计算脉冲在非线性耦合器中演化的Matlab 程序 Z/r =4 AO R{Xm % This Matlab script file solves the coupled nonlinear Schrodinger equations of
]r^/:M % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
*u i !|; % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
1 ^x "P #u % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
PLkwtDi+& RWe$ZZSz! %fid=fopen('e21.dat','w');
8R) 0|v&; N = 128; % Number of Fourier modes (Time domain sampling points)
|[ RoR M1 =3000; % Total number of space steps
a+U^mPe J =100; % Steps between output of space
ZCT\4Llv# T =10; % length of time windows:T*T0
<K(qv^C T0=0.1; % input pulse width
7O=N78M MN1=0; % initial value for the space output location
C
V{kP8# dt = T/N; % time step
"}ms | n = [-N/2:1:N/2-1]'; % Index
JZa^GW:YQh t = n.*dt;
Hd/|f; u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
uX!5G:x] u20=u10.*0.0; % input to waveguide 2
&!xePKvO6k u1=u10; u2=u20;
J|uxn<E<> U1 = u1;
l8XgzaW U2 = u2; % Compute initial condition; save it in U
9?jD90@
} ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
_6tir'z w=2*pi*n./T;
VIXY?Ua g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
#K:!s<_" L=4; % length of evoluation to compare with S. Trillo's paper
u["3| `C5 dz=L/M1; % space step, make sure nonlinear<0.05
bvxol\7 ; for m1 = 1:1:M1 % Start space evolution
/tG0"1{ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
JJHfg) u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
_+OnH!G0 ca1 = fftshift(fft(u1)); % Take Fourier transform
-KuC31s_W ca2 = fftshift(fft(u2));
4
Wb^$i! c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
j5rB+ c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
kE8\\ }B7 u2 = ifft(fftshift(c2)); % Return to physical space
Z~?1xJ& u1 = ifft(fftshift(c1));
sRMz[n 5k if rem(m1,J) == 0 % Save output every J steps.
($h`Y;4 U1 = [U1 u1]; % put solutions in U array
R/_bk7o]H U2=[U2 u2];
!R 2;]d* MN1=[MN1 m1];
o4^|n1vN z1=dz*MN1'; % output location
TZl^M h[a end
oc^j<!Rh end
+2KYty I hg=abs(U1').*abs(U1'); % for data write to excel
?g6xy[ ha=[z1 hg]; % for data write to excel
v_ U$jjO1 t1=[0 t'];
D('
w<9. hh=[t1' ha']; % for data write to excel file
ef Moi 'v %dlmwrite('aa',hh,'\t'); % save data in the excel format
<-]qU}- figure(1)
Az`c ?
W% waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
]T?Py) figure(2)
RZ6[+Ygn waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
mSg{0 _: XK";-7TZt 非线性超快脉冲耦合的数值方法的Matlab程序 c SV`?[a mB.j?@Y% 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。
jDV;tEY#^ 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
'o!{YLJ fM MR?5p8S#g -J06H&/k Bh#?:h&f % This Matlab script file solves the nonlinear Schrodinger equations
xpO'.xEs % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
{\-9^RL % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
6w"_sK?
% pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
!jySID?q =^9I)JW C=1;
]SO-NR M1=120, % integer for amplitude
' 1 }ybSG M3=5000; % integer for length of coupler
X%Lhu6F N = 512; % Number of Fourier modes (Time domain sampling points)
z>6hK:27 dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
j6JK4{ T =40; % length of time:T*T0.
pef)c,U$ dt = T/N; % time step
pkKcTY1Fx n = [-N/2:1:N/2-1]'; % Index
jO5,PTV t = n.*dt;
^5GyW`a}
ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
DO^ J=e w=2*pi*n./T;
[Zpx
:r} g1=-i*ww./2;
<Wwcd8d g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
Qms ,kX g3=-i*ww./2;
S#:y l>2 P1=0;
%3:[0o={d P2=0;
}3TTtd 7 P3=1;
^E#i5d+'N P=0;
C9 FzTg/c for m1=1:M1
# h/# h\ p=0.032*m1; %input amplitude
9'5`0$,|^ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
blk4 @pg s1=s10;
,bGYixIfYZ s20=0.*s10; %input in waveguide 2
jR_o!n~5 s30=0.*s10; %input in waveguide 3
"C/X#y
s2=s20;
TOx >Z s3=s30;
Jqp;8DV} p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
0XWhSrHM %energy in waveguide 1
XzD+#+By p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
kR
!O-@GJ] %energy in waveguide 2
6SqS\ 8 p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
TpH-_ft %energy in waveguide 3
TS Ev^u)3 for m3 = 1:1:M3 % Start space evolution
8{f~tPY s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
%S$+ 3q%F s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
.*k$abb s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
h6(\ tRd!\ sca1 = fftshift(fft(s1)); % Take Fourier transform
|lG7/\A sca2 = fftshift(fft(s2));
I)AbH<G{ sca3 = fftshift(fft(s3));
K-2oSS56 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
b3M`vJ+{ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
}HKt{k&$ sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
QE Q/ s3 = ifft(fftshift(sc3));
unB` n'L s2 = ifft(fftshift(sc2)); % Return to physical space
sq45fRAi s1 = ifft(fftshift(sc1));
%ZR<z$ end
O}3|UI!` p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
,vh $G 7D p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
4/?@ % p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
;xQNa}"V P1=[P1 p1/p10];
WZQ
EBXs P2=[P2 p2/p10];
uf/4vz, P3=[P3 p3/p10];
&~K4 I P=[P p*p];
NW 4tQ;ad end
%E k!3t figure(1)
=MjkD)l plot(P,P1, P,P2, P,P3);
Gpf 9uj% dZ,IXA yB 转自：
http://blog.163.com/opto_wang/
