计算脉冲在非线性耦合器中演化的Matlab 程序 +X}i%F' *H>rvE.K? % This Matlab script file solves the coupled nonlinear Schrodinger equations of
{@Mr7*u % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
{$*N1$(% % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
&p0e)o~Ux % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
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%fid=fopen('e21.dat','w');
wp[Ug2 ;G N = 128; % Number of Fourier modes (Time domain sampling points)
Vz{+3vfra6 M1 =3000; % Total number of space steps
6cQgp]% J =100; % Steps between output of space
<n"BPXF~ T =10; % length of time windows:T*T0
[6/ QU D8 T0=0.1; % input pulse width
QTV*m>D MN1=0; % initial value for the space output location
cr7MvXF- dt = T/N; % time step
XYE|=Tr] n = [-N/2:1:N/2-1]'; % Index
%u -x9 t = n.*dt;
G#M)5'Q]U u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
EE/mxN(< u20=u10.*0.0; % input to waveguide 2
; *
[:~5Wc u1=u10; u2=u20;
o5<<vvdA U1 = u1;
l'@-?p(Vuw U2 = u2; % Compute initial condition; save it in U
k ;WD[SV ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
GK(CuwJe w=2*pi*n./T;
P&-o>mM g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
92+8zX L=4; % length of evoluation to compare with S. Trillo's paper
{pzj@b 1S dz=L/M1; % space step, make sure nonlinear<0.05
p{FI_6db for m1 = 1:1:M1 % Start space evolution
KWTV!Wxb=K u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
]BQYVx/ u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
t>"%exdoZ ca1 = fftshift(fft(u1)); % Take Fourier transform
x -^6U ca2 = fftshift(fft(u2));
gT+/nSrLV c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
xNP_>Qa~ c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
D7Q+w u2 = ifft(fftshift(c2)); % Return to physical space
gr= h!'m u1 = ifft(fftshift(c1));
p7h#.m~Qu if rem(m1,J) == 0 % Save output every J steps.
1+o]+Jz| U1 = [U1 u1]; % put solutions in U array
+^)v"@,VP U2=[U2 u2];
P T"}2sR) MN1=[MN1 m1];
_KT! OYH z1=dz*MN1'; % output location
,pNx(a end
R[WiW RfD end
}`"`VLh hg=abs(U1').*abs(U1'); % for data write to excel
4
1_gak; ha=[z1 hg]; % for data write to excel
jm_-f t1=[0 t'];
7>JYwU{ hh=[t1' ha']; % for data write to excel file
&)eg3P)7 %dlmwrite('aa',hh,'\t'); % save data in the excel format
+)]YvZ6%[, figure(1)
p!.~hw9 waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
g(7 -3q8eq figure(2)
J~YT~D 2L waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
GK?ua l1 'U@o!\=a 非线性超快脉冲耦合的数值方法的Matlab程序 h}bfZL KKeMi@N 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。
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EUC@ 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
i`,FXF) ?Ua ,ba* 49$P Z g; $vIhn % This Matlab script file solves the nonlinear Schrodinger equations
UHBXq;?&q % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
pO]gf$ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
^aFm6HS1 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
*Cy54Z # &&ioGy}1 C=1;
^xo<$zn M1=120, % integer for amplitude
UA[`{rf M3=5000; % integer for length of coupler
5 *0zI\ N = 512; % Number of Fourier modes (Time domain sampling points)
,'#TdLe dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
qsj{0 Go T =40; % length of time:T*T0.
F_-Lu]*
dt = T/N; % time step
f~IJ4T2#N n = [-N/2:1:N/2-1]'; % Index
b* |~F t = n.*dt;
^:nc'C gP ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
XTol|a = w=2*pi*n./T;
f%Q)_F[0D4 g1=-i*ww./2;
R! nf^*~ g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
A|A~$v("R g3=-i*ww./2;
/-=fWtA P1=0;
{>&~kM@ P2=0;
De $AJl P3=1;
ju~$FNt8R P=0;
b0P3S!E for m1=1:M1
dBWn y& p=0.032*m1; %input amplitude
Z9{~t s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
A=|XlP$6 s1=s10;
_ \!]MV s20=0.*s10; %input in waveguide 2
MJn-] E s30=0.*s10; %input in waveguide 3
}nx)|J*p s2=s20;
0.GFg${v` s3=s30;
,0l
Od < p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
\Lx=iKs< %energy in waveguide 1
4vhf! !1 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
= C %)(| %energy in waveguide 2
<'y<8gpM p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
q? ,PFvs" %energy in waveguide 3
;\MWxh,K for m3 = 1:1:M3 % Start space evolution
Pz4#>tP s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
1ni+)p >] s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
K;K0D@>]HR s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
;Iu _*U9) sca1 = fftshift(fft(s1)); % Take Fourier transform
0 b& # w sca2 = fftshift(fft(s2));
Pwh}hG1s a sca3 = fftshift(fft(s3));
dwj?; sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
U S^% $Z: sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
)>a~ %~: sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
xATx2*@X2 s3 = ifft(fftshift(sc3));
EOPx 4+o s2 = ifft(fftshift(sc2)); % Return to physical space
.jrNi=BP* s1 = ifft(fftshift(sc1));
FW]tDGJOw end
/A_:`MAZ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
R >x d*A p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
)e(<YST p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
m^ X51,+< P1=[P1 p1/p10];
*&U~Io"U P2=[P2 p2/p10];
aNbS0R>l P3=[P3 p3/p10];
dP Ue5k)G_ P=[P p*p];
D(b01EQ;d end
:e<jD_.X figure(1)
NAYLlW}A plot(P,P1, P,P2, P,P3);
3(YvqPp& ?kjQ_K 转自：
http://blog.163.com/opto_wang/
