| 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 S*n@81Z ZfB"
E % This Matlab script file solves the coupled nonlinear Schrodinger equations of >Bgw}PI % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of A$w4PVS % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear A7n\h-b % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 |M+<m">E &cu lbcz %fid=fopen('e21.dat','w'); qBCK40 N = 128; % Number of Fourier modes (Time domain sampling points) {\(L%\sV@ M1 =3000; % Total number of space steps ;
k)@DX J =100; % Steps between output of space d`F&aC T =10; % length of time windows:T*T0 3%E74 mOcD T0=0.1; % input pulse width u07pq4Ly MN1=0; % initial value for the space output location IEzaK dt = T/N; % time step ,JEFGI{ n = [-N/2:1:N/2-1]'; % Index '60 L~`K t = n.*dt; *;fw%PW u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10 (t4&,W_spA u20=u10.*0.0; % input to waveguide 2 Q_Gi]M9 u1=u10; u2=u20; dX)GPC-D7 U1 = u1; Et/&^&=\- U2 = u2; % Compute initial condition; save it in U D&/L: ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. dS<C@( w=2*pi*n./T; uNHF'?X g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T /<]{KI L=4; % length of evoluation to compare with S. Trillo's paper m`FNIY dz=L/M1; % space step, make sure nonlinear<0.05
0gfA#|' for m1 = 1:1:M1 % Start space evolution x(eb5YS u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS z
d-Tv`L# u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; u6bXv( ca1 = fftshift(fft(u1)); % Take Fourier transform !H}vu]R ca2 = fftshift(fft(u2)); nTz6LVF c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation <Ce2r"U1e c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift uECsh2Uin u2 = ifft(fftshift(c2)); % Return to physical space >J>b>SU=- u1 = ifft(fftshift(c1)); =-}[^u1 if rem(m1,J) == 0 % Save output every J steps. nVI!@qW U1 = [U1 u1]; % put solutions in U array |\g5+fv9 U2=[U2 u2]; \
5,MyB2/` MN1=[MN1 m1]; }sOwp}FV8X z1=dz*MN1'; % output location sn?]n~z end WuZ/C_ end >G~R,{6U hg=abs(U1').*abs(U1'); % for data write to excel @!8ZPiW< ha=[z1 hg]; % for data write to excel YR;^hs? t1=[0 t']; x4/M}%h!;B hh=[t1' ha']; % for data write to excel file Y>&Ew*Y %dlmwrite('aa',hh,'\t'); % save data in the excel format b/Xbs0q figure(1) BouTcC waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn .({smN,B figure(2) Ey4z.s'-l waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn P'O#I}Dmw< = hN
!;7G 非线性超快脉冲耦合的数值方法的Matlab程序 B0ndcB- R?p00 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。 ]Qe{e3p; 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 iT)z_ v= N!SaK{ DHY@akhrK Qr$;AZ G % This Matlab script file solves the nonlinear Schrodinger equations P8?Fm` % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of KR%{a(V;7 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear uSR~@Lj ~ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 p+Y>F\r&w w/IZDMBf| C=1; XZ5 /=z M1=120, % integer for amplitude uy}%0vLo M3=5000; % integer for length of coupler +tD[9b!
m N = 512; % Number of Fourier modes (Time domain sampling points) b? j< BvQ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05. %bdjBa} T =40; % length of time:T*T0. 3dDX8M? dt = T/N; % time step 0]jA<vLR n = [-N/2:1:N/2-1]'; % Index >N.]|\V t = n.*dt; >(snII ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. &RTX6%'KY w=2*pi*n./T; YLVPAODY g1=-i*ww./2; v$ub~Q6W g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; ;IpT} , g3=-i*ww./2; %DQhM ,c@ P1=0; D91e\|] P2=0; P06RJE P3=1; H`geS P=0; rgOfNVyJG< for m1=1:M1 =ID
2 p=0.032*m1; %input amplitude A?@@*$& s10=p.*sech(p.*t); %input soliton pulse in waveguide 1 T =2=k&| s1=s10; p^pOuy8 s20=0.*s10; %input in waveguide 2 HyR!O> s30=0.*s10; %input in waveguide 3 =Z+nX0qF s2=s20; .n=Z:*JqQ s3=s30; /P
2[:[w p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1)))); o'$jNciOW %energy in waveguide 1 .m`y><.5 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1)))); A'%1ZQ33O %energy in waveguide 2 h48SItY p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1)))); zR32PG>9 %energy in waveguide 3 JO@|*/mL for m3 = 1:1:M3 % Start space evolution h)me\U7UC s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS r
lKlpl s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; -D^}S"' s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; I=!rbF;Z sca1 = fftshift(fft(s1)); % Take Fourier transform +GAf O0 sca2 = fftshift(fft(s2)); QL$S4 J" sca3 = fftshift(fft(s3)); NzW`B^p sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift Z,.G%"i3C sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
kZ=s'QRgL sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); d
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|Xsb s3 = ifft(fftshift(sc3)); \))=gu)I s2 = ifft(fftshift(sc2)); % Return to physical space . ]8E7 s1 = ifft(fftshift(sc1)); wlPx,UqZ end leCVK. p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); dCFlM&(i p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); $ F S_E p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); c c P1=[P1 p1/p10]; NOS>8sy P2=[P2 p2/p10]; w%zRHf8C P3=[P3 p3/p10]; aSP4a+\* P=[P p*p]; |G/7_+J6 end efY8M2 figure(1) O,.!2wVrN plot(P,P1, P,P2, P,P3); Mzd[fR5a8 dgo3'ZO
转自:http://blog.163.com/opto_wang/
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