| 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 &NjZD4m`= rg^\BUa-W, % This Matlab script file solves the coupled nonlinear Schrodinger equations of !VX_'GyK % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of 7Y|>xx=v % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear xO<-<sRA % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ^Pg
YP 0aTbzOn& %fid=fopen('e21.dat','w'); ~wf~bzs N = 128; % Number of Fourier modes (Time domain sampling points) }0*ra37z> M1 =3000; % Total number of space steps jnp6qpY{ J =100; % Steps between output of space T:%wX9W T =10; % length of time windows:T*T0 liw 9:@+V T0=0.1; % input pulse width fyq]M_5 MN1=0; % initial value for the space output location :.[5(' dt = T/N; % time step uxMy1oy n = [-N/2:1:N/2-1]'; % Index FR,#s^kF t = n.*dt; 6a]f&={E u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10 K:
o|kd u20=u10.*0.0; % input to waveguide 2 Ya&\ly
/i u1=u10; u2=u20; _2X6bIE U1 = u1; *_/eAi/WG U2 = u2; % Compute initial condition; save it in U iC|6roO!jk ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. EXW
6yXLV w=2*pi*n./T; CDwIq>0j g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T Pv %vx U L=4; % length of evoluation to compare with S. Trillo's paper 5?{ >9j5 dz=L/M1; % space step, make sure nonlinear<0.05 %{~mk[d3 for m1 = 1:1:M1 % Start space evolution D0y,TF u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS TQ\wHJ u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; ssX6kgq_( ca1 = fftshift(fft(u1)); % Take Fourier transform lmtQr5U ca2 = fftshift(fft(u2)); [+MH[1Vr={ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation Z>Kcz^a# c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift gvc'
$9% u2 = ifft(fftshift(c2)); % Return to physical space o(X90X u1 = ifft(fftshift(c1)); n?e@): if rem(m1,J) == 0 % Save output every J steps. sx( l U1 = [U1 u1]; % put solutions in U array G9'YgW+$7 U2=[U2 u2]; \B>[je-d MN1=[MN1 m1]; !/Bw,y ri< z1=dz*MN1'; % output location (m3I#L end wO_pcNYZ8 end 4&]To@> hg=abs(U1').*abs(U1'); % for data write to excel j^$3vj5E[ ha=[z1 hg]; % for data write to excel uWR,6\_jY t1=[0 t']; t=W$'*P0} hh=[t1' ha']; % for data write to excel file kf^-m/ %dlmwrite('aa',hh,'\t'); % save data in the excel format 34m' ]n figure(1) [Z5}2gB& waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn !skb=B# figure(2) q(&^9" waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn q0b`HD Z\*5:a] 非线性超快脉冲耦合的数值方法的Matlab程序 C?/r}ly<\ Bgk~R.l 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。 fD\^M{5f 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 qtdxMX]iR 0.u9f`04 [!:-m61 cFI7}#,5 % This Matlab script file solves the nonlinear Schrodinger equations qrM{b= % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of @ yg|OA} % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 7SA-OFM % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 VeD+U~ d nv_m!JG7 C=1; XC7Ty'#"KX M1=120, % integer for amplitude 0$f_or9T M3=5000; % integer for length of coupler N'eQ>2>O@ N = 512; % Number of Fourier modes (Time domain sampling points) -
5o<Q'( dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05. Y>78h2AU T =40; % length of time:T*T0. =2;mxJ# o dt = T/N; % time step B{OW}D$P# n = [-N/2:1:N/2-1]'; % Index 1C}pv{0:& t = n.*dt; ~ F?G5cN5 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. ]uStn w=2*pi*n./T; e_I; y g1=-i*ww./2; vR%j#v|s g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; @Hspg^ g3=-i*ww./2; )8x:x7? P1=0; 7,W]zKH P2=0; {FV,j.D P3=1; W2F+^ P=0; C;d|\[7Z for m1=1:M1 }sTH.% p=0.032*m1; %input amplitude L)kb (TH s10=p.*sech(p.*t); %input soliton pulse in waveguide 1 ]HJ{dcF s1=s10; ;1*m}uNz s20=0.*s10; %input in waveguide 2 B&4fYpn s30=0.*s10; %input in waveguide 3 B91S
h` s2=s20; 5T$9'5V7 s3=s30; iioct_7,g< p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1)))); TZ&4 %energy in waveguide 1 [|:QE~U@ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1)))); 54ak<&? %energy in waveguide 2 RsqRR`|X? p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1)))); QQ^Gd8nQ %energy in waveguide 3 _"?c9 for m3 = 1:1:M3 % Start space evolution ot|N;=ZKo s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS Xk{!' 0 s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; LPq*ZZK s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; Cbgj@4H sca1 = fftshift(fft(s1)); % Take Fourier transform pr62: sca2 = fftshift(fft(s2)); (TT3(|v sca3 = fftshift(fft(s3)); 5 `4}A%@& sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift fnLR
sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); avu*>SB sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); XPHQAo[(s s3 = ifft(fftshift(sc3)); Gt^|+[gD s2 = ifft(fftshift(sc2)); % Return to physical space 8BYIxHHz s1 = ifft(fftshift(sc1)); 2gQY8h8 end 8Zcol$XS' p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); ! 6p>P4TT p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); i_|9<7a
p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); c&E*KfOG P1=[P1 p1/p10]; l 8O"w& P2=[P2 p2/p10]; &ui:DZAxj| P3=[P3 p3/p10]; C-s>1\I P=[P p*p]; |Hx%f end kJ%{ [1fr figure(1) /[\6oa plot(P,P1, P,P2, P,P3); D+|
K%_Qq ~mN g[] 转自:http://blog.163.com/opto_wang/
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