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 Cr&ua|%F ?gkK*\x2 % This Matlab script file solves the coupled nonlinear Schrodinger equations of ]/a?:24 [ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of l})uYae/ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear d<whb2l % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 9uq|
VU5 cB<Zez %fid=fopen('e21.dat','w'); c{E-4PYbah N = 128; % Number of Fourier modes (Time domain sampling points) 8xNKVj)@ M1 =3000; % Total number of space steps S`-z$ph} J =100; % Steps between output of space Lt*H|9 T =10; % length of time windows:T*T0 6q5V*sJ& T0=0.1; % input pulse width YRwS{e*u MN1=0; % initial value for the space output location J/mLB7^R dt = T/N; % time step ]M2> %Dvw n = [-N/2:1:N/2-1]'; % Index fpzTv3D=I t = n.*dt; F'"-4YV>& u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10 >s{[d$ u20=u10.*0.0; % input to waveguide 2 f5O*Njl u1=u10; u2=u20; {u!,TDt* U1 = u1; yn7n U2 = u2; % Compute initial condition; save it in U SY)o<MD ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. x|Q6[Y w=2*pi*n./T; YX~H!6l g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T Fa;CWyt L=4; % length of evoluation to compare with S. Trillo's paper iA:CPBv_mu dz=L/M1; % space step, make sure nonlinear<0.05 \^_F>M for m1 = 1:1:M1 % Start space evolution Z,!Rj7wZ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS Im#3sn u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; Sd{>(YWx~ ca1 = fftshift(fft(u1)); % Take Fourier transform l
lQ<x ca2 = fftshift(fft(u2)); _)p% c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation (5atU |8r c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift YAO.Cc z u2 = ifft(fftshift(c2)); % Return to physical space HC$_p,9OV u1 = ifft(fftshift(c1)); R^K<u#>K if rem(m1,J) == 0 % Save output every J steps. @ws3X\`<C U1 = [U1 u1]; % put solutions in U array 1W;+hXx U2=[U2 u2]; oW-luC+ MN1=[MN1 m1]; 2#sE\D z1=dz*MN1'; % output location \n /_Px end (}}BZS&. end u<):gI hg=abs(U1').*abs(U1'); % for data write to excel &ts!D!Hj ha=[z1 hg]; % for data write to excel ]T+{]t t1=[0 t']; tdEu4)6 hh=[t1' ha']; % for data write to excel file 4Jht{#IIG %dlmwrite('aa',hh,'\t'); % save data in the excel format WM9QC59 figure(1) }"_S;[{d waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn R$v{ p[ figure(2) ,u!c|4 waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn Ib]{rmaP ='YR; 非线性超快脉冲耦合的数值方法的Matlab程序 VNaa(Q 0hCJovSG% 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。 nIXq2TzJ 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 0;o`7f (5VP*67 k4s >sd3 5 dxxD%lHCF % This Matlab script file solves the nonlinear Schrodinger equations YI&7s_%
- % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of X8F _Mb* % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear <?QY\wyikz % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 N!aV~\E J*qepq`_ C=1; Spt[b.4m F M1=120, % integer for amplitude Z=4Krfn M3=5000; % integer for length of coupler Peh(*D{ N = 512; % Number of Fourier modes (Time domain sampling points) ]MRE^Je\h dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05. qFt%{~a
S T =40; % length of time:T*T0. .}%$l.#a dt = T/N; % time step %TvunV7NQS n = [-N/2:1:N/2-1]'; % Index ~1i,R1_\Y t = n.*dt; f!eC|:D ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. |l`X]dsfQ w=2*pi*n./T; '&'?
S g1=-i*ww./2; ,H[-.}OO g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; m},nKsO g3=-i*ww./2; )d_)CuUBe P1=0; &(IL`% P2=0; ?7YX@x P3=1; ?20y6c < P=0; +TfMj1Zx for m1=1:M1 ko>SnE|w# p=0.032*m1; %input amplitude KSMe#Qnw s10=p.*sech(p.*t); %input soliton pulse in waveguide 1 :~{XL >:S s1=s10; !f V.#9AB# s20=0.*s10; %input in waveguide 2 {y)s85:t s30=0.*s10; %input in waveguide 3 qL,QsRwN s2=s20; /Vg
R[ s3=s30; RT F9;]Ti p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1)))); )U`H7\*) %energy in waveguide 1 uZW
? 0W p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1)))); ph<Z/wlz %energy in waveguide 2 Gg{@]9 p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1)))); k'xnl"q %energy in waveguide 3 rPZ< for m3 = 1:1:M3 % Start space evolution iShB^ s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS 7Q/v#_e( s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; gOx4qxy/m| s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; 0v,DQJ?w8 sca1 = fftshift(fft(s1)); % Take Fourier transform ;_F iiBk7( sca2 = fftshift(fft(s2)); v}M, M&? sca3 = fftshift(fft(s3)); EJNj.c-# sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift VjMd&>G sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); k&n7_[]n sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); FJ!N)`[ s3 = ifft(fftshift(sc3)); q@8Rlc& s2 = ifft(fftshift(sc2)); % Return to physical space oB&s | |