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 Xak~He z C``G<TB % This Matlab script file solves the coupled nonlinear Schrodinger equations of J|>P,x#G % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of @!Pq"/ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear g_q{3PW. % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 {4I sz-P Z<wg` %fid=fopen('e21.dat','w'); 'J\%JAR@ N = 128; % Number of Fourier modes (Time domain sampling points) abF_i# M1 =3000; % Total number of space steps 4ASc`w*0 J =100; % Steps between output of space ND`~|6yb T =10; % length of time windows:T*T0 rUuM__;d T0=0.1; % input pulse width LPXwfEHOm MN1=0; % initial value for the space output location ;^xku%u dt = T/N; % time step UR\*KR;yM n = [-N/2:1:N/2-1]'; % Index 4f>Vg$4 t = n.*dt; 2
o.Mh/D0 u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10 dW=]|t& u20=u10.*0.0; % input to waveguide 2 AvwX 2?tc u1=u10; u2=u20; E;X'.7[c U1 = u1; QM$?}>: U2 = u2; % Compute initial condition; save it in U +[>m`XTq ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. mbd@4u w=2*pi*n./T; w ggl,+7 g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T >97V2W L=4; % length of evoluation to compare with S. Trillo's paper +Oxl1fDf dz=L/M1; % space step, make sure nonlinear<0.05 Hu;#uAnxQ for m1 = 1:1:M1 % Start space evolution @Pa ;h u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS =A,i9Z& u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; {>~|xW ca1 = fftshift(fft(u1)); % Take Fourier transform .NPai4V' ca2 = fftshift(fft(u2)); jKtbGVZ7r c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation !]"T`^5,Y c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift 9iv!+(ni u2 = ifft(fftshift(c2)); % Return to physical space kmuF*0Bjk u1 = ifft(fftshift(c1)); %II |;< if rem(m1,J) == 0 % Save output every J steps. tn}9(Oa) U1 = [U1 u1]; % put solutions in U array K}*s^*X U2=[U2 u2]; /6f$%:q MN1=[MN1 m1]; }96^OQPE z1=dz*MN1'; % output location h-6kf:XP% end =XqmFr;h end \oaO7w,:" hg=abs(U1').*abs(U1'); % for data write to excel <8'}H`w% ha=[z1 hg]; % for data write to excel n0cqM}P@;! t1=[0 t']; w
5,- +&; hh=[t1' ha']; % for data write to excel file WyO10yvR %dlmwrite('aa',hh,'\t'); % save data in the excel format `M|fwlAJQ figure(1) VkUMMq{ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn **oN/5 figure(2) @ Gl=1 waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn n}YRE`>D b2 ZKhS8 非线性超快脉冲耦合的数值方法的Matlab程序 cm-!6'` O>}aK.H 在研究脉冲在非线性耦合器中的演变时,我们需要求解非线性偏微分方程组。在如下的论文中,我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。 vQ
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p Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 8?ZK^+]y 3 p") yQ h":"$k k|&@xEbS
% This Matlab script file solves the nonlinear Schrodinger equations 7=}`"7i~ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of V+DN<F- % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear l].dOso$` % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 Q
xKC5`1 2 y,f C=1; \|Us/_h M1=120, % integer for amplitude Z}WMpp^r M3=5000; % integer for length of coupler EdLbVrN, N = 512; % Number of Fourier modes (Time domain sampling points) *Z<`TB)<X dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05. "*<9)vQ6| T =40; % length of time:T*T0. 3g)pLW dt = T/N; % time step j^>J*gLM}W n = [-N/2:1:N/2-1]'; % Index 6 fL=2a t = n.*dt; \&"gCv# ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. 4OC^IS w=2*pi*n./T; `cCsJm$V" g1=-i*ww./2; w8c71C g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; vDqmD{%4N g3=-i*ww./2; +AO(e P1=0; [Jwo,?w P2=0; REli`"bR P3=1; >]s|'HTxF P=0; 3D(/k%;) for m1=1:M1 1o
V\QK& p=0.032*m1; %input amplitude %?^IS&]Z s10=p.*sech(p.*t); %input soliton pulse in waveguide 1 IyOb0WiEj s1=s10; }f/ 1 s20=0.*s10; %input in waveguide 2 t[Qf|#g s30=0.*s10; %input in waveguide 3 S&q@M s2=s20; +7.\>Ucq` s3=s30; lmfvT}$B p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1)))); w9G (^jS6 %energy in waveguide 1 jEo)#j];`< p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1)))); WRe9ki=R %energy in waveguide 2 `O5wM\Z p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1)))); scT,yNV %energy in waveguide 3 xk7MMRb for m3 = 1:1:M3 % Start space evolution fp^{612O? s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS TgoaEufS< s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; 3rBSwgRl s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; 0Q`Dp;a5& sca1 = fftshift(fft(s1)); % Take Fourier transform 5<^$9(' sca2 = fftshift(fft(s2)); ~=67#&(R sca3 = fftshift(fft(s3)); F0(P2j sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift H,u {zU') sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); x-1RmL_% sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); #ue WU s3 = ifft(fftshift(sc3)); g0O~5.f s2 = ifft(fftshift(sc2)); % Return to physical space g(& hu S s1 = ifft(fftshift(sc1)); XYj!nx{k, end LDc?/
Z1 p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); C9OEB6 p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); Ve)P/Zz}^ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); iI.pxo
s P1=[P1 p1/p10]; xq$(=WPI P2=[P2 p2/p10]; tpPP5C{ P3=[P3 p3/p10]; &6wD P=[P p*p]; w`KqB(36 end 4&N#d;ErC figure(1) +-2o b90_m plot(P,P1, P,P2, P,P3); ,Pi!%an w }:+SA 转自:http://blog.163.com/opto_wang/
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