| 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 _9faBrzd Tu@8}C % This Matlab script file solves the coupled nonlinear Schrodinger equations of Scp7X7{N % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of &Flglj~7l % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear M8INk,si % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 T:t]"d}} A3rPt&<a %fid=fopen('e21.dat','w'); ]p*l%(dhY N = 128; % Number of Fourier modes (Time domain sampling points) +~'865 { M1 =3000; % Total number of space steps 0n@rLF J =100; % Steps between output of space DamCF T =10; % length of time windows:T*T0 3j,Q`+l/6d T0=0.1; % input pulse width 0T@ Zb={ MN1=0; % initial value for the space output location ]P#XVDn+; dt = T/N; % time step flk=>h| n = [-N/2:1:N/2-1]'; % Index ,^?^dB t = n.*dt; @L>q(Kg u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10 N<f"] u20=u10.*0.0; % input to waveguide 2 '/`= R u1=u10; u2=u20; ?bPRxR U1 = u1; $>*3/H U2 = u2; % Compute initial condition; save it in U MJ7 Y#<u ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. x6(~;J w=2*pi*n./T; EzDk}uKY0R g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T z8{a(nK P L=4; % length of evoluation to compare with S. Trillo's paper kV?y0J. dz=L/M1; % space step, make sure nonlinear<0.05 dODt(J}% for m1 = 1:1:M1 % Start space evolution
-%2[2p u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS "Weg7mc# u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; iDMJicW!+F ca1 = fftshift(fft(u1)); % Take Fourier transform pV.Av ca2 = fftshift(fft(u2)); T~QWRBO c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation =Qh\D c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift :/y1yM u2 = ifft(fftshift(c2)); % Return to physical space N U|d u1 = ifft(fftshift(c1)); bx<RV7>0 if rem(m1,J) == 0 % Save output every J steps. kspTp>~ U1 = [U1 u1]; % put solutions in U array J%x6 U2=[U2 u2]; @b"t]#V(E MN1=[MN1 m1]; OTMJ6)n7 z1=dz*MN1'; % output location ] x\-$~E end "[vu6 `m? end S M!Txe# hg=abs(U1').*abs(U1'); % for data write to excel r~N"ere26 ha=[z1 hg]; % for data write to excel ~vs}.kb t1=[0 t']; 5Ycco,x hh=[t1' ha']; % for data write to excel file }-ftyl7 %dlmwrite('aa',hh,'\t'); % save data in the excel format [`p=(/I&L figure(1) I([!]z waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn ulu9'ch figure(2) ?dD&p8{ waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn <.pU,T/ ?g?L3vRK 非线性超快脉冲耦合的数值方法的Matlab程序 ,z3{u162 0|2%vh >J 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。 _$=
_du Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 >2~+.WePu
0dhF&*h|L i-bJS6 %FXfqF9 % This Matlab script file solves the nonlinear Schrodinger equations NLS%S q % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of cs T2B[f9D % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear j;s"q]"x] % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 *:>"q ej qY~`8
x C=1; M%1}/!J3 M1=120, % integer for amplitude !O-C,uSm M3=5000; % integer for length of coupler m-H-6`] N = 512; % Number of Fourier modes (Time domain sampling points) AK\$i$@6 dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05. ,Vh.T&X5 T =40; % length of time:T*T0. Vnx,5E& dt = T/N; % time step R&|mdY8 n = [-N/2:1:N/2-1]'; % Index ^&bRX4pYo t = n.*dt;
=i_-F$pV ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. a["2VY6Eq@ w=2*pi*n./T; s:p[DEj- g1=-i*ww./2; ~n[xtWO0 g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; rA2g& g3=-i*ww./2; M@4UGM`J P1=0; 2R=DB`3 P2=0; rFaF
Bd P3=1; Eq$&qV-?( P=0; =
QQ5f5\l for m1=1:M1 `!Ds6 p=0.032*m1; %input amplitude Ggl~nxz s10=p.*sech(p.*t); %input soliton pulse in waveguide 1 }e2(T s1=s10; Q -MQ9' s20=0.*s10; %input in waveguide 2 w=LP"bqlI s30=0.*s10; %input in waveguide 3 f 1w~!O9 s2=s20; (>`5z(X s3=s30; H|RT?Q p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1)))); X5X?&* %{ %energy in waveguide 1 f>piHh? p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1)))); l5\"9 ,< %energy in waveguide 2 )dY=0"4Z p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1)))); u:m]CPz %energy in waveguide 3 ,hq)1u for m3 = 1:1:M3 % Start space evolution BT)X8>ct s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS U
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(C s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; jy giG&H s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; T :/,2.l sca1 = fftshift(fft(s1)); % Take Fourier transform A,%C,*)Cg sca2 = fftshift(fft(s2)); ~_Lr=C D;4 sca3 = fftshift(fft(s3)); J9\a{c;. sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift ({JHZ6uZ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); YqPQ%
sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); )RO<o O s3 = ifft(fftshift(sc3)); TjHwjRa s2 = ifft(fftshift(sc2)); % Return to physical space /1x,h"T\< s1 = ifft(fftshift(sc1)); $/=nU*pd end iC W*]U p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); tZ `z p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); ?t+5s] p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); K4]g[z P1=[P1 p1/p10]; bYi`R) P2=[P2 p2/p10]; YO}1(m P3=[P3 p3/p10]; u0#}9UKQ P=[P p*p]; 'ihhoW8 end td4[[ / figure(1) u%]shm plot(P,P1, P,P2, P,P3); c)A{p HsnLm67' 转自:http://blog.163.com/opto_wang/
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