| 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 r k;k:<c -! Hn,93 % This Matlab script file solves the coupled nonlinear Schrodinger equations of 9nlfb~F~P % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of abkl)X>k % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear e.jrX;;$!& % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 *Hy-D</w% [ ps5; %fid=fopen('e21.dat','w'); ]7n+|@3x N = 128; % Number of Fourier modes (Time domain sampling points) "Q6oPDX( M1 =3000; % Total number of space steps @6 uB78U4O J =100; % Steps between output of space eWSA T =10; % length of time windows:T*T0 Ehu^_HZ T0=0.1; % input pulse width [ !/u, MN1=0; % initial value for the space output location Y&KI/]ly,L dt = T/N; % time step I~?D^ n = [-N/2:1:N/2-1]'; % Index (:Rj:8{ t = n.*dt; wgxr8;8`q u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10 js)M
c*]& u20=u10.*0.0; % input to waveguide 2 t7tX<|aN u1=u10; u2=u20; `z%f@/:fG U1 = u1; 0]=|3-n U2 = u2; % Compute initial condition; save it in U r$}M,! J ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. z&[Rw<{Psb w=2*pi*n./T; Ahk6{uz g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T 4Ei*\: L=4; % length of evoluation to compare with S. Trillo's paper Z
.VIb| dz=L/M1; % space step, make sure nonlinear<0.05 Gs;wx_k^ for m1 = 1:1:M1 % Start space evolution )isz
}?Dj u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS }Tf~)x u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; \,)('tUE ca1 = fftshift(fft(u1)); % Take Fourier transform /]m5HW(P7K ca2 = fftshift(fft(u2)); SYd4 3PA c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation Z8*E-y0 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift F8mS5oB|^
u2 = ifft(fftshift(c2)); % Return to physical space L#mf[a@pCn u1 = ifft(fftshift(c1)); <VI.A" Qk~ if rem(m1,J) == 0 % Save output every J steps. ^N#B(F U1 = [U1 u1]; % put solutions in U array 6U5L>sQ U2=[U2 u2]; 2\80S[f MN1=[MN1 m1]; 7{>mm$^|V z1=dz*MN1'; % output location Uo?g@D end _ K["qm{X_ end H<41H;m hg=abs(U1').*abs(U1'); % for data write to excel vFm8 T58 7 ha=[z1 hg]; % for data write to excel %0l'Nuz t1=[0 t']; b>SG5EqU@ hh=[t1' ha']; % for data write to excel file ,]RMa\Q4Wg %dlmwrite('aa',hh,'\t'); % save data in the excel format cB#5LXbCE figure(1) y "6;O 0 waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn =p~k5k4 figure(2) 6D3hX>K4 waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn mh&wvT<:{ o;5 J= 非线性超快脉冲耦合的数值方法的Matlab程序 Em8q1P$tm> =y+gS%o$ 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。 Gy 0 m 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 k|V%*BvY> e>z &zkuL 2$ m#)*\ % This Matlab script file solves the nonlinear Schrodinger equations VwJ A % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of ?5'E P|< % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear qj|P0N{7 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 cW%QKdTQY0 I!sh+e C=1; &w15GO;4 M1=120, % integer for amplitude \%&BK.t M3=5000; % integer for length of coupler ;;>hWAS N = 512; % Number of Fourier modes (Time domain sampling points) Y$JGpeq8w dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05. A#NJ8_ T =40; % length of time:T*T0. ; '6`hZ dt = T/N; % time step 9~3;upWu! n = [-N/2:1:N/2-1]'; % Index s4V-brCM$| t = n.*dt; ZAATV+Z ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. -DAkVFsN w=2*pi*n./T; |q|?y`X4/ g1=-i*ww./2; _[%2QwAUj* g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; b;Nm$`2 g3=-i*ww./2; c,@&Z#IZ` P1=0; Rhw- 49AWx P2=0; ?X
$#J'U; P3=1; .M(')$\U P=0; gR5
EK$ for m1=1:M1 ZVu_E.4. p=0.032*m1; %input amplitude o,qq*}= s10=p.*sech(p.*t); %input soliton pulse in waveguide 1 q|7i6jq\*R s1=s10; R:N4_4& C~ s20=0.*s10; %input in waveguide 2 srS2v\1: s30=0.*s10; %input in waveguide 3 <'T:9 s2=s20; +lYo5\1= s3=s30; @FNaCmBX p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1)))); {"v~1W) %energy in waveguide 1 ^Pwtu p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1)))); S7!+8$2mc_ %energy in waveguide 2 Fh8 8DDJ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1)))); DsJ ikg(J %energy in waveguide 3 g2RrBK, for m3 = 1:1:M3 % Start space evolution \_vjc]? s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS ~Un+Zs%24 s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; 7{z\^R^O s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; =Ff _)k
sca1 = fftshift(fft(s1)); % Take Fourier transform 5&
2([ sca2 = fftshift(fft(s2)); 8'sT zB] sca3 = fftshift(fft(s3)); 7];AB;0" sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift yN@3uYBF sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); ()}(3>O- sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); $Wy(Wtrx| s3 = ifft(fftshift(sc3)); 8_W=)w6 s2 = ifft(fftshift(sc2)); % Return to physical space rtSG-_[i s1 = ifft(fftshift(sc1)); 9ZJn 8ki end -s3q(SH p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); ZA1:Y{V p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); :QoW*Gs1 p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); omP\qOc P1=[P1 p1/p10]; r5,V-5b P2=[P2 p2/p10]; qkbGM-H%U P3=[P3 p3/p10]; REg&[e+% P=[P p*p]; Sj'Iz # end
N%f%
U figure(1) :kMF.9U: plot(P,P1, P,P2, P,P3); AAXlBY6Y- b)+;=o% 转自:http://blog.163.com/opto_wang/
|
|