计算脉冲在非线性耦合器中演化的Matlab 程序 [|oOP $u *d,Z ?S/ % This Matlab script file solves the coupled nonlinear Schrodinger equations of
?H(']3X5@ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
?89 _2W % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
2vX!j!_ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
iig@ $
i# rn%q*_3-o %fid=fopen('e21.dat','w');
Om C
F8:\/ N = 128; % Number of Fourier modes (Time domain sampling points)
tJZ3P@ L M1 =3000; % Total number of space steps
'jd fUB J =100; % Steps between output of space
7&
G#&d T =10; % length of time windows:T*T0
1A; f[Rze T0=0.1; % input pulse width
C!S( !Z, MN1=0; % initial value for the space output location
5vqh09-FB dt = T/N; % time step
Q%^!j _# n = [-N/2:1:N/2-1]'; % Index
=9cN{&qf t = n.*dt;
{,zn#hU.R u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
~ZZJ/Cu u20=u10.*0.0; % input to waveguide 2
)w&k&TY4H u1=u10; u2=u20;
YV/JZc f U1 = u1;
X,i^OM_ U2 = u2; % Compute initial condition; save it in U
xC.Tipn> ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
f| -%., w=2*pi*n./T;
ZH8Oidj` g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
xBK is\b L=4; % length of evoluation to compare with S. Trillo's paper
k JG0X%+w dz=L/M1; % space step, make sure nonlinear<0.05
s2 iL5N|"Q for m1 = 1:1:M1 % Start space evolution
8d*W7>rq u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
Dro2R_j{ u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
=@0/. oSD ca1 = fftshift(fft(u1)); % Take Fourier transform
2]f? c%)I ca2 = fftshift(fft(u2));
zkmfu~_) c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
a;[=b p c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
xE%sPWbj u2 = ifft(fftshift(c2)); % Return to physical space
/U =eB?> u1 = ifft(fftshift(c1));
FW--|X]8 if rem(m1,J) == 0 % Save output every J steps.
#a=~a=c(^ U1 = [U1 u1]; % put solutions in U array
N2Q%/}+, U2=[U2 u2];
f%5 s8) MN1=[MN1 m1];
^h\Y. z1=dz*MN1'; % output location
':LV"c4 t end
;$$.L
bb8 end
X*Cvh| hg=abs(U1').*abs(U1'); % for data write to excel
-/ h'uG ha=[z1 hg]; % for data write to excel
'r_NA!R t1=[0 t'];
!Au 9C
hh=[t1' ha']; % for data write to excel file
mnS F=l;; %dlmwrite('aa',hh,'\t'); % save data in the excel format
|\_d^U &` figure(1)
bf1EMai" waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
>pq= .)X} figure(2)
U CF'%R waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
mj9r#v3. i*-L_!cc: 非线性超快脉冲耦合的数值方法的Matlab程序 }Gg:y? K~ShV 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。
F9 q 9BH 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
La#otuw+? 1feS/l$ ?wQaM3 |^: WyD L ah^/ % This Matlab script file solves the nonlinear Schrodinger equations
UpIt"+d2& % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
6Om)e=gU/ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
8KhE`C9z % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
wc.T ;( :Mq-4U .e C=1;
ppu WcGo M1=120, % integer for amplitude
A,'JmF$d
M3=5000; % integer for length of coupler
qe"t0w|U? N = 512; % Number of Fourier modes (Time domain sampling points)
fKN&0N |^R dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
`(@}O?w!1 T =40; % length of time:T*T0.
?*h 2:a $ dt = T/N; % time step
?YTngIa n = [-N/2:1:N/2-1]'; % Index
\6z_ ; t = n.*dt;
6I`Lszs ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
G(6M Lh1 w=2*pi*n./T;
a= *qsgPGL g1=-i*ww./2;
"U DV4<|^k g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
m z kv/ g3=-i*ww./2;
,
e6 }p P1=0;
N
2\lBi P2=0;
sq~9
l|F P3=1;
O)E8'Oe"Q P=0;
D3BT>zTGK for m1=1:M1
)lsR8 Hi8 p=0.032*m1; %input amplitude
X|iWnz+^ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
1ehl=WN s1=s10;
| JD"iP : s20=0.*s10; %input in waveguide 2
G$)f5_]7{ s30=0.*s10; %input in waveguide 3
6*]g~)7`Q~ s2=s20;
sWc_,[b s3=s30;
F}Kkhs
{ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
sKK*{+,kh; %energy in waveguide 1
_R 6+bB$ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
fI ([vI %energy in waveguide 2
w xx3']: p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
2a 3RRP %energy in waveguide 3
f,_EPh> for m3 = 1:1:M3 % Start space evolution
Z:2a_A tm s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
6pCQ P
c*A s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
~O s1ir. s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
Arzyq_ Yk sca1 = fftshift(fft(s1)); % Take Fourier transform
~dFdO7 sca2 = fftshift(fft(s2));
{hmC=j sca3 = fftshift(fft(s3));
h /a|-V}m& sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
--}5%6 sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
)=vQrMyB sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
X?8 EPCk s3 = ifft(fftshift(sc3));
S);SfNh%CL s2 = ifft(fftshift(sc2)); % Return to physical space
yD-L:)@" s1 = ifft(fftshift(sc1));
F^/ 1 u end
%gb4(~E +N p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
sOY+ X p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
v3ky;~ke p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
..5rW0lr P1=[P1 p1/p10];
&Is }<Ew P2=[P2 p2/p10];
>& z=ktB P3=[P3 p3/p10];
4N- T=Ig P=[P p*p];
:47bf<w|Y end
PqJB&:ZV figure(1)
(5Z*m<]c plot(P,P1, P,P2, P,P3);
@g{FNXY$ m |v6kZ0B< 转自：
http://blog.163.com/opto_wang/
