| 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 3T|xUY)G4 "s!|8F6$ % This Matlab script file solves the coupled nonlinear Schrodinger equations of p;Lp-9H\33 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of i.(kX`~J1 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear z+k[HE^S % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 )5O E~}> hA6D*8oXD %fid=fopen('e21.dat','w'); 8(b
C. N = 128; % Number of Fourier modes (Time domain sampling points) GjfPba4> M1 =3000; % Total number of space steps k,kr7'Q J =100; % Steps between output of space 1c%ee$Q T =10; % length of time windows:T*T0 !L=RhMI T0=0.1; % input pulse width k\NwH?ppu MN1=0; % initial value for the space output location [\rnJ
lE dt = T/N; % time step ]m(C}} n = [-N/2:1:N/2-1]'; % Index [`]h23vRW t = n.*dt; 4^jIV!V u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10 lQ]8PR
t8 u20=u10.*0.0; % input to waveguide 2 @uJ^k
>B u1=u10; u2=u20; fGz++;b<S U1 = u1; NY,ZTl_ U2 = u2; % Compute initial condition; save it in U oQS_rv\Ber ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. :Nt_LsH w=2*pi*n./T; ?C6DK{S( g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T G""L1? L=4; % length of evoluation to compare with S. Trillo's paper *>#mI/#} dz=L/M1; % space step, make sure nonlinear<0.05 )^)j=xs for m1 = 1:1:M1 % Start space evolution WA$Ug u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS Wj}PtQ%lp/ u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; 'WC>
_L ca1 = fftshift(fft(u1)); % Take Fourier transform #j?SdQ ca2 = fftshift(fft(u2)); >B~vE2^tQ~ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation jMP!/t
:w c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift =rB=! ; u2 = ifft(fftshift(c2)); % Return to physical space 6M/*]jLq4 u1 = ifft(fftshift(c1)); \d&/,?,Ey if rem(m1,J) == 0 % Save output every J steps. R=ipK63 U1 = [U1 u1]; % put solutions in U array $OAak U2=[U2 u2]; t
V:oBT* MN1=[MN1 m1]; 2l YA% n z1=dz*MN1'; % output location (=/%_jj end O7x'q<PFU end 7F;dLd' hg=abs(U1').*abs(U1'); % for data write to excel c'XvZNf .C ha=[z1 hg]; % for data write to excel G8Qo]E9-/ t1=[0 t']; @8;0p hh=[t1' ha']; % for data write to excel file ?vd_8C2B %dlmwrite('aa',hh,'\t'); % save data in the excel format $UX^$gG figure(1) 1yg5d9 waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn 5e|2b] f$ figure(2) bY>JLRQJ- waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn hHoc>S6^M
YO3$I!( 非线性超快脉冲耦合的数值方法的Matlab程序 B4>kx#LR ]JUb;B;Z 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。 jr=>L: 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 iax6o+OG| YM(`E9{h K~MTbdg #dKHU@+U" % This Matlab script file solves the nonlinear Schrodinger equations Vjc*D] % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of D{J+}*y % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear [tP6FdS/M= % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 "92Z"I~1 j_I C=1; |fd}B5!c M1=120, % integer for amplitude ENEn Hu^ M3=5000; % integer for length of coupler mK);NvJ! N = 512; % Number of Fourier modes (Time domain sampling points) HfN:oww dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05. w{HDCPuS T =40; % length of time:T*T0. -$8M#n, dt = T/N; % time step Bv)4YU n = [-N/2:1:N/2-1]'; % Index 4wa8Vw` t = n.*dt;
F[65)"^ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. bns([F w=2*pi*n./T; :q+D`s g1=-i*ww./2; LM~,`#3Ru g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; EA/+~ux g3=-i*ww./2; potb6jc? P1=0; c[DC P2=0; 2Q/#.lNL P3=1; 7LB#\2 P=0; JuD$CHg;# for m1=1:M1 ^&|$&7
p=0.032*m1; %input amplitude 8r 4
L4 s10=p.*sech(p.*t); %input soliton pulse in waveguide 1 HxgH*IMs s1=s10; ~5f|L(ODX s20=0.*s10; %input in waveguide 2 | gou#zi s30=0.*s10; %input in waveguide 3 P!Mz5QZ+ s2=s20; =h"*1` s3=s30; CLU[')H0 p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1)))); !{L6
4qI %energy in waveguide 1 lYz$~/sd p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1)))); NyJ=^=F# %energy in waveguide 2 >;ucwLi p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1)))); j+p=ik %energy in waveguide 3 XP$ 1CWI for m3 = 1:1:M3 % Start space evolution lk5}bnd5 s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS 0k];%HV| s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; u}[Z=V s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; &>!WhC16 sca1 = fftshift(fft(s1)); % Take Fourier transform :h|nV
~ sca2 = fftshift(fft(s2)); D-zqu~f` sca3 = fftshift(fft(s3)); %mda=%Yn sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift (:p&[HNuN sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); Dyx3N5?C sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); !7:~"kk s3 = ifft(fftshift(sc3)); lIN`1vX( s2 = ifft(fftshift(sc2)); % Return to physical space p:,(r{*? s1 = ifft(fftshift(sc1)); f"0{e9O]2 end S"Q$ Ol" p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); FDHa|<oz p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); qP"<vZ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); *d,u)l :S P1=[P1 p1/p10]; CPI7&jqu P2=[P2 p2/p10]; }
r#by%P P3=[P3 p3/p10]; ;tR,w
P=[P p*p]; e3L<;MAt end XG5mfKMt+ figure(1) 8: KlU(J plot(P,P1, P,P2, P,P3); jocu=Se@ 8bB'[gJ]{ 转自:http://blog.163.com/opto_wang/
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