计算脉冲在非线性耦合器中演化的Matlab 程序 k1g-%DB =pmG.>Si % This Matlab script file solves the coupled nonlinear Schrodinger equations of
X6B, Mply % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
T} ?b,hNl$ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
<f}:YDY' % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
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U}c6/ &?p( UY7'" %fid=fopen('e21.dat','w');
,ko#z}Z4r, N = 128; % Number of Fourier modes (Time domain sampling points)
Sru0j/|H\ M1 =3000; % Total number of space steps
I8@leT\9M J =100; % Steps between output of space
QhTn 9S:D T =10; % length of time windows:T*T0
aLLI\3 T0=0.1; % input pulse width
&x*l{s[ MN1=0; % initial value for the space output location
*uK!w(;2 dt = T/N; % time step
=ePwGm1:c n = [-N/2:1:N/2-1]'; % Index
%LHt {:9. t = n.*dt;
p"6[ S u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
Cz 5U u20=u10.*0.0; % input to waveguide 2
a 01s'9Be u1=u10; u2=u20;
| *ZM{$ U1 = u1;
]==7P;_- U2 = u2; % Compute initial condition; save it in U
9k62_]w@6 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
T:%0i8 p w=2*pi*n./T;
&
\5 Ur^t g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
3zfpFgD! L=4; % length of evoluation to compare with S. Trillo's paper
@Kt!uKrI dz=L/M1; % space step, make sure nonlinear<0.05
1xkk5\ 3] for m1 = 1:1:M1 % Start space evolution
m7A3i<6p u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
U . <c#S u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
B/Q>i'e ca1 = fftshift(fft(u1)); % Take Fourier transform
8 * m,# ca2 = fftshift(fft(u2));
O:, Gmft + c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
t vW0 W c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
JY:Fu u2 = ifft(fftshift(c2)); % Return to physical space
".A W u1 = ifft(fftshift(c1));
rKOa9M if rem(m1,J) == 0 % Save output every J steps.
JB5%\ U1 = [U1 u1]; % put solutions in U array
A$\/D2S7! U2=[U2 u2];
X}={:T+6s MN1=[MN1 m1];
753gcY#i z1=dz*MN1'; % output location
lxD~l#)^ln end
M`=\ijUwN end
$b^ niL hg=abs(U1').*abs(U1'); % for data write to excel
YGyw^$.w ha=[z1 hg]; % for data write to excel
LoJEchRK t1=[0 t'];
{<Y!'WL{ hh=[t1' ha']; % for data write to excel file
6 AY~ >p %dlmwrite('aa',hh,'\t'); % save data in the excel format
h;(m b2 [R figure(1)
J7EWaXGbz waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
e&(Wn2)o figure(2)
,5~ C($-t waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
P?8$VAkj 06pY10 <>X 非线性超快脉冲耦合的数值方法的Matlab程序 (yT&&_zY4 N N:zQ_RT 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。
E 6Uj8]P` 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
]w -W \:JY[s/ |a\,([aU r|bGn#^ % This Matlab script file solves the nonlinear Schrodinger equations
.[:WMCc\ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
Qe9}%k6@E % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
WwKpZ67$R % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
u1z!OofN> 3s*mq@~1X C=1;
$ b_~ M1=120, % integer for amplitude
`09[25? M3=5000; % integer for length of coupler
)iPU N = 512; % Number of Fourier modes (Time domain sampling points)
:q2RgZE dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
n -wOLH T =40; % length of time:T*T0.
g+&wgyq5 dt = T/N; % time step
WdJeh:h n = [-N/2:1:N/2-1]'; % Index
3][
t = n.*dt;
p[!9 objU ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
$['`H)z w=2*pi*n./T;
/Vv)00 g1=-i*ww./2;
s9u7zqCF g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
-s91/|n g3=-i*ww./2;
hn&NypI P1=0;
S =sL: FC P2=0;
ph ~#{B(\ P3=1;
7{rRQ~s&g9 P=0;
?IO3w{fmH for m1=1:M1
q.ppYXJUXi p=0.032*m1; %input amplitude
`RqV\ 6G+ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
eNFA.*p< s1=s10;
,mD $h?g s20=0.*s10; %input in waveguide 2
JQ]MkP s30=0.*s10; %input in waveguide 3
P^BSl7cT s2=s20;
@Js@\)P79 s3=s30;
dr"@ 2=Z p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
m&_!*3BAG %energy in waveguide 1
.+ic6 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
4J[csU %energy in waveguide 2
Tkh?F5l p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
&b19s=Z, %energy in waveguide 3
FlH=P qc for m3 = 1:1:M3 % Start space evolution
AX{yfL s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
/hGu42YG s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
p,)pz_M s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
Ei@al>. \ sca1 = fftshift(fft(s1)); % Take Fourier transform
qyBo|AQ5 sca2 = fftshift(fft(s2));
!-B|x0fs sca3 = fftshift(fft(s3));
iSMVV<7 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
3KKq1][ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
#t ">tL sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
{\k:?w4 s3 = ifft(fftshift(sc3));
(rf8"T!" s2 = ifft(fftshift(sc2)); % Return to physical space
vrsOA@ee3H s1 = ifft(fftshift(sc1));
lYr W"(2 end
yMb.~A^$J p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
':T"nORC p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
7<F{a"5P p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
`9G1Bd8k P1=[P1 p1/p10];
0t 00X/ P2=[P2 p2/p10];
d]l(B+\vf P3=[P3 p3/p10];
RJOyPZ] P=[P p*p];
O~F8lQ end
{/qq *0wa figure(1)
m\| ie8 plot(P,P1, P,P2, P,P3);
Biy$p6 YYd!/@|N5 转自：
http://blog.163.com/opto_wang/
