计算脉冲在非线性耦合器中演化的Matlab 程序 Y P,>vzW ~/qBOeU3 % This Matlab script file solves the coupled nonlinear Schrodinger equations of
|xF!3GGms % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
OZ33w-X< % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
U[? f@.& % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
w^9< I] {FX]1: %fid=fopen('e21.dat','w');
erKi*GssZ N = 128; % Number of Fourier modes (Time domain sampling points)
u#y#(1
= M1 =3000; % Total number of space steps
<#wVQ\0C J =100; % Steps between output of space
8|(],NyEJ T =10; % length of time windows:T*T0
i;atYltEJ2 T0=0.1; % input pulse width
CZE!@1"<{ MN1=0; % initial value for the space output location
5 B t~tt dt = T/N; % time step
jgiS/oW n = [-N/2:1:N/2-1]'; % Index
gA`QV''/: t = n.*dt;
T^F83Py< u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
+cbF $, M4 u20=u10.*0.0; % input to waveguide 2
t,n2N13 u1=u10; u2=u20;
:dQRrmM U1 = u1;
q6ZewuV. U2 = u2; % Compute initial condition; save it in U
+v~x_E5FP ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
qyAnq%B} w=2*pi*n./T;
a`8]TD g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
;%Px~g L=4; % length of evoluation to compare with S. Trillo's paper
G3 |x%/Fbp dz=L/M1; % space step, make sure nonlinear<0.05
UM`{V5NG# for m1 = 1:1:M1 % Start space evolution
O c.fvP^ZD u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
puLgc$? u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
B&7NF}CF2 ca1 = fftshift(fft(u1)); % Take Fourier transform
-k@1# c+z ca2 = fftshift(fft(u2));
L [Ot$ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
A;^ i y]" c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
4*L* "vKa u2 = ifft(fftshift(c2)); % Return to physical space
Ms Bm0r`a u1 = ifft(fftshift(c1));
E[7E%^:Mg if rem(m1,J) == 0 % Save output every J steps.
fs:yx'mxV U1 = [U1 u1]; % put solutions in U array
#
E_S.. U2=[U2 u2];
6O,:I MN1=[MN1 m1];
=@pD>h/~ z1=dz*MN1'; % output location
8;L;R ~Q end
(@qPyM6~} end
m"-kkH{I hg=abs(U1').*abs(U1'); % for data write to excel
|N^"?bSt ha=[z1 hg]; % for data write to excel
o='A1 P t1=[0 t'];
^_i)X dPU hh=[t1' ha']; % for data write to excel file
Aix6O=K6 %dlmwrite('aa',hh,'\t'); % save data in the excel format
97U O H figure(1)
$2,tT;50g waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
+q;{ %3C figure(2)
)iM(
\=1ff waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
1C<d^D_!p YU" /p|!1 非线性超快脉冲耦合的数值方法的Matlab程序 SO.u0! _5H~1G%q 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 PDRMGR@i 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
7#d:TXS Q"B8l[ QeC\(4? 7y&6q`y E % This Matlab script file solves the nonlinear Schrodinger equations
z HvE_ - % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
$, J0) ~ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
h`n '{s % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
*oeXmY t0jE\6r C=1;
k*n~&y: O M1=120, % integer for amplitude
%#rtNDi M3=5000; % integer for length of coupler
Nf<f}` N = 512; % Number of Fourier modes (Time domain sampling points)
5'e BeNxM dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
+uSp3gE" T =40; % length of time:T*T0.
?ueL'4Mm dt = T/N; % time step
tq~4W% p/ n = [-N/2:1:N/2-1]'; % Index
_@y uaMoW= t = n.*dt;
CuH4~6 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
xZ )K#\ w=2*pi*n./T;
e"wz b< b g1=-i*ww./2;
!L8q]]'XM g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
W^h,O+vk g3=-i*ww./2;
#*/nUbsg P1=0;
A$N%deb P2=0;
qR!ZtJ5j P3=1;
BO4;S/ O P=0;
wM4{\ f\ for m1=1:M1
C3Q #[ p=0.032*m1; %input amplitude
2I}+AW!!= s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
(*P`
s1=s10;
?4U4o<
s20=0.*s10; %input in waveguide 2
z/`+jIB s30=0.*s10; %input in waveguide 3
OblHN* s2=s20;
oJ
%Nt&q s3=s30;
Jk-WD"J6 p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
>J3m ta3 %energy in waveguide 1
yna!L@ *@, p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
/KWdIP# %energy in waveguide 2
HEbL'fw^s p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
y705 %energy in waveguide 3
%6 Av1cv for m3 = 1:1:M3 % Start space evolution
]T'8O` s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
>oWPwXA s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
S+~;PmN9qL s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
MymsDdQ] sca1 = fftshift(fft(s1)); % Take Fourier transform
]o]`X$n sca2 = fftshift(fft(s2));
m jP sca3 = fftshift(fft(s3));
5I 2 h(Td sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
z^`4n_(Ygu sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
&WBpd}|+Y sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
F?R6zvive s3 = ifft(fftshift(sc3));
;"0bVs`.^e s2 = ifft(fftshift(sc2)); % Return to physical space
M&V4 |D s1 = ifft(fftshift(sc1));
EBW*v ' end
d;p3cW" p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
Yg '( p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
`Wj q$* p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
.eg'Z@o P1=[P1 p1/p10];
_g/d/{-{Q P2=[P2 p2/p10];
Bj2iYk_cLa P3=[P3 p3/p10];
)cRHt: P=[P p*p];
r3U7`P end
W|@SXO)DY figure(1)
O0z-jZ,]) plot(P,P1, P,P2, P,P3);
{ CR`~)v& FT~c|ep. 转自：
http://blog.163.com/opto_wang/
