| 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 %/~6Qq P[ n`X % This Matlab script file solves the coupled nonlinear Schrodinger equations of AR`X2m ' % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of L{bcmo\U % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear .oH0yNFX % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 r^ S4 I& ;WJ}zjo > %fid=fopen('e21.dat','w'); /tc*jXB N = 128; % Number of Fourier modes (Time domain sampling points) F)j-D(c4 M1 =3000; % Total number of space steps mC
n,I J =100; % Steps between output of space vi4u ` T =10; % length of time windows:T*T0 5xwztcR- T0=0.1; % input pulse width *GbC`X) MN1=0; % initial value for the space output location ylLQKdcL dt = T/N; % time step 9bl&\Ykt. n = [-N/2:1:N/2-1]'; % Index r|:|\"Yk t = n.*dt; uaNJTob u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10 O;ZU{VY u20=u10.*0.0; % input to waveguide 2 VxLq,$B76 u1=u10; u2=u20; l?NRQTG U1 = u1; _Z.lr\ U2 = u2; % Compute initial condition; save it in U M<r'j $g ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. 7_.z3Km: w=2*pi*n./T; Fo3[KW)8I g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T { r`l L=4; % length of evoluation to compare with S. Trillo's paper Q mOG2 dz=L/M1; % space step, make sure nonlinear<0.05 @R9zLL6#7 for m1 = 1:1:M1 % Start space evolution Pr{? A]dQ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS '$ ~.x| u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; }C/u>89%q ca1 = fftshift(fft(u1)); % Take Fourier transform L^KGY<hp4 ca2 = fftshift(fft(u2)); mwZesSxB_ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation <wFR%Y/j c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift ^ox^gw) u2 = ifft(fftshift(c2)); % Return to physical space nj!)\U u1 = ifft(fftshift(c1)); }+nC}A"BC if rem(m1,J) == 0 % Save output every J steps. %'kaNpBz U1 = [U1 u1]; % put solutions in U array 4
`Z @^W U2=[U2 u2]; ?1?^>M MN1=[MN1 m1]; ^5qX+!3r{ z1=dz*MN1'; % output location L=iaL[zdJ end e7t).s)b{ end sD1L
P hg=abs(U1').*abs(U1'); % for data write to excel muQH!Q ha=[z1 hg]; % for data write to excel R<Ojaj=V t1=[0 t']; mAhtC* hh=[t1' ha']; % for data write to excel file mk~i (Ee %dlmwrite('aa',hh,'\t'); % save data in the excel format 9hHQWv7TgK figure(1) )@ZJ3l. waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn ({yuwH?tH figure(2) %:h)8e-; waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn T3[\;ib} KM g`O3_16 非线性超快脉冲耦合的数值方法的Matlab程序 ^b~&}uU }pbyC 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。 B~cq T/\? 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 %.r{+m FAjO-T4( K7FuMB F8 ;M++ % This Matlab script file solves the nonlinear Schrodinger equations p^&' C_? % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of hmtRs]7 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear )-Zpr1kD % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 tV9W4`Z2q 6dV@.(][a C=1; o{4ya jt M1=120, % integer for amplitude l,1 }1{k& M3=5000; % integer for length of coupler 1.o-2:]E N = 512; % Number of Fourier modes (Time domain sampling points) brb8C%j}9 dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05. QUaz;kNC7 T =40; % length of time:T*T0. U`,&Q] dt = T/N; % time step KunK.m n = [-N/2:1:N/2-1]'; % Index `4.Wdi-Si t = n.*dt; ]cc4+}L~ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. uTpKT7t w=2*pi*n./T; lN,b@; g1=-i*ww./2; !aeL*`; g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; 7$z")JB g3=-i*ww./2; !w[<?+%%n P1=0; :@wO'
o P2=0; /&$'v:VB P3=1; }zj w\ P=0; :M`|*~V~$ for m1=1:M1 9;&2LT7z p=0.032*m1; %input amplitude S6 $S%$ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1 ,cWO Ak s1=s10; 82~UI'f \ s20=0.*s10; %input in waveguide 2 D=mU!rjr1 s30=0.*s10; %input in waveguide 3 nUQcoSY# s2=s20; mbsdiab#N s3=s30; ,yWTkql p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1)))); r%xp^j} %energy in waveguide 1 uwj/]#` p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1)))); \_!FOUPz( %energy in waveguide 2 Uey.@ 2Q p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1)))); Y`LZ/Tgk %energy in waveguide 3 R9o:{U] for m3 = 1:1:M3 % Start space evolution 6^wg'u]c s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS ?f1%)]>
s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; %bt2^ s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; _R1UEE3M sca1 = fftshift(fft(s1)); % Take Fourier transform N(dn"`8 sca2 = fftshift(fft(s2)); %\}|& | |