计算脉冲在非线性耦合器中演化的Matlab 程序 F2yc&mXyk 6mr5` 5~w % This Matlab script file solves the coupled nonlinear Schrodinger equations of
W8:?y*6 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
iX8& mUR % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
~U+SK4SK:o % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
eJ+V!K'H2 u%FG%
j?C %fid=fopen('e21.dat','w');
F WNO/)~t N = 128; % Number of Fourier modes (Time domain sampling points)
{umdW
x.* M1 =3000; % Total number of space steps
)J& 1uMp{ J =100; % Steps between output of space
F0O"rN{ T =10; % length of time windows:T*T0
R=jIVw' T0=0.1; % input pulse width
[b d fp
a MN1=0; % initial value for the space output location
d(RSn|[0 dt = T/N; % time step
` V}e $ n = [-N/2:1:N/2-1]'; % Index
`a}!t=~#w t = n.*dt;
l$$N~F N u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
b&BSigrvou u20=u10.*0.0; % input to waveguide 2
d5gYJ/Qv u1=u10; u2=u20;
Wpo:'?!(M^ U1 = u1;
,/n<Qg"` U2 = u2; % Compute initial condition; save it in U
"G\OKt'Z ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
8<}f:9/ w=2*pi*n./T;
;h> s=D,r g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
?[>+'6 L=4; % length of evoluation to compare with S. Trillo's paper
KD9Y dz=L/M1; % space step, make sure nonlinear<0.05
+$Q33@F5l for m1 = 1:1:M1 % Start space evolution
^ ;0.P)yGA u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
Xk[;MZ[ u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
WyH2` xxX ca1 = fftshift(fft(u1)); % Take Fourier transform
"71@WLlN ca2 = fftshift(fft(u2));
ju PW!u c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
2x-67_BHY= c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
g3@Qn?(j! u2 = ifft(fftshift(c2)); % Return to physical space
o*7`r ~ u1 = ifft(fftshift(c1));
#Jt9U1WbF if rem(m1,J) == 0 % Save output every J steps.
]r;-L x{F U1 = [U1 u1]; % put solutions in U array
O-r,&W U2=[U2 u2];
5/<?Y&x MN1=[MN1 m1];
%jKbRiz1u z1=dz*MN1'; % output location
f8u m.Xnp6 end
Ay ZL( end
zoYw[YP 9 hg=abs(U1').*abs(U1'); % for data write to excel
V=}AFGC85 ha=[z1 hg]; % for data write to excel
|I L..C t1=[0 t'];
Iuk!A?XV hh=[t1' ha']; % for data write to excel file
(rV#EA+6[` %dlmwrite('aa',hh,'\t'); % save data in the excel format
.du FMJl figure(1)
..RCR_DIp waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
T/Q#V)Tp figure(2)
$OK}jSH*v) waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
~A ul 7[IH #w3cImgp2 非线性超快脉冲耦合的数值方法的Matlab程序 YK Nz[x$| <
&[=,R0 @ 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。
Q C?*O?~# 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
;E0Xn-o_ yD6lzuk{X 5!Y51R^c ydFZ$W_}w % This Matlab script file solves the nonlinear Schrodinger equations
N< V,5 % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
Yhu
6QyRV % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
$ftcYBZa % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
"I.PV$Rxl 5(kRFb'31F C=1;
hawE2k0p( M1=120, % integer for amplitude
|U}al[ M3=5000; % integer for length of coupler
/ 0Z_$Q&e N = 512; % Number of Fourier modes (Time domain sampling points)
FFGG6r dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
4O Lq T =40; % length of time:T*T0.
qE73M5L& dt = T/N; % time step
H2oAek( n = [-N/2:1:N/2-1]'; % Index
][R#Q;y< t = n.*dt;
o 'S& YD ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
]DcQ8D w=2*pi*n./T;
fy at-wbb g1=-i*ww./2;
ghq#-N/t g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
ki `7S g3=-i*ww./2;
<{U "0jY!9 P1=0;
bN-ljw0& P2=0;
W ~sP7&sp P3=1;
&y-(UOqbkP P=0;
B= K & + for m1=1:M1
( vHB`@x p=0.032*m1; %input amplitude
ZsjDe {TH s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
*3 _@#Uu7 s1=s10;
>*v!2= s20=0.*s10; %input in waveguide 2
ZujPk- s30=0.*s10; %input in waveguide 3
e-vwve s2=s20;
z)$ X/v s3=s30;
v{7Jzjd p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
Cf# [E~2 4 %energy in waveguide 1
`e m}vdY p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
J)R;NYl %energy in waveguide 2
>gNVL
( p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
0. _)X %energy in waveguide 3
m4FT^ ^3yE for m3 = 1:1:M3 % Start space evolution
% j4 s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
5e^t; s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
U2 0@B`< s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
+c@s
sca1 = fftshift(fft(s1)); % Take Fourier transform
D;%(Z! sca2 = fftshift(fft(s2));
at_~b Ox6X sca3 = fftshift(fft(s3));
XI#1) sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
O=c^Ak sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
7;H!F!K] sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
Nrp0z: s3 = ifft(fftshift(sc3));
RtZK2 s2 = ifft(fftshift(sc2)); % Return to physical space
~4HS
2\ s1 = ifft(fftshift(sc1));
u;$g1 3 end
[wS ~. p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
4N&4TUIM p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
+
k1|+zzS p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
rv/O^aL`Y P1=[P1 p1/p10];
W10=SM } P2=[P2 p2/p10];
tE"aNA#= P3=[P3 p3/p10];
@"[xX}xK; P=[P p*p];
)@"iWQ 3K end
(<RZZ{m figure(1)
,1-n=eTQ plot(P,P1, P,P2, P,P3);
1&_9 3 ;{xk[f m= 转自：
http://blog.163.com/opto_wang/
