| 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 W6&".2 ?ZdHuuDN~ % This Matlab script file solves the coupled nonlinear Schrodinger equations of ex $d~ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of NeCTEe|V % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear RK/SeS % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 gTW(2?xYf g-oHu8 %fid=fopen('e21.dat','w'); eN>=x40 N = 128; % Number of Fourier modes (Time domain sampling points) #1z}~1- M1 =3000; % Total number of space steps '68{dyFZL J =100; % Steps between output of space rv;w`f T =10; % length of time windows:T*T0 7\JRHw T0=0.1; % input pulse width >T.U\,om7 MN1=0; % initial value for the space output location Il'+^u_ < dt = T/N; % time step p4<&N MG n = [-N/2:1:N/2-1]'; % Index [@#P3g\:>W t = n.*dt; r&0v,WSp&S u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10 $Xk1'AzB8 u20=u10.*0.0; % input to waveguide 2 wi:]o o# u1=u10; u2=u20; -[`,MZf U1 = u1; j?/T7a^ U2 = u2; % Compute initial condition; save it in U
Rla1,{1 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. :uZcN w=2*pi*n./T; SR%h=`t g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T -78
t0-lM L=4; % length of evoluation to compare with S. Trillo's paper O9=vz% dz=L/M1; % space step, make sure nonlinear<0.05 oO$a4|&, for m1 = 1:1:M1 % Start space evolution *7nlel u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS +_06{7@h u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; *<xEM- ca1 = fftshift(fft(u1)); % Take Fourier transform U|uvSJ)X ca2 = fftshift(fft(u2)); /0!6;PC< c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation _tb)F"4V c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift A"I:cw"KY u2 = ifft(fftshift(c2)); % Return to physical space `WC~cb\ u1 = ifft(fftshift(c1)); 0#G&8*FMN if rem(m1,J) == 0 % Save output every J steps. q,^^c1f U1 = [U1 u1]; % put solutions in U array ;,JCA#
N U2=[U2 u2]; 477jS6 ^e& MN1=[MN1 m1]; I Vq9z z1=dz*MN1'; % output location N02N
w(pi end dW,$yH_ end t{Q9Kv hg=abs(U1').*abs(U1'); % for data write to excel ;?yd;GOt) ha=[z1 hg]; % for data write to excel )<1M'2 t1=[0 t']; 72&xEx hh=[t1' ha']; % for data write to excel file 9@Cqg5Kx' %dlmwrite('aa',hh,'\t'); % save data in the excel format IM}#k$vM: figure(1) .?[2,4F; waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn 1;4TA}'H figure(2) oslrv7EK waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn W _yVVr ]EE}ax%#aq 非线性超快脉冲耦合的数值方法的Matlab程序 ts{Tk5+ ^WVH 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。 xx#;)]WT 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 w~;1R\?| !HY+6!hk Qi w "x, o D*h@yL % This Matlab script file solves the nonlinear Schrodinger equations FlrLXTx0 % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of {O]Cj~} % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear ]gQgNn? % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 rts@1JY[ ORA+> C=1; [q?{e1 M1=120, % integer for amplitude +'N?`l6< M3=5000; % integer for length of coupler =sG C N = 512; % Number of Fourier modes (Time domain sampling points) /V2Ih dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05. k,0JW=Vh>| T =40; % length of time:T*T0. hof:36 < dt = T/N; % time step ES(b#BlrP/ n = [-N/2:1:N/2-1]'; % Index rMH\;\
I|U t = n.*dt; 3*/y<Z'H ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. $eCxpb.. w=2*pi*n./T; u1~H1
]Ii g1=-i*ww./2; <omSK-
T- g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; f*0[[J0] g3=-i*ww./2; 38tRb"3zP P1=0; bsmZR(EnU P2=0; G9 ;X=c P3=1; E"b+Q P=0; pyq~_Bng for m1=1:M1 "S,,Bj L p=0.032*m1; %input amplitude ol^OvG:TQ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1 ^{DXin 1O` s1=s10; quTM|>=_R s20=0.*s10; %input in waveguide 2 N41)?-7F s30=0.*s10; %input in waveguide 3 lSPQXu*[ s2=s20; ?R(fxx s3=s30; %u,H2* p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1)))); [O2xE037h` %energy in waveguide 1 fk<0~tE p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1)))); 5*/~) wN\U %energy in waveguide 2 $>hPB[ [ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
u<!8dQ8 %energy in waveguide 3 wI'T Je, for m3 = 1:1:M3 % Start space evolution _rdEur C6 s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS ?xWO>#/ s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; Tv_KdOv8 s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; hbl:~O&a/ sca1 = fftshift(fft(s1)); % Take Fourier transform F/tGk9v sca2 = fftshift(fft(s2)); 5V':3o;D__ sca3 = fftshift(fft(s3)); C*a>B,H sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift tda#9i[pkH sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); z\]]d?d?; sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); bJ4} )P& s3 = ifft(fftshift(sc3)); l~b# Y& s2 = ifft(fftshift(sc2)); % Return to physical space SP?~i@H s1 = ifft(fftshift(sc1)); vO`~rUA end F{WV}o=MY p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); pZ,=iqr p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); M+j V`J! p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); 6!sC P1=[P1 p1/p10]; sG7G$G*ta! P2=[P2 p2/p10]; 4W5[1GE. P3=[P3 p3/p10]; 3k(A&]~v P=[P p*p]; s1.EE|h,5 end
?12[8 figure(1) J~Uq'1? plot(P,P1, P,P2, P,P3); /'' |bIPa -+?ZJ^A 转自:http://blog.163.com/opto_wang/
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