| 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 #QdBI{2 $ZSjq % This Matlab script file solves the coupled nonlinear Schrodinger equations of PPiN`GM % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of eR,ePyA; % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear (UWV#AR % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 U_ j\UQC }^).Y7{g[ %fid=fopen('e21.dat','w'); M*|,05> N = 128; % Number of Fourier modes (Time domain sampling points) G]Fp}, M1 =3000; % Total number of space steps VfS&V*un J =100; % Steps between output of space #'}?.m T =10; % length of time windows:T*T0 2y/|/IW= T0=0.1; % input pulse width aw
z(W> MN1=0; % initial value for the space output location i
v7^! dt = T/N; % time step qV^Z@N+, n = [-N/2:1:N/2-1]'; % Index d{?X:*F t = n.*dt; wO6
D\# u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10 37Z@a!# u20=u10.*0.0; % input to waveguide 2 V=%j]`Os u1=u10; u2=u20; 6?an._ C U1 = u1; #*QnO\. U2 = u2; % Compute initial condition; save it in U X 4\ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. JQCQpn/ w=2*pi*n./T; yu ~Rk g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T hV,)u3 L=4; % length of evoluation to compare with S. Trillo's paper 9V5}%4k%+ dz=L/M1; % space step, make sure nonlinear<0.05 |X :"AH"S for m1 = 1:1:M1 % Start space evolution |G^w2"D_Z u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS ?7Kl)p3 u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; #bN'N@| ca1 = fftshift(fft(u1)); % Take Fourier transform X6lkz*M. ca2 = fftshift(fft(u2)); AN-qcp6=o c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation 6_`9
4+ c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift N"A863> u2 = ifft(fftshift(c2)); % Return to physical space }=.:bwX5 u1 = ifft(fftshift(c1)); )$[.XKoT if rem(m1,J) == 0 % Save output every J steps. y8jwfO3 U1 = [U1 u1]; % put solutions in U array T0=8 U;
= U2=[U2 u2]; ~4e4Gyx c MN1=[MN1 m1]; mUFg(;ya z1=dz*MN1'; % output location MM_c{gFF end 1ztL._Td end QahM)Gb hg=abs(U1').*abs(U1'); % for data write to excel |Nx7jGd:i ha=[z1 hg]; % for data write to excel ?)x"+[2 t1=[0 t']; :Fe}.* t hh=[t1' ha']; % for data write to excel file #9Src\V %dlmwrite('aa',hh,'\t'); % save data in the excel format ;onhc*{lv figure(1) 6x?3%0Km waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn :xd)]Ns figure(2) z=YHRS waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn >"}z
% # mU
d['Z 非线性超快脉冲耦合的数值方法的Matlab程序 >x/;'Y. Pe-1o#7~W 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。 E'_3U5U 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 3<c_`BWu zTP|H5HyK Szz:$!t ~yrEB:w`_ % This Matlab script file solves the nonlinear Schrodinger equations h!>K[* % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of X:3W9`s)* % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear >ZX&2 { % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 Gp&o l)1FCDV C=1; YfB8
M1=120, % integer for amplitude ZA1u M3=5000; % integer for length of coupler Wzm!:U2R* N = 512; % Number of Fourier modes (Time domain sampling points) ,\2w+L5TD dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05. (g>8!Gl T =40; % length of time:T*T0. 'aLTiF+ dt = T/N; % time step ^p@ # n = [-N/2:1:N/2-1]'; % Index D'
d^rT| H t = n.*dt; 3W<_J_[ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. I=vGS w=2*pi*n./T; 7Pb:z4j g1=-i*ww./2; yu^n;gWH g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; i.~*G8!DM g3=-i*ww./2; cN]e{| P1=0; m+3U[KKvG P2=0; Py}] {? P3=1; ^nPk;%`0 P=0; f_{OU
E for m1=1:M1 *_Sx^`"X`l p=0.032*m1; %input amplitude @'D ,T^I s10=p.*sech(p.*t); %input soliton pulse in waveguide 1 "}91wfG9 s1=s10; UoD@ix&0 s20=0.*s10; %input in waveguide 2 pb`!_GmB s30=0.*s10; %input in waveguide 3 $N@EH;{_0 s2=s20; :4HZ>!i s3=s30; ggP#2I\ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1)))); E;*JD x %energy in waveguide 1 06r-@iY.] p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1)))); G/y@`A) %energy in waveguide 2 DrY5Q&S p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1)))); Zo12F**{ %energy in waveguide 3
{Xj2c]A1 for m3 = 1:1:M3 % Start space evolution =
nIl$9 s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS 6/4?x)l3- s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; xllk hD4F s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; f\/'Fy0 sca1 = fftshift(fft(s1)); % Take Fourier transform I7[F,xci sca2 = fftshift(fft(s2)); $>Mqo sca3 = fftshift(fft(s3)); .#BWu(EYV sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift Pl9Ky(Q`V sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); z]\CI: sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); ]CL9N s3 = ifft(fftshift(sc3)); BS(XEmJn&j s2 = ifft(fftshift(sc2)); % Return to physical space `8D)j>Yh~ s1 = ifft(fftshift(sc1)); D=!e6E<>@ end C{5^UCJkg p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); zA<Hj;9SM p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); 8`$lsD p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); 0r |mg::' P1=[P1 p1/p10]; DqQ+8 w P2=[P2 p2/p10]; *!W<yNrR P3=[P3 p3/p10]; Y)7LkZO(y P=[P p*p]; 0=,vdT end Gl@-RLo figure(1) /8s+eHn&% plot(P,P1, P,P2, P,P3); yn;sd+:z <gtqwH] 转自:http://blog.163.com/opto_wang/
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