计算脉冲在非线性耦合器中演化的Matlab 程序 =I4.Gf"~f }=GM ?,7b % This Matlab script file solves the coupled nonlinear Schrodinger equations of
_vrWj<wyf % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
1kFjas `g % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
YdOUv|tZC % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
W"sr$K2m| jXIEp01 %fid=fopen('e21.dat','w');
= HE
m) N = 128; % Number of Fourier modes (Time domain sampling points)
,b' 4CF M1 =3000; % Total number of space steps
[&VxaJ("3 J =100; % Steps between output of space
?SX_gYe9 T =10; % length of time windows:T*T0
DX@}!6|T T0=0.1; % input pulse width
MW@ DXbKVl MN1=0; % initial value for the space output location
Y6eEGo"K.+ dt = T/N; % time step
r z6jx n = [-N/2:1:N/2-1]'; % Index
:R+],m il t = n.*dt;
v]bAWo u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
FMS2.E u20=u10.*0.0; % input to waveguide 2
Q4%IxR? u1=u10; u2=u20;
a$+#V=b A U1 = u1;
gMZ&,n4 U2 = u2; % Compute initial condition; save it in U
;nk@XFJ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
, L% p w=2*pi*n./T;
60PYCqWc g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
E~He~wHWe L=4; % length of evoluation to compare with S. Trillo's paper
&& C~@WY,r dz=L/M1; % space step, make sure nonlinear<0.05
"6V_/u5M;= for m1 = 1:1:M1 % Start space evolution
ay[+ 2" u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
w-:
D u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
jOl 1_ ca1 = fftshift(fft(u1)); % Take Fourier transform
1URsHV!xcM ca2 = fftshift(fft(u2));
4 (m3c< 'P c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
?UK:sF| (O c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
d| \#?W& u2 = ifft(fftshift(c2)); % Return to physical space
? ).(fP u1 = ifft(fftshift(c1));
nHU3%%%cU if rem(m1,J) == 0 % Save output every J steps.
z(UX't (q U1 = [U1 u1]; % put solutions in U array
:y D@5) U2=[U2 u2];
A_Gp&acs$ MN1=[MN1 m1];
1UyH 0`& z1=dz*MN1'; % output location
y''V"Be end
Kq6qXc\x end
@7|)RSBQz hg=abs(U1').*abs(U1'); % for data write to excel
^'Zh;WjI7 ha=[z1 hg]; % for data write to excel
N7B}O*; t1=[0 t'];
B}5XRgq hh=[t1' ha']; % for data write to excel file
*2:Yf7rvI+ %dlmwrite('aa',hh,'\t'); % save data in the excel format
` w=!o.1 figure(1)
v<fWc971 waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
/O"0L/hc^ figure(2)
%0(>! SY waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
MZi8F o ' ]Hj`2\KD.d 非线性超快脉冲耦合的数值方法的Matlab程序 fW[.r== Kf Y D+QX@ 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。
*EE|?vn 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
A'v[SUW'm 5oa]dco Z{16S=0 %>]#vQ| % This Matlab script file solves the nonlinear Schrodinger equations
% NwoU%q % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
sp,(&Y]US % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
P#9-bYNU % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
WFks|D:sB U a!Odju*w C=1;
v _.j/2U M1=120, % integer for amplitude
.=aMjrME M3=5000; % integer for length of coupler
6!o/~I# N = 512; % Number of Fourier modes (Time domain sampling points)
:if5z2PE/ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
^)'| |Ly T =40; % length of time:T*T0.
_4S7wOq5 dt = T/N; % time step
-*5yY#fw} n = [-N/2:1:N/2-1]'; % Index
k dUc& t = n.*dt;
Ut=0~x.=< ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
n7'<3t w=2*pi*n./T;
-y<rM0"NE g1=-i*ww./2;
c{ZqQtfM g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
JG1LS$p^ g3=-i*ww./2;
Is~yVB02 P1=0;
yl|R:/2V P2=0;
,9+nfj P3=1;
<C2c" =b P=0;
T&e% / for m1=1:M1
i@%L_[MtA p=0.032*m1; %input amplitude
(jt*u (C&Y s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
$Jt8d|UP s1=s10;
Y-?51g [u s20=0.*s10; %input in waveguide 2
> 4Fd xa s30=0.*s10; %input in waveguide 3
ROcY'- s2=s20;
">0 /8] l s3=s30;
g8B&u u # p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
<: H %energy in waveguide 1
(p'/p p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
:1%VZvWk* %energy in waveguide 2
_p ? I{1O p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
!k ;[^> %energy in waveguide 3
&7JEb]1C for m3 = 1:1:M3 % Start space evolution
p` ^:Q*C" s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
+X{cN5Y K s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
F5Cqv0H V s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
k$Nx6?8E sca1 = fftshift(fft(s1)); % Take Fourier transform
oKZ [0(4< sca2 = fftshift(fft(s2));
:a# | sca3 = fftshift(fft(s3));
i] V
F'tG sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
pyGFDB5_P sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
75' Ua$ sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
BNF++<s s3 = ifft(fftshift(sc3));
||bA s2 = ifft(fftshift(sc2)); % Return to physical space
](idf ( j s1 = ifft(fftshift(sc1));
_
+u sn. end
t>fA!K%{ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
/6? tgr p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
xUV_2n+ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
$,!dan<eA P1=[P1 p1/p10];
!^rITiy P2=[P2 p2/p10];
U]1>?,Nk'3 P3=[P3 p3/p10];
>:(6 {}b P=[P p*p];
3g4vpKg6c end
AqTR.}H figure(1)
h/fb<jIP1 plot(P,P1, P,P2, P,P3);
)L&n)w _CYmG "mY 转自：
http://blog.163.com/opto_wang/
