计算脉冲在非线性耦合器中演化的Matlab 程序 `m5iZxhw W2RS G~| % This Matlab script file solves the coupled nonlinear Schrodinger equations of
43Q&<r$[T % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
"<n{/x( % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
tyh %s " % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
[>E0(S] ?4_;9MkN %fid=fopen('e21.dat','w');
-nW-I\d% N = 128; % Number of Fourier modes (Time domain sampling points)
l< Y x M1 =3000; % Total number of space steps
4J s>yP J =100; % Steps between output of space
\xt! b^d0 T =10; % length of time windows:T*T0
{q^KlSjm T0=0.1; % input pulse width
[ LCi, MN1=0; % initial value for the space output location
@azS)4L dt = T/N; % time step
Rd2[xk n = [-N/2:1:N/2-1]'; % Index
08 Q:1 ' t = n.*dt;
{R K#W~h u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
wP%; 9y2B u20=u10.*0.0; % input to waveguide 2
;(V=disU/ u1=u10; u2=u20;
<YC{q>EMc U1 = u1;
f: R h9 U2 = u2; % Compute initial condition; save it in U
cMj<k8.{ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
MIgIt"M jz w=2*pi*n./T;
^JTfRZ :a g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
-&c@c@dC L=4; % length of evoluation to compare with S. Trillo's paper
z"<PveVo dz=L/M1; % space step, make sure nonlinear<0.05
gVGq for m1 = 1:1:M1 % Start space evolution
=Zj9F1E[i u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
n}l Z u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
&HWH
UWB ca1 = fftshift(fft(u1)); % Take Fourier transform
thh, V ca2 = fftshift(fft(u2));
Y !` H_Qo c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
nJ,56}
c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
e "v Eh u2 = ifft(fftshift(c2)); % Return to physical space
G
5)?! u1 = ifft(fftshift(c1));
vjHbg#0 % if rem(m1,J) == 0 % Save output every J steps.
\R~Lf+q U1 = [U1 u1]; % put solutions in U array
\1tce`+ U2=[U2 u2];
txi
m|) MN1=[MN1 m1];
8w{V[@QLn z1=dz*MN1'; % output location
k=LY 6 end
?B-aj end
{S|uQgs6j hg=abs(U1').*abs(U1'); % for data write to excel
eN/Jb;W ha=[z1 hg]; % for data write to excel
m+o>`1>a t1=[0 t'];
l B-Njr hh=[t1' ha']; % for data write to excel file
{vaq,2_w %dlmwrite('aa',hh,'\t'); % save data in the excel format
;>PV]0bOm> figure(1)
3LEN~ N} waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
0Vg8o @ figure(2)
%hXa5}JL waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
e@6}?q; IRpCbTIXK 非线性超快脉冲耦合的数值方法的Matlab程序 U8moVj8w1 R8ZW1 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。
5~\W!|j/ 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
=~R 0U blLX ncyD W7.]V)$wM $Q?UyEi % This Matlab script file solves the nonlinear Schrodinger equations
(j2]:B V u % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
@.%ll n % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
}@x0@sI9 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
3 iY`kf _mcD* V C=1;
]+J]}C]\d M1=120, % integer for amplitude
l!GAMK 6o M3=5000; % integer for length of coupler
0n5N-b?G-@ N = 512; % Number of Fourier modes (Time domain sampling points)
HIF.;ImG^ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
]E, T =40; % length of time:T*T0.
(Y-7B dt = T/N; % time step
3uN;*f n = [-N/2:1:N/2-1]'; % Index
A H`6)v <f t = n.*dt;
0T q6\: ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
m,-:( 82 w=2*pi*n./T;
M*%iMz g1=-i*ww./2;
SV-pS># g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
RF qbwPX g3=-i*ww./2;
{AJ s pLcG P1=0;
*ozeoX'5D P2=0;
ujHqw Rh P3=1;
~]}7|VN.} P=0;
ptX;-'j( for m1=1:M1
`^RpT] S p=0.032*m1; %input amplitude
)bqO}_ B s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
M,NYF`;a s1=s10;
7Qz Uw s20=0.*s10; %input in waveguide 2
'r3I/qg*m s30=0.*s10; %input in waveguide 3
-(~CZ s2=s20;
gR%fv s3=s30;
XD9 lox p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
Qb/qUUQO;0 %energy in waveguide 1
![ Fb~Egc p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
9FK%"s` %energy in waveguide 2
5_{C \S`T p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
g;vG6!;E\ %energy in waveguide 3
?PLf+S for m3 = 1:1:M3 % Start space evolution
LY/K ,6^a s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
Q!MS_
#O s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
Q
R;Xj3]v s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
$GEY*uIOa sca1 = fftshift(fft(s1)); % Take Fourier transform
,{7Z OzA sca2 = fftshift(fft(s2));
v-EcJj % sca3 = fftshift(fft(s3));
Ee d2`~ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
JuS#p5E # sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
c V=h 8F sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
E\ 5t&jZr s3 = ifft(fftshift(sc3));
d_]zX;_ s2 = ifft(fftshift(sc2)); % Return to physical space
*e!0ZB3J s1 = ifft(fftshift(sc1));
2{% U\^- end
Q"S;r1 D p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
*ax$R6a#X p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
hr(E, TAe p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
?x=;?7 P1=[P1 p1/p10];
V'^Hn?1^ P2=[P2 p2/p10];
~+7q.XL$$K P3=[P3 p3/p10];
b+9M? k" P=[P p*p];
D `c
YQ- end
=Z2Cg{z figure(1)
rgJKXl;@s plot(P,P1, P,P2, P,P3);
{rBS52,Z# Q!iM7C!8 转自：
http://blog.163.com/opto_wang/
