| 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 r-xP6 vqQ)Pu?T % This Matlab script file solves the coupled nonlinear Schrodinger equations of ,%N[FZ`| % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of nK+ke)'Zv= % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear _[rQt8zn % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 w xte ^2 H-_ %fid=fopen('e21.dat','w'); xyM|q9Gf@ N = 128; % Number of Fourier modes (Time domain sampling points) H~vrCi~t" M1 =3000; % Total number of space steps Sw"h!\c` J =100; % Steps between output of space Z|N$qm} T =10; % length of time windows:T*T0 i^iu#WC T0=0.1; % input pulse width Oso**WUOZ& MN1=0; % initial value for the space output location cLwnV. dt = T/N; % time step U9^1A* n = [-N/2:1:N/2-1]'; % Index Iy4%,8C]g t = n.*dt; lVq5>:'}^; u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10 p4k}B. f u20=u10.*0.0; % input to waveguide 2 Ee7+ob u1=u10; u2=u20; GH-Fqz U1 = u1; IvkYM`% U2 = u2; % Compute initial condition; save it in U GiM-8y~ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. #\}FQl6 w=2*pi*n./T; 7=u
Gf$/ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T V>Z4gZp5sc L=4; % length of evoluation to compare with S. Trillo's paper p U !: dz=L/M1; % space step, make sure nonlinear<0.05 ~CV.Ci.dG for m1 = 1:1:M1 % Start space evolution 6("bdx;! u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS +a|Q)Ob u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; kqj)&0|X ca1 = fftshift(fft(u1)); % Take Fourier transform Pp8G2|bz ca2 = fftshift(fft(u2)); BgUp~zdo c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation ^Mq@} 0 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift ,"gPd!HD( u2 = ifft(fftshift(c2)); % Return to physical space %Gyn.9\ u1 = ifft(fftshift(c1)); Q8h0.(#- if rem(m1,J) == 0 % Save output every J steps. G,$nq4 U1 = [U1 u1]; % put solutions in U array ercXw7{ U2=[U2 u2]; Keo<#Cc? MN1=[MN1 m1]; sU*?H`U3d z1=dz*MN1'; % output location Z:N;>.3i end 'm6bfS^T end <&) hg: hg=abs(U1').*abs(U1'); % for data write to excel -2[4 @ ha=[z1 hg]; % for data write to excel 9@ fSO< t1=[0 t'];
]ilLed hh=[t1' ha']; % for data write to excel file 1Hr1Ir<KR %dlmwrite('aa',hh,'\t'); % save data in the excel format :n{{\SSIgX figure(1) L8h!%56s waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn @M-w8!.~ figure(2) XLaD#J waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn ~D|,$E tX4 ]jVE 非线性超快脉冲耦合的数值方法的Matlab程序 wn.6l
` lGR0-Gh2 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。 %(khE-SW 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 9m2FH~ UxHI6,b 4D<C;>*/b <W8%eRfU % This Matlab script file solves the nonlinear Schrodinger equations =d ;#Nu- % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of *aM7d>nG5 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear tl!dRV92 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 gU|:Y&lFZg =6:9y}~ C=1; \SQ4yc M1=120, % integer for amplitude G]k[A=dg M3=5000; % integer for length of coupler &a=rJvnIO& N = 512; % Number of Fourier modes (Time domain sampling points) F>#F@j^c dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05. j;y(to-e>D T =40; % length of time:T*T0. :fL7"\
pf~ dt = T/N; % time step \C>IVz<O n = [-N/2:1:N/2-1]'; % Index ~?aFc) t = n.*dt; F5cNF5 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. $},XRo&R w=2*pi*n./T; H3R{+7 g1=-i*ww./2; NI,>$@{ g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; -o"b$[sf=Z g3=-i*ww./2; D-C]0Jf3 P1=0; Un)Xe P2=0; *Us}E7/"' P3=1; )6p6<y P=0; Fy E#@ R for m1=1:M1 ;DnUeE8 p=0.032*m1; %input amplitude #>:S&R?2t s10=p.*sech(p.*t); %input soliton pulse in waveguide 1 U@yhFj_y s1=s10; LB]3-FsU+ s20=0.*s10; %input in waveguide 2 B%Qo6*b s30=0.*s10; %input in waveguide 3 }ixCbuD s2=s20; 0H4|}+e s3=s30; #V/{DPz p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1)))); viYrPhH+z %energy in waveguide 1
*?1\S^7R p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1)))); T}Wbt=\M %energy in waveguide 2
ZLKbF9lo p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1)))); IZ>l %energy in waveguide 3 VV$#<D<) for m3 = 1:1:M3 % Start space evolution $X Uck[ s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
qP;1LAX s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; Q~wS2f`) s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; fOSk>
gK sca1 = fftshift(fft(s1)); % Take Fourier transform pl@K"PRE sca2 = fftshift(fft(s2)); w$iPFZC' sca3 = fftshift(fft(s3)); f!YlYk5 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
J?Y,3cc. sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); jGkDD8K [ sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); k.54lNl s3 = ifft(fftshift(sc3)); ZEDvY=@a s2 = ifft(fftshift(sc2)); % Return to physical space d\3 %5Y s1 = ifft(fftshift(sc1)); +(:Qf+: end #0h}{y
E
p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); @,,G]4zZ! p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); dB#c$1 p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); yLCMu | + P1=[P1 p1/p10]; L |#0CRiN P2=[P2 p2/p10]; +\ "NPK@3 P3=[P3 p3/p10]; |n;);T( P=[P p*p]; _\k?uUo&,^ end
H6nH figure(1)
&gT@oS{ plot(P,P1, P,P2, P,P3); ^.@%n1I"5y V+lS\E. 转自:http://blog.163.com/opto_wang/
|
|