计算脉冲在非线性耦合器中演化的Matlab 程序 w4fJ`, fFZ` rPb % This Matlab script file solves the coupled nonlinear Schrodinger equations of
@7l=+`.i % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
lmtQr5U % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
oF b mz* % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
$:u7Dv}\ a EFe!_QY %fid=fopen('e21.dat','w');
$Y 4c h ko N = 128; % Number of Fourier modes (Time domain sampling points)
@t; O"q'| M1 =3000; % Total number of space steps
vgQhdtt J =100; % Steps between output of space
%<J(lC9,C T =10; % length of time windows:T*T0
j&[3Be'pQ T0=0.1; % input pulse width
vi! r8k MN1=0; % initial value for the space output location
FM" GK ' dt = T/N; % time step
P vg n = [-N/2:1:N/2-1]'; % Index
*4 hOCQ[ t = n.*dt;
8A8xY446) u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
Tu= eQS|' u20=u10.*0.0; % input to waveguide 2
!: EW21m u1=u10; u2=u20;
d JQ }{,+6 U1 = u1;
ttbQergS U2 = u2; % Compute initial condition; save it in U
{F(-s"1;xO ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
7\0|`{|R@ w=2*pi*n./T;
!skb=B# g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
jWv3O&+?X L=4; % length of evoluation to compare with S. Trillo's paper
=2g[tsY dz=L/M1; % space step, make sure nonlinear<0.05
# McK46B z for m1 = 1:1:M1 % Start space evolution
n$m]58w u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
71 L\t3fG u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
9-a2L JI ca1 = fftshift(fft(u1)); % Take Fourier transform
,p*ntj{ ca2 = fftshift(fft(u2));
VO @
4A6 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
xu"94y+ c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
x<{;1F,k3 u2 = ifft(fftshift(c2)); % Return to physical space
fUp|3bBE u1 = ifft(fftshift(c1));
RQ*|+ ~H if rem(m1,J) == 0 % Save output every J steps.
MgH1d&R U1 = [U1 u1]; % put solutions in U array
@\6nXf U2=[U2 u2];
e}?1T7NPG] MN1=[MN1 m1];
@;m@Luk z1=dz*MN1'; % output location
-VreBKn end
J/]o WC`u end
2sd ) w hg=abs(U1').*abs(U1'); % for data write to excel
EG(`E9DZ ha=[z1 hg]; % for data write to excel
5Aa31"43n t1=[0 t'];
7}#*3*] hh=[t1' ha']; % for data write to excel file
yd0=h7s %dlmwrite('aa',hh,'\t'); % save data in the excel format
,Ou1!`6?t figure(1)
U+9- li waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
]uStn figure(2)
qL%.5OCn( waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
"LP,
T C "UhK]i*@l 非线性超快脉冲耦合的数值方法的Matlab程序 nCf fBc +K$5t T6b 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
%?]{U($? 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
Qr|N) NRHr6!f> ( E"&UC[ (<]\,pP0_ % This Matlab script file solves the nonlinear Schrodinger equations
Lo|NE[b:G % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
< K DH % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
,<0Rf % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
5eiZ s ^Txu ~r0@ C=1;
{2} tPT[a( M1=120, % integer for amplitude
9:9N)cNvfX M3=5000; % integer for length of coupler
n=<NFkeX N = 512; % Number of Fourier modes (Time domain sampling points)
vi[#? ;pkF dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
||{T5E-.F T =40; % length of time:T*T0.
+ AcKB82 dt = T/N; % time step
q:`77 n = [-N/2:1:N/2-1]'; % Index
T@K7DkP@ t = n.*dt;
45Nv_4s ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
K;<NBnH w=2*pi*n./T;
pY{; Yn&t g1=-i*ww./2;
]+}ZfHp g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
`DgaO-Dg3 g3=-i*ww./2;
71k!k&Im P1=0;
F e_::NVvk P2=0;
38V $ <w P3=1;
9]]!8_0=r P=0;
hw&ke$Fg# for m1=1:M1
b{~fVil$y p=0.032*m1; %input amplitude
]k[ Q] :q s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
1KeJd&e s1=s10;
- :)DX++ s20=0.*s10; %input in waveguide 2
J- t=1 s30=0.*s10; %input in waveguide 3
wb(*7 &eP: s2=s20;
A|p@\3 P*A s3=s30;
c&E*KfO G p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
@wd!&%yzO %energy in waveguide 1
`FZ(#GDF p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
i&A{L}eCr: %energy in waveguide 2
2x-'>i_|g p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
l?3vNa FeR %energy in waveguide 3
TqENaC#& for m3 = 1:1:M3 % Start space evolution
a(PjcQ4dY s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
HBt|}uZ?6i s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
?ada>"~GR_ s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
,bB( 24LD sca1 = fftshift(fft(s1)); % Take Fourier transform
lTa1pp
Zw sca2 = fftshift(fft(s2));
R(M}0JRm sca3 = fftshift(fft(s3));
Hnfvo*6d.e sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
Ivz+Jj w sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
G wgFi@itN sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
_ oQtk^fp s3 = ifft(fftshift(sc3));
[Xxw]C6\>( s2 = ifft(fftshift(sc2)); % Return to physical space
e(?:g@]-r s1 = ifft(fftshift(sc1));
n?y 'c^ end
jK3g iT p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
\w{@u)h p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
WuBmdjZ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
9k+N3vA P1=[P1 p1/p10];
l _^T&xq8 P2=[P2 p2/p10];
^36M0h|R P3=[P3 p3/p10];
pwa.q P=[P p*p];
]O6KK z end
~Y\QGuT figure(1)
4st~3,lR$ plot(P,P1, P,P2, P,P3);
9uuta4&uI p@#]mVJ>9 转自：
http://blog.163.com/opto_wang/
