计算脉冲在非线性耦合器中演化的Matlab 程序 zK{ } U~t!
% This Matlab script file solves the coupled nonlinear Schrodinger equations of
OdL/%Zp} % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
7zJ2n/`m* % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
%6m' |(- % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
bZK^q B 8lS
RK% %fid=fopen('e21.dat','w');
c': 4e) N = 128; % Number of Fourier modes (Time domain sampling points)
Y6v# 0pT M1 =3000; % Total number of space steps
n:b,zssP J =100; % Steps between output of space
ccp9nX v T =10; % length of time windows:T*T0
25 :v c0 T0=0.1; % input pulse width
5,V*aP MN1=0; % initial value for the space output location
yL K %lP dt = T/N; % time step
B., B P n = [-N/2:1:N/2-1]'; % Index
`Mcg&M i~ t = n.*dt;
f5l\3oL u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
C8)Paop$ u20=u10.*0.0; % input to waveguide 2
%}Y &qT? u1=u10; u2=u20;
</?ef& U1 = u1;
_@gg,2
u- U2 = u2; % Compute initial condition; save it in U
6E:H ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
d6 -q" w=2*pi*n./T;
L~by `q N_ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
sG[qlzR=8 L=4; % length of evoluation to compare with S. Trillo's paper
SW+;%+ ` dz=L/M1; % space step, make sure nonlinear<0.05
p9mGiK4! for m1 = 1:1:M1 % Start space evolution
& 0:Gj3` u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
UvB\kIH u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
>i.$s ca1 = fftshift(fft(u1)); % Take Fourier transform
~ b66
; ca2 = fftshift(fft(u2));
RL/7>YQ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
TBba3% c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
^P/OH uDL u2 = ifft(fftshift(c2)); % Return to physical space
rd$T6 !I u1 = ifft(fftshift(c1));
e^\#DDm if rem(m1,J) == 0 % Save output every J steps.
aG4 ^xOD U1 = [U1 u1]; % put solutions in U array
-f1}N|hy U2=[U2 u2];
Im H 9 F\ MN1=[MN1 m1];
]Y76~!N z1=dz*MN1'; % output location
_5O~ ]} end
'&K' 0qG end
,!g/1m hg=abs(U1').*abs(U1'); % for data write to excel
9f5~hBlo ha=[z1 hg]; % for data write to excel
.*>C[^ t1=[0 t'];
u|u)8;'9( hh=[t1' ha']; % for data write to excel file
~| ZAS] %dlmwrite('aa',hh,'\t'); % save data in the excel format
H1KXAy`& figure(1)
G v
} waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
:eB+t`M figure(2)
O&~
@ior waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
nU\.`.39
+ B9cWxe4R# 非线性超快脉冲耦合的数值方法的Matlab程序 *ezft&{)` T?=]&9Y' 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。
<mTo54g 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
>c5 b].U/=Hs [eTEK W] 7M5H vG#w% % This Matlab script file solves the nonlinear Schrodinger equations
p } eO % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
FYe fn3b % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
2bw.mp &v1 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
vS3Y9|-: w
T_l>u C=1;
l
6aD3?8LN M1=120, % integer for amplitude
g}a+%Obb M3=5000; % integer for length of coupler
[C~N#S[] N = 512; % Number of Fourier modes (Time domain sampling points)
BC1smSlJ
dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
lU&2 K$` T =40; % length of time:T*T0.
+u\w4byl dt = T/N; % time step
~HT:BO$ n = [-N/2:1:N/2-1]'; % Index
n-qle5s j t = n.*dt;
cd=H4:<T5 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
US9@/V*2 w=2*pi*n./T;
R3)ccom g1=-i*ww./2;
v~ ._]f$: g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
aYHs 35 g3=-i*ww./2;
^"vmIC.h P1=0;
EU H9R8) P2=0;
^( 7l! P3=1;
HTMo.hr P=0;
<4 /q5*& for m1=1:M1
v{ * 2F p=0.032*m1; %input amplitude
}v_|N"@ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
dpt P(H s1=s10;
r( wtuD23q s20=0.*s10; %input in waveguide 2
n%~r^ C_ s30=0.*s10; %input in waveguide 3
&f? JtpB s2=s20;
P# 8lO%; s3=s30;
Y( K`3? A p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
Py+ B 2G| %energy in waveguide 1
a8k`Wog p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
1 un! %energy in waveguide 2
t 0p p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
G2@'S&2@s %energy in waveguide 3
+x4*T for m3 = 1:1:M3 % Start space evolution
,5 3`t s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
('d, Sh s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
,MHF s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
/!/Pk'p=/ sca1 = fftshift(fft(s1)); % Take Fourier transform
B/hQvA;( sca2 = fftshift(fft(s2));
`7V1 F.\ sca3 = fftshift(fft(s3));
d$?+>t/ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
A
L |,\s sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
Fy.!amXu sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
7 nW <kA s3 = ifft(fftshift(sc3));
s(L!]d.S$y s2 = ifft(fftshift(sc2)); % Return to physical space
"(';UFa s1 = ifft(fftshift(sc1));
g0;6}n end
jr-9 KxE p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
&Fk|"f+ p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
l6IT o@&J p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
0Q
cJ Ek P1=[P1 p1/p10];
ke/4l?zs P2=[P2 p2/p10];
hW;n^\lF#e P3=[P3 p3/p10];
jrttW T P=[P p*p];
~ySsv end
-G=.3
bux figure(1)
TvRm 7 plot(P,P1, P,P2, P,P3);
6D{70onY+ ~= otdJ 转自：
http://blog.163.com/opto_wang/
