计算脉冲在非线性耦合器中演化的Matlab 程序 huC{SzXM _<S!tW % This Matlab script file solves the coupled nonlinear Schrodinger equations of
#kC ~ qux^ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
arL>{mj % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
=?OU^ u`C % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
y74Q ( N!K%aH~O %fid=fopen('e21.dat','w');
Pm/<^z% N = 128; % Number of Fourier modes (Time domain sampling points)
r{ R-X3s M1 =3000; % Total number of space steps
vywB{%p J =100; % Steps between output of space
Wu][ A\3D1 T =10; % length of time windows:T*T0
:'p)xw4K| T0=0.1; % input pulse width
M/<ypJ MN1=0; % initial value for the space output location
JH . XZM& dt = T/N; % time step
uuY^Q;^I* n = [-N/2:1:N/2-1]'; % Index
kd'b_D[$H t = n.*dt;
9\_s&p=:. u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
J8:s=#5 u20=u10.*0.0; % input to waveguide 2
s>>&3jfM u1=u10; u2=u20;
Ypyi(_G(?> U1 = u1;
GY$Rkg6d U2 = u2; % Compute initial condition; save it in U
Q#p)?:o/ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
T)zk2\u w=2*pi*n./T;
Nn05me"X g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
qd0G sr}j L=4; % length of evoluation to compare with S. Trillo's paper
F1yn@a "=J dz=L/M1; % space step, make sure nonlinear<0.05
V8n { k' for m1 = 1:1:M1 % Start space evolution
:=NXwY3 ~M u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
g6Vkns4 u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
\ja 6g ca1 = fftshift(fft(u1)); % Take Fourier transform
ZG=]b% ca2 = fftshift(fft(u2));
%L.S~dN 6 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
Ub3$ ` c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
#&|"t< } u2 = ifft(fftshift(c2)); % Return to physical space
']nIa7 u1 = ifft(fftshift(c1));
.V;,6Vq if rem(m1,J) == 0 % Save output every J steps.
\tgY2 : U1 = [U1 u1]; % put solutions in U array
a OmG, +o U2=[U2 u2];
JT
7WZc) MN1=[MN1 m1];
sV"tN2W@ z1=dz*MN1'; % output location
)>ff"| X end
aqSOC(jU end
1EV bGe%b hg=abs(U1').*abs(U1'); % for data write to excel
?6 2zv[# ha=[z1 hg]; % for data write to excel
;<i
u*a t1=[0 t'];
!{l% 3'2 hh=[t1' ha']; % for data write to excel file
?w/p 9j# %dlmwrite('aa',hh,'\t'); % save data in the excel format
5]i#l3") figure(1)
%E%=Za waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
0L>3 i8' figure(2)
EeYL~ORdi waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
v
o:KL%) %/2
` u 非线性超快脉冲耦合的数值方法的Matlab程序 `O7vPE ^6Aa^| 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。
Jz''UJY/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
>.SO2w +vZYuEq_ =)bOteWM IEm?'o: % This Matlab script file solves the nonlinear Schrodinger equations
7}xQ4M\u$ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
Y's=31G@ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
G:e=9qTf % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
}zA|M9%E @C-dCC? C=1;
1
k!gR M1=120, % integer for amplitude
*c#DB{N M3=5000; % integer for length of coupler
/%m?D o N = 512; % Number of Fourier modes (Time domain sampling points)
UusAsezm: dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
b$2=w^* T =40; % length of time:T*T0.
{ZUk!o>m@ dt = T/N; % time step
zDYJe_m ~ n = [-N/2:1:N/2-1]'; % Index
`_yksh3zL4 t = n.*dt;
k8E2?kbF ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
OC5oxL2HTe w=2*pi*n./T;
!o|
ex+z; g1=-i*ww./2;
+!@x H]; g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
-AnJLFY g3=-i*ww./2;
4 4QW&qL!( P1=0;
(l][_6Q P2=0;
eZ)
|m P3=1;
LEKE+775 P=0;
oi Q3E for m1=1:M1
4P Sbr$ p=0.032*m1; %input amplitude
L e~D"d8 s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
OY"BaSEOw} s1=s10;
tQj=m_ s20=0.*s10; %input in waveguide 2
ft8 s30=0.*s10; %input in waveguide 3
$I`,nN s2=s20;
v*excl~ s3=s30;
2;:]Q.g p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
S%p,.0_ %energy in waveguide 1
)cN=/i p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
V13^SVM %energy in waveguide 2
qUe2(/TQu p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
/_<_X
7 %energy in waveguide 3
" QfF]/: for m3 = 1:1:M3 % Start space evolution
( Vey]J s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
( |W6p%( s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
` iuQ .I s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
(N}\ Wft% sca1 = fftshift(fft(s1)); % Take Fourier transform
-{3^~vW|< sca2 = fftshift(fft(s2));
D{ ]w + sca3 = fftshift(fft(s3));
= r=/L sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
O,@QGUoA sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
e,vgD kI; sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
ke*&*mx"L s3 = ifft(fftshift(sc3));
9Lt3^MKa" s2 = ifft(fftshift(sc2)); % Return to physical space
'e))i#/ VF s1 = ifft(fftshift(sc1));
On4Vqbks end
I<lkociUCG p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
$v{s b, p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
l5e`m^GK p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
i+-Y"vRi P1=[P1 p1/p10];
gO~ >*q & P2=[P2 p2/p10];
tchpO3u, P3=[P3 p3/p10];
AxJf\B8 P=[P p*p];
UL8"{-`_\ end
Iq;a!Lya- figure(1)
d#, plot(P,P1, P,P2, P,P3);
K<ldl. %'F[(VB 转自：
http://blog.163.com/opto_wang/
