计算脉冲在非线性耦合器中演化的Matlab 程序 ZnRT$ l O rR :ZTfJs" % This Matlab script file solves the coupled nonlinear Schrodinger equations of
]"b:IWPeI % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
{0w2K82 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
:;.^r,QAI % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
)~)l^0X uxB )dS %fid=fopen('e21.dat','w');
:ujpLIjvVG N = 128; % Number of Fourier modes (Time domain sampling points)
(_"Zbw%cJy M1 =3000; % Total number of space steps
^)?Wm,{"w J =100; % Steps between output of space
(;;ji!i T =10; % length of time windows:T*T0
in/~' u T0=0.1; % input pulse width
{'tfU MN1=0; % initial value for the space output location
[U/h'A.j dt = T/N; % time step
\ c4 jGJ n = [-N/2:1:N/2-1]'; % Index
E`I(x&_ t = n.*dt;
aqN{@| u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
\?
)S { u20=u10.*0.0; % input to waveguide 2
n|)((W u1=u10; u2=u20;
JR#4{P@A U1 = u1;
J)Y`G4l2@ U2 = u2; % Compute initial condition; save it in U
m9A%Z bQ^ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
R lk3AWl2u w=2*pi*n./T;
o=_ 7KWOA g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
(87| :{ L=4; % length of evoluation to compare with S. Trillo's paper
i oD8- dz=L/M1; % space step, make sure nonlinear<0.05
T2S_>
#."l for m1 = 1:1:M1 % Start space evolution
p$9Aadi] u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
6T'UWh0S u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
O^`EuaL ca1 = fftshift(fft(u1)); % Take Fourier transform
A~P R ca2 = fftshift(fft(u2));
G9^`cTvv'8 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
t&?{+?p:
9 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
zP%s] >hH u2 = ifft(fftshift(c2)); % Return to physical space
!i~(h&z u1 = ifft(fftshift(c1));
17Cb{ Q if rem(m1,J) == 0 % Save output every J steps.
wQUl!s7M; U1 = [U1 u1]; % put solutions in U array
:vb5J33U U2=[U2 u2];
#4O4,F>e MN1=[MN1 m1];
vvv '!\'# z1=dz*MN1'; % output location
u_$4xNmQ end
1#6emMV.` end
m%`YAD@2z hg=abs(U1').*abs(U1'); % for data write to excel
] "Uzn ha=[z1 hg]; % for data write to excel
qIQ=OY=6 t1=[0 t'];
ih".y3 hh=[t1' ha']; % for data write to excel file
xyL)'C %dlmwrite('aa',hh,'\t'); % save data in the excel format
JE-*o"& figure(1)
m G\QF0h waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
(Of6Ij? figure(2)
H %@f ^ waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
P-Y_$Nv0g ]6^<VC`5D 非线性超快脉冲耦合的数值方法的Matlab程序 E+O{^C= ' c7nh{F 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。
8l5>t 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
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<U|\-? uKP4ur@1 uL/wV~g 71R,R, % This Matlab script file solves the nonlinear Schrodinger equations
ce\d35x! % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
qX-ptsQ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
4n1g4c-
% pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
b!@PS$BTxq d#0:U
Y% ~ C=1;
4tZ *%!I' M1=120, % integer for amplitude
adP :{j M3=5000; % integer for length of coupler
UA8hYWRP N = 512; % Number of Fourier modes (Time domain sampling points)
Mqd'XU0L dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
60!%^O = T =40; % length of time:T*T0.
z)^|. dt = T/N; % time step
H JAiQ[m5s n = [-N/2:1:N/2-1]'; % Index
PK2;Ywk` t = n.*dt;
fQa*> **j; ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
WT ;2aS: w=2*pi*n./T;
%,
psUOY g1=-i*ww./2;
G(a5@9F g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
MT&aH~Y B g3=-i*ww./2;
=tP9n ;D P1=0;
T ?[28| P2=0;
rQimQ| + P3=1;
fwz:k]vk P=0;
=o##z5j
K for m1=1:M1
& !CVF p=0.032*m1; %input amplitude
t`H1]`c? s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
9S|sTf s1=s10;
TF/NA\0c$ s20=0.*s10; %input in waveguide 2
O% T?+1E s30=0.*s10; %input in waveguide 3
o%?)};o s2=s20;
.kBkYK8*t s3=s30;
*lSu= dk+ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
(+|+E LfqW %energy in waveguide 1
V8M ()7uJ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
3@V?L: J %energy in waveguide 2
27D*FItc
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
,- AF8BP %energy in waveguide 3
dxs5woP for m3 = 1:1:M3 % Start space evolution
ez'NHodwk2 s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
#<*.{"T s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
[ey#
,&T s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
@A1f#Ed< sca1 = fftshift(fft(s1)); % Take Fourier transform
e3 v^j$ sca2 = fftshift(fft(s2));
"u^Erj# / sca3 = fftshift(fft(s3));
:RnUNz sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
u8zL[] > sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
.|O T#"LP sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
G]ek-[- s3 = ifft(fftshift(sc3));
I8gNg
Z s2 = ifft(fftshift(sc2)); % Return to physical space
vkE`T5?? s1 = ifft(fftshift(sc1));
"b hK %N; end
|0i{z(B p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
_c>ww<*3 p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
F\D iT|?} p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
:01d9|# P1=[P1 p1/p10];
yI:
;+K P2=[P2 p2/p10];
zIrOMh P3=[P3 p3/p10];
DJ"PP 5d P=[P p*p];
iM<$
n2t end
hQ@k|3=Re figure(1)
w.x &3aG plot(P,P1, P,P2, P,P3);
Q-oD mjU %/Wk+r9uu 转自：
http://blog.163.com/opto_wang/
