计算脉冲在非线性耦合器中演化的Matlab 程序 #JR$RH er<_;"`1 % This Matlab script file solves the coupled nonlinear Schrodinger equations of
S~M/!Xb % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
n(_wt##wE~ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
;8w
CQ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
d}wE4(]b \W|ymV_Ki %fid=fopen('e21.dat','w');
+pe\9F N = 128; % Number of Fourier modes (Time domain sampling points)
K6 ,d{n M1 =3000; % Total number of space steps
IiV]lxiE] J =100; % Steps between output of space
_~;K ] T =10; % length of time windows:T*T0
? 8)k6: T0=0.1; % input pulse width
Gz2 \&rmN MN1=0; % initial value for the space output location
:0p$r
pJP dt = T/N; % time step
y2nT)nL n = [-N/2:1:N/2-1]'; % Index
Z>*a:| t = n.*dt;
W r+1e1[ u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
uJa.]J~L= u20=u10.*0.0; % input to waveguide 2
;aH3{TS u1=u10; u2=u20;
=FQH5iSd U1 = u1;
EmyE%$*T U2 = u2; % Compute initial condition; save it in U
=[0| qGzg ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
\)W Z D w=2*pi*n./T;
(W#^- *$R g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
yc f)*0k L=4; % length of evoluation to compare with S. Trillo's paper
P.djR) YI dz=L/M1; % space step, make sure nonlinear<0.05
| NyANsI for m1 = 1:1:M1 % Start space evolution
gCbS$Pw u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
mNJCV8 < u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
34L1Gxf
ca1 = fftshift(fft(u1)); % Take Fourier transform
QFFFxaeJg ca2 = fftshift(fft(u2));
j%gle%_ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
+5GPU 9k c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
HT6$|j u2 = ifft(fftshift(c2)); % Return to physical space
:g{ybTSEe u1 = ifft(fftshift(c1));
biRkq c; if rem(m1,J) == 0 % Save output every J steps.
Us_1 #$p, U1 = [U1 u1]; % put solutions in U array
Yi <1z:\ U2=[U2 u2];
Ged } qXn MN1=[MN1 m1];
4r #4h4`y| z1=dz*MN1'; % output location
|{MXDx end
- *qoF(/ U end
(~fv; }}v hg=abs(U1').*abs(U1'); % for data write to excel
wGWv<<Qw" ha=[z1 hg]; % for data write to excel
|<%v`* t1=[0 t'];
s%G%s,d hh=[t1' ha']; % for data write to excel file
9zm2}6r4 %dlmwrite('aa',hh,'\t'); % save data in the excel format
{
PS0.UZ figure(1)
CD4@ 0Z+ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
cI-@nV figure(2)
< Yc)F.: waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
li0)<("/ BE!l{ 非线性超快脉冲耦合的数值方法的Matlab程序 6_K7!?YG7 o3:BH@@ 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。
v`U;.W 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
Hx n#vAc Bv e',.xH AuY*x;~ H#G3CD2& % This Matlab script file solves the nonlinear Schrodinger equations
,:0!+1 % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
z`,dEGfh^ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
lUw=YM % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
h)s&Nqg1B ^?|d< J:{ C=1;
&ViK9 M1=120, % integer for amplitude
g!Ui|]BI9 M3=5000; % integer for length of coupler
WA.c .{w\ N = 512; % Number of Fourier modes (Time domain sampling points)
kV4L4yE dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
mZ.gS1Dq T =40; % length of time:T*T0.
KL "_h`UW dt = T/N; % time step
uH#X:Vne n = [-N/2:1:N/2-1]'; % Index
O\h%ZLjfO t = n.*dt;
ux)Wh.5 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
VO /b&% w=2*pi*n./T;
GGU wS g1=-i*ww./2;
%g69kizoWi g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
@9l$j Z~x g3=-i*ww./2;
6XnUs1O P1=0;
2>f3 n W P2=0;
gLlA'` ! P3=1;
s.a @uR^ P=0;
h?vny->uJ for m1=1:M1
\\{78WDA p=0.032*m1; %input amplitude
t{` uN s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
yZb})4. s1=s10;
(%G>TV s20=0.*s10; %input in waveguide 2
h!tg+9 % s30=0.*s10; %input in waveguide 3
- %?> 1n s2=s20;
Y oZd,} i s3=s30;
>y$*|V}k p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
Q8_5g$X\ %energy in waveguide 1
Nh !U p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
5i'KG L %energy in waveguide 2
[8vqw(2Tm( p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
bNHs jx@ %energy in waveguide 3
,+x\NY2d for m3 = 1:1:M3 % Start space evolution
Wxgs66 s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
Q+'fT mT[, s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
hMgk+4* s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
X?] Mzcu sca1 = fftshift(fft(s1)); % Take Fourier transform
Z=l2Po n sca2 = fftshift(fft(s2));
C Y"i|s sca3 = fftshift(fft(s3));
Hi U/fi ` sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
IvI;Q0E-3 sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
`W7; - sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
#IeG/ t( s3 = ifft(fftshift(sc3));
!:~C /B{ s2 = ifft(fftshift(sc2)); % Return to physical space
Kr`. q:0GK s1 = ifft(fftshift(sc1));
F5{GMn;j end
COd~H p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
'=d y
= p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
Y 2^y73&k p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
9h<iw\ $' P1=[P1 p1/p10];
PGb}Y { P2=[P2 p2/p10];
> n1UK5QD P3=[P3 p3/p10];
) P|/<>z P=[P p*p];
C *Q x end
m-q O yt figure(1)
lxBcO/ plot(P,P1, P,P2, P,P3);
@;[. #hK 7e{w,.ny! 转自：
http://blog.163.com/opto_wang/
