKe u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; 7&qunK' ca1 = fftshift(fft(u1)); % Take Fourier transform _}8O15B| ca2 = fftshift(fft(u2)); C5$1K'X@ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation = ;4cDmZh c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift ]`b/_LJN$F u2 = ifft(fftshift(c2)); % Return to physical space 9m/v^ u1 = ifft(fftshift(c1)); +' QX` if rem(m1,J) == 0 % Save output every J steps. aTxss:7] U1 = [U1 u1]; % put solutions in U array TkM8GK-3 U2=[U2 u2]; 'D;v>r MN1=[MN1 m1]; jA?A)YNQb z1=dz*MN1'; % output location 4 bw8^ end @Xts}(L end 7LbBS:@3z_ hg=abs(U1').*abs(U1'); % for data write to excel }.>( [\q ha=[z1 hg]; % for data write to excel
qH1[BsOx t1=[0 t']; ]6bh #N;. hh=[t1' ha']; % for data write to excel file Rt} H.D
# %dlmwrite('aa',hh,'\t'); % save data in the excel format Tu"bbc figure(1) pWa'Fd waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn _
fJ5z figure(2) _Ryt|# y waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn i 3?=up! 0z1m!tr 非线性超快脉冲耦合的数值方法的Matlab程序 0Ihp`QGU: JR] /\( 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。 G:7HL5u 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 q$L=G roSdcQTeT DO`
K_B ">_<L.,I % This Matlab script file solves the nonlinear Schrodinger equations S:aAR*<6 % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of I]+xerVd % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 1zqIB")s> % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 O9?t,1 n;+CV~ C=1; j}t"M|` M1=120, % integer for amplitude 'Z5l'Ac M3=5000; % integer for length of coupler GrPKJ~{6 N = 512; % Number of Fourier modes (Time domain sampling points) dCc"Qr[k dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05. JcV'O)& T =40; % length of time:T*T0. (cAWT, dt = T/N; % time step
RdaAS{>Sk n = [-N/2:1:N/2-1]'; % Index DLggR3K_\ t = n.*dt; *'[8FZ|dQ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. Zq1ZrwPF w=2*pi*n./T; &\6Buw_ g1=-i*ww./2; }x!=F<Q!r g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; J< Ljg<t+ g3=-i*ww./2; 9j<qi\SSI P1=0; %EV\nwn6 P2=0; #@%DY*w]v P3=1; ^F\RM4|, P=0; OD{()E?1B for m1=1:M1 T6mbGE*IeE p=0.032*m1; %input amplitude M:TN^ rA| s10=p.*sech(p.*t); %input soliton pulse in waveguide 1 E/+H~YzO s1=s10; @ByD= s20=0.*s10; %input in waveguide 2 VS`
tj s30=0.*s10; %input in waveguide 3 ', +YWlW s2=s20; ^EtBo7^t
s3=s30; $[(amj-;l p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1)))); ZW+M<G %energy in waveguide 1 4gD;X NrV p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1)))); 0ndk=V %energy in waveguide 2 @G'&7-(h* p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1)))); _UP=zW %energy in waveguide 3 ;|yd}q=p for m3 = 1:1:M3 % Start space evolution z3-A2#c s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS ?OjZb'+=K s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; J:D{5sE<| s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; s|HpN sca1 = fftshift(fft(s1)); % Take Fourier transform fhwJ sca2 = fftshift(fft(s2)); ?`T0zpC sca3 = fftshift(fft(s3)); IhR;YM[K sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift KYw~(+gHv2 sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); a%nksuP3 sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); <DeC^[-P s3 = ifft(fftshift(sc3)); ^lvYj
E s2 = ifft(fftshift(sc2)); % Return to physical space j(xVbUa s1 = ifft(fftshift(sc1)); Y9<N#h# end 1Jm'9iy3 p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); 2eC`^ p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); vM3 b\yp p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); yV.E+~y P1=[P1 p1/p10]; L/Tsq= P2=[P2 p2/p10]; <ztcCRov P3=[P3 p3/p10]; xVnk]:c P=[P p*p]; reP)&Fo end e};\"^HH figure(1) Ty&Ok* plot(P,P1, P,P2, P,P3); g$/C-j4A[ JX)%iJq# 转自:http://blog.163.com/opto_wang/
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