计算脉冲在非线性耦合器中演化的Matlab 程序 ^xe+(83S2? lDL&":t % This Matlab script file solves the coupled nonlinear Schrodinger equations of
C|ZPnm>f30 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
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{.% % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
VWft/2p~ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
4l 67B]o P%2v( %fid=fopen('e21.dat','w');
TIGtX]` N = 128; % Number of Fourier modes (Time domain sampling points)
`
-_! %m/ M1 =3000; % Total number of space steps
'rB% a< J =100; % Steps between output of space
NY7yk3 T =10; % length of time windows:T*T0
U WT%0t_T T0=0.1; % input pulse width
GD4S/fn3 MN1=0; % initial value for the space output location
yd;e;Bb7* dt = T/N; % time step
ovKM;cRs/ n = [-N/2:1:N/2-1]'; % Index
t6"%u3W8M t = n.*dt;
|nNcV~%~ u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
bWTf P8gT u20=u10.*0.0; % input to waveguide 2
sh
:$J[ u1=u10; u2=u20;
v~mVf.j1 U1 = u1;
}zGx0Q U2 = u2; % Compute initial condition; save it in U
U}w'/:H ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
re*}a)iL w=2*pi*n./T;
Yc[umn^K g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
%jL^sA2;c+ L=4; % length of evoluation to compare with S. Trillo's paper
y C xYFi dz=L/M1; % space step, make sure nonlinear<0.05
E0ED[d, for m1 = 1:1:M1 % Start space evolution
gGrVpOzBj u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
0he3[m}Nr u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
X.b8qbnq[ ca1 = fftshift(fft(u1)); % Take Fourier transform
Mq\=pxC@ ca2 = fftshift(fft(u2));
H$%MIBz >$ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
f"s_dR c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
^L%_kL_7 u2 = ifft(fftshift(c2)); % Return to physical space
_ /1/ { u1 = ifft(fftshift(c1));
FJ3S
if rem(m1,J) == 0 % Save output every J steps.
-`faXFW ' U1 = [U1 u1]; % put solutions in U array
*D|a`R!Y U2=[U2 u2];
o h{>nwH MN1=[MN1 m1];
9tHK_),9 z1=dz*MN1'; % output location
PK+sGV end
RBQ8+ ^ end
6=f)3!= hg=abs(U1').*abs(U1'); % for data write to excel
.lc p5D[( ha=[z1 hg]; % for data write to excel
@}
Ig*@ t1=[0 t'];
:-RB< Lj hh=[t1' ha']; % for data write to excel file
cC-8.2 %dlmwrite('aa',hh,'\t'); % save data in the excel format
Lap?L/NS figure(1)
&l+Qn'N waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
U<'N=#A
J figure(2)
UyRy>:n waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
:qE.(k1@5 6 - 3?&+ 非线性超快脉冲耦合的数值方法的Matlab程序 HTL6;87w+] 8"&!3_ 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。
m}l) ;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
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+~)_ % This Matlab script file solves the nonlinear Schrodinger equations
:|bL2T@>[ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
uZl d9u % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
TnQ>v{Rx % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
i %o%bib# H@(O{ 9Yl; C=1;
QATRrIj{e M1=120, % integer for amplitude
>
'R{,1# U M3=5000; % integer for length of coupler
j- 9)Sijj{ N = 512; % Number of Fourier modes (Time domain sampling points)
"1,*6(;: dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
]he~KO[j< T =40; % length of time:T*T0.
HR-'8?)R.A dt = T/N; % time step
hNXZL>6 n = [-N/2:1:N/2-1]'; % Index
ZS.=GjK t = n.*dt;
|" }rd OV) ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
,NGHv?.N w=2*pi*n./T;
A e7FtJO g1=-i*ww./2;
54p{J g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
BvP\c_ g3=-i*ww./2;
@1o X&# P1=0;
$z_yx
`5 P2=0;
20}HTV {v P3=1;
5M=U *BI P=0;
Ovx
* for m1=1:M1
~lV#- m* p=0.032*m1; %input amplitude
9Y3"V3EZ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
k@7# 8(3 s1=s10;
uqc G3Pi s20=0.*s10; %input in waveguide 2
My>q%lF=fw s30=0.*s10; %input in waveguide 3
48 - j s2=s20;
%1
)c{7 s3=s30;
43k'96[2d p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
pEwo}NS*H %energy in waveguide 1
2{j$1EdI@- p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
45 ^ Z5t %energy in waveguide 2
vN(~}gOd\ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
>T;!Z 5L1 %energy in waveguide 3
y^H5iB[SPL for m3 = 1:1:M3 % Start space evolution
! \s}A7 s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
?pIELezfK s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
_o9axBJs s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
+=/j+S` sca1 = fftshift(fft(s1)); % Take Fourier transform
Dspvc sca2 = fftshift(fft(s2));
F %V|Aa sca3 = fftshift(fft(s3));
h2'6W) sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
6
5zx < sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
62ru%<x = sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
4
Y=0>FlY0 s3 = ifft(fftshift(sc3));
(EcP'F*;;y s2 = ifft(fftshift(sc2)); % Return to physical space
, LwinjHA* s1 = ifft(fftshift(sc1));
Osz=OO{ end
"3VX9{'%@ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
fB h" p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
2Rw<0.i| p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
z9
0JZA P1=[P1 p1/p10];
J3y _JoS P2=[P2 p2/p10];
oOprzxf"+Z P3=[P3 p3/p10];
`]65&hWZL P=[P p*p];
'|g smO end
N/F_,>E figure(1)
fK:4jl-r plot(P,P1, P,P2, P,P3);
V06*qQ[ v FL$wr 转自：
http://blog.163.com/opto_wang/
