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 *&=sL \6{w#HsP8 % This Matlab script file solves the coupled nonlinear Schrodinger equations of o4^|n1vN % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of `/"rs@ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear fLtN-w6t % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 nQtp 4 |g$n-t %fid=fopen('e21.dat','w'); cbton<r~ N = 128; % Number of Fourier modes (Time domain sampling points) ]g3RVA%\l M1 =3000; % Total number of space steps )wt mc4' J =100; % Steps between output of space l\HLlwYO T =10; % length of time windows:T*T0 @X|Mguq5 T0=0.1; % input pulse width K1gZ>FEY|N MN1=0; % initial value for the space output location 8JFns-5 dt = T/N; % time step b-`=^ny)K n = [-N/2:1:N/2-1]'; % Index }Ai_peO0a t = n.*dt; x$:P;# u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10 Un~8N u20=u10.*0.0; % input to waveguide 2 c)b/" u1=u10; u2=u20; 7xhBdi[ dQ U1 = u1; X0}+X'3 U2 = u2; % Compute initial condition; save it in U L/[b~D>T% ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. {\-9^RL w=2*pi*n./T; 6w"_sK?
g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T SyB2A\A L=4; % length of evoluation to compare with S. Trillo's paper w|k?2 ?& dz=L/M1; % space step, make sure nonlinear<0.05 x(tf0[g for m1 = 1:1:M1 % Start space evolution ]U,c`?[7# u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS BM
vGw u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; wDv G5 ca1 = fftshift(fft(u1)); % Take Fourier transform UZV\]Y ca2 = fftshift(fft(u2)); |*T`3@R;3 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation Vq IzDs c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift C)a;zU;9 u2 = ifft(fftshift(c2)); % Return to physical space UG!528;7 u1 = ifft(fftshift(c1)); XHh!Q0v; if rem(m1,J) == 0 % Save output every J steps. F?Fs x)2k U1 = [U1 u1]; % put solutions in U array YAc~,N U2=[U2 u2]; ,(@J Ntx MN1=[MN1 m1]; TpSv7k T] z1=dz*MN1'; % output location k$ORV U end MmbS["A end :;g7T -_q hg=abs(U1').*abs(U1'); % for data write to excel *B3 4 ha=[z1 hg]; % for data write to excel 4%GwCEnS t1=[0 t']; jY +u OH hh=[t1' ha']; % for data write to excel file V#P`FX %dlmwrite('aa',hh,'\t'); % save data in the excel format :f/T$fa* figure(1) D^30R*gV waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn &Rp/y%9 figure(2) }<9IH%sgF waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn 0DB8[#i%: r-s9]0"7~ 非线性超快脉冲耦合的数值方法的Matlab程序 kR
!O-@GJ] v\3
\n3[u 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。 <Rb[0E$ 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 #GbfFoE SqosJ}K }ZKG-~ b;5&V_ % This Matlab script file solves the nonlinear Schrodinger equations "T4buTXJ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of O!U8"Yr$ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear y(fJ{k % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 DCheG7lo{ QSNPraT C=1; E |K|AdL M1=120, % integer for amplitude Pl\r|gS; M3=5000; % integer for length of coupler Oj,v88= N = 512; % Number of Fourier modes (Time domain sampling points) "|^-Yk\U dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05. gy*c$[NS$ T =40; % length of time:T*T0. xCYK"v6\ dt = T/N; % time step @r*w 84 n = [-N/2:1:N/2-1]'; % Index `bJ?8~ 8* t = n.*dt; TZ+- >CG ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. :AYhBhitC w=2*pi*n./T; 5kx-s6`! g1=-i*ww./2; 3Jh!YzI8 g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; ]5',`~jkF g3=-i*ww./2; H2JKQm_ P1=0; 6.'j\ P2=0; 3Ow bU P3=1; @9e}kiW P=0; xh:A*ZI=7 for m1=1:M1 p&$O}AX| p=0.032*m1; %input amplitude WdZ_^ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1 w\zNn4B})A s1=s10; )C>8B`^S s20=0.*s10; %input in waveguide 2 gjL+8Rk s30=0.*s10; %input in waveguide 3 |r+w(TG s2=s20; k4-S:kVo s3=s30; { u %xc"0y p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1)))); gA:unsI %energy in waveguide 1 wM1&_%N p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1)))); j_{f(.5 %energy in waveguide 2 ey@{Ng# p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1)))); +:kMYL3 %energy in waveguide 3 2Bz\Tsp for m3 = 1:1:M3 % Start space evolution O)8$aAJ)V s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS CxD=8X9m s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; H{4_,2h=m s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; '>k1h.i sca1 = fftshift(fft(s1)); % Take Fourier transform ,v#O{ma sca2 = fftshift(fft(s2)); T$"sw7< sca3 = fftshift(fft(s3)); n/ZX$?tKAK sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift p|>m 2(| sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); O<P(UT" sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); _ -|+k s3 = ifft(fftshift(sc3)); "SA* s2 = ifft(fftshift(sc2)); % Return to physical space T"/dn%21 s1 = ifft(fftshift(sc1)); "9X1T] end Vtv~jJ{m p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); 64qqJmG3 p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); #H]c/ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); "BZL*hHq P1=[P1 p1/p10]; <<PXh&wu0 P2=[P2 p2/p10]; t\WU}aKML P3=[P3 p3/p10]; sV;q(,oru P=[P p*p]; -
VdCj%r> end pnTz.)'46 figure(1) $/crb8-C plot(P,P1, P,P2, P,P3); 8[H bg FA{'Ki` 转自:http://blog.163.com/opto_wang/
|
|