| 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 G88g@Exk y-vBC3 % This Matlab script file solves the coupled nonlinear Schrodinger equations of T28Q(\C:} % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of MT.D#jv& % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear /Y*6mQ: % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 WSV% Oy3V 2L?Pw %fid=fopen('e21.dat','w'); XNB4KjT N = 128; % Number of Fourier modes (Time domain sampling points)
Ndqhc M1 =3000; % Total number of space steps yv.(Oy J =100; % Steps between output of space 4:qM'z T =10; % length of time windows:T*T0 c +]5[6 T0=0.1; % input pulse width *7!*kqg!u MN1=0; % initial value for the space output location G+jcR; s dt = T/N; % time step o%?~9rf]] n = [-N/2:1:N/2-1]'; % Index )Jd{WC. t = n.*dt; Ec|5'Kz] u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10 __,}/|K2 u20=u10.*0.0; % input to waveguide 2 1EA} [x u1=u10; u2=u20; R>`TV(W`9 U1 = u1; A*+KlhT
U2 = u2; % Compute initial condition; save it in U SR&'38UCe ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. m*H6\on: w=2*pi*n./T; FLOSdMYdw g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T 1$rrfg L=4; % length of evoluation to compare with S. Trillo's paper )\0LxsZ dz=L/M1; % space step, make sure nonlinear<0.05 "(SZ;y for m1 = 1:1:M1 % Start space evolution ~JxAo\2i u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS rTLo6wI u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; ~0XV[$`L ca1 = fftshift(fft(u1)); % Take Fourier transform FR 1se ca2 = fftshift(fft(u2)); $eUJd Aetk c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation naWW i]9 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift (= ,w$ u2 = ifft(fftshift(c2)); % Return to physical space O=wu0n u1 = ifft(fftshift(c1)); /,#&Htk if rem(m1,J) == 0 % Save output every J steps. }e0)=*;l U1 = [U1 u1]; % put solutions in U array A+1>n^^_< U2=[U2 u2]; pbb6?R, MN1=[MN1 m1]; A;#GU` z1=dz*MN1'; % output location 5K % end V/i7Z h#2: end Xw[|$#QKM hg=abs(U1').*abs(U1'); % for data write to excel z9[BQ(9t ha=[z1 hg]; % for data write to excel !)TO2?,^ t1=[0 t']; ]NgEN hh=[t1' ha']; % for data write to excel file :6X?EbXhK %dlmwrite('aa',hh,'\t'); % save data in the excel format =f{YwtG figure(1) f8?c[%br waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn (xhV>hsA figure(2) [ZkK)78}k waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn l:rT{l=8* q(cSHHv+ 非线性超快脉冲耦合的数值方法的Matlab程序 h$eVhN&Vv 7BDoF!kCx 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。 EkE U}2 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 $f]dL}; jFMf=u&U .ITR3]$ &WGG
kn % This Matlab script file solves the nonlinear Schrodinger equations A('_.J= % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of a4iq_F#NF % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear "vG~2J % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 KQ(7% W >X!A/;$ C=1; -%#F5br% M1=120, % integer for amplitude T1Y_Jf*KJ M3=5000; % integer for length of coupler woCFkO;'O N = 512; % Number of Fourier modes (Time domain sampling points) H]/!J] dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05. P1f@?R&t+ T =40; % length of time:T*T0.
;iMgv5= dt = T/N; % time step $9Yk]~ n = [-N/2:1:N/2-1]'; % Index (77EZ07% t = n.*dt; ?yqTLj ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. 4S+sz?W2j w=2*pi*n./T; J|A:C[7 2 g1=-i*ww./2; YKT=0 g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; @on\@~Ug g3=-i*ww./2; Ei[>%Ah P1=0; l
/\n7: P2=0; 4]$$ar) P3=1; 6$|!_94>*) P=0; X}s}E
;v9 for m1=1:M1 j[Xci<m p=0.032*m1; %input amplitude &0*=F%Fd s10=p.*sech(p.*t); %input soliton pulse in waveguide 1 CnA0^JX s1=s10; {v>orP? s20=0.*s10; %input in waveguide 2 wpLC, s30=0.*s10; %input in waveguide 3 atA:v3" s2=s20; Q7-d]xJ^ s3=s30; Z-D4~?Tv p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1)))); #I(Ho:b %energy in waveguide 1 aJi0!6oy p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1)))); uqg#(ADy?R %energy in waveguide 2 oI6l `K$ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1)))); }dt7n65 %energy in waveguide 3 g,N"o72) for m3 = 1:1:M3 % Start space evolution }L1-2 s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS #nS s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; X( H-U
q*( s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; ^Q'^9M2) sca1 = fftshift(fft(s1)); % Take Fourier transform /?,c4K,ap sca2 = fftshift(fft(s2)); hnbF}AD sca3 = fftshift(fft(s3)); (3>Z NTm sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift 5#SD$^ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); {IlX@qWr sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); qd7 86~ s3 = ifft(fftshift(sc3)); s}pn5zMp:8 s2 = ifft(fftshift(sc2)); % Return to physical space !VJ5(b s1 = ifft(fftshift(sc1)); #6%9*Rh end PafsO,i- p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); wwtk6;8@ p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); @}{~Ofs p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); i!!1^DMrw P1=[P1 p1/p10]; eaI!}#>R+ P2=[P2 p2/p10]; "$VqOSo P3=[P3 p3/p10]; zu~E} P=[P p*p]; KF#,Q end X~ AE?? figure(1) &u_s* plot(P,P1, P,P2, P,P3); w/`I2uYu D6KYkN(,v 转自:http://blog.163.com/opto_wang/
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