| 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 U||w6:W5 I!soV0VU] % This Matlab script file solves the coupled nonlinear Schrodinger equations of N.Wdi % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of vS24;:f % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 6iV"Tl{z- % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ?( dYW7S TJ%]{%F %fid=fopen('e21.dat','w'); C&CsI] @g N = 128; % Number of Fourier modes (Time domain sampling points) $<>EwW M1 =3000; % Total number of space steps aJa^~*N/Aa J =100; % Steps between output of space &xiDG=I# T =10; % length of time windows:T*T0 4HJZ^bq9| T0=0.1; % input pulse width #.<F5
MN1=0; % initial value for the space output location r
PRuSk-f dt = T/N; % time step !>Qc2&ZV n = [-N/2:1:N/2-1]'; % Index 5qtmb4R~ t = n.*dt; @7[.>I( u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10 ek;&<Z_ ] u20=u10.*0.0; % input to waveguide 2 ah!O&ECh u1=u10; u2=u20; *|gs-<[#X U1 = u1; ,Q /nS$ U2 = u2; % Compute initial condition; save it in U /Vm}+"BCS ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. &8_#hne_ w=2*pi*n./T; kvgs $ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T l
SVW}t L=4; % length of evoluation to compare with S. Trillo's paper S'-`\%@7 dz=L/M1; % space step, make sure nonlinear<0.05 uZiY<(X for m1 = 1:1:M1 % Start space evolution F#}1{$)%
/ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS eE riv@v u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; eDM0417O( ca1 = fftshift(fft(u1)); % Take Fourier transform *_).UAP. ca2 = fftshift(fft(u2)); E][{RTs c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation vo( j@+dz c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift moJT8tb u2 = ifft(fftshift(c2)); % Return to physical space }MavI' u1 = ifft(fftshift(c1)); ^tKOxW#
a if rem(m1,J) == 0 % Save output every J steps. /4B4IT U1 = [U1 u1]; % put solutions in U array MkNURy>n& U2=[U2 u2]; HT,kx MN1=[MN1 m1]; {EoyMJgz z1=dz*MN1'; % output location kW2nrkF end W6xjqNU end EAd:`X,Y hg=abs(U1').*abs(U1'); % for data write to excel >pH775I= ha=[z1 hg]; % for data write to excel ,8"[ /@ t1=[0 t']; 2eR+dT hh=[t1' ha']; % for data write to excel file _hyxKrm'
6 %dlmwrite('aa',hh,'\t'); % save data in the excel format , w'$T) figure(1)
&pY G waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn SX=0f^ figure(2) k-ex<el)# waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn On.x~t 4bFVyv 非线性超快脉冲耦合的数值方法的Matlab程序 :%b2;&A[ V&+$Vq 在研究脉冲在非线性耦合器中的演变时,我们需要求解非线性偏微分方程组。在如下的论文中,我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。 Oc/_T> Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 C94UF7al eZod}~J8 ^.1VhTB Fee WZe0i % This Matlab script file solves the nonlinear Schrodinger equations v{{2<,l % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of "`3^MvC % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear ^'I5]cRa % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 |m 5;M$M) )(!Z90@ C=1; .f<VmUca M1=120, % integer for amplitude .yfqS|( M3=5000; % integer for length of coupler )>M@hIV5> N = 512; % Number of Fourier modes (Time domain sampling points) #Xw[i dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05. L%O8vn^3 T =40; % length of time:T*T0. (:HbtrI dt = T/N; % time step Cz);mOb%M% n = [-N/2:1:N/2-1]'; % Index 9"lW"lG! t = n.*dt; ;ld~21#m ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. {ZM2WFpE w=2*pi*n./T; No&[ \; g1=-i*ww./2; >Wit"p g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; F4<2.V)#- g3=-i*ww./2; wYMX1= P1=0; 6`";)T[ G9 P2=0; /^eemx P3=1; G{Enh<V P=0; 9c %Tv for m1=1:M1 ^?]H$e p=0.032*m1; %input amplitude 3R:i*8C s10=p.*sech(p.*t); %input soliton pulse in waveguide 1 {5IG3' s1=s10; J9=0?^v-:B s20=0.*s10; %input in waveguide 2 @OY-(cW s30=0.*s10; %input in waveguide 3 BI^]juH-c s2=s20; 5"~^;O s3=s30; )$4DH:WN p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1)))); 5t#]lg[06' %energy in waveguide 1 b-zX3R; p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1)))); jh&vq=PH %energy in waveguide 2 'I>#0VRr p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1)))); 4bzn^ %energy in waveguide 3 D=sc41] for m3 = 1:1:M3 % Start space evolution _";pk _ s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS 9x{prCr s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; +vSE} s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; fO(S+} sca1 = fftshift(fft(s1)); % Take Fourier transform AX RNV sca2 = fftshift(fft(s2)); T`ZJ=gv sca3 = fftshift(fft(s3)); "[S
6w sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift AR6vc sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); l4reG:uYG sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); jyH_/X5i7 s3 = ifft(fftshift(sc3)); h:sG23@= s2 = ifft(fftshift(sc2)); % Return to physical space kD7(}N8YR s1 = ifft(fftshift(sc1)); iQ"F`C end Hll}8d6[ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); &*GX:0=/> p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); slfVQ809 p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); \o)4m[oF P1=[P1 p1/p10]; :=eUNH P2=[P2 p2/p10]; J\D3fh97- P3=[P3 p3/p10]; 2B dr#qr P=[P p*p]; :Rj,'uH+h) end 1 ZFSz{ figure(1) ea>\.D-S plot(P,P1, P,P2, P,P3); 4H)"d |bnjC $b * 转自:http://blog.163.com/opto_wang/
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