计算脉冲在非线性耦合器中演化的Matlab 程序 r2
o-/$ -4'yC_8t % This Matlab script file solves the coupled nonlinear Schrodinger equations of
;&G8e* bM2 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
z q&,KZ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
~85Pgb< % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
p*Hbc|?{Q& Z CS{D %fid=fopen('e21.dat','w');
5x; y{qT N = 128; % Number of Fourier modes (Time domain sampling points)
x?MSHOia`P M1 =3000; % Total number of space steps
*,d>(\&[f J =100; % Steps between output of space
VC@{cVT T =10; % length of time windows:T*T0
. ;q 4<_ T0=0.1; % input pulse width
? $LKn2C MN1=0; % initial value for the space output location
B?)=d,E dt = T/N; % time step
GwaU7[6 n = [-N/2:1:N/2-1]'; % Index
F,-S&d t = n.*dt;
_o-D},f*e u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
V_"K u20=u10.*0.0; % input to waveguide 2
|KxFi H u1=u10; u2=u20;
h_Ca c@F0 U1 = u1;
^UAL5}CQt U2 = u2; % Compute initial condition; save it in U
=D2x@ank[ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
aPMqJ#fIr w=2*pi*n./T;
ZNvnVW< g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
$!_]mz6* L=4; % length of evoluation to compare with S. Trillo's paper
30v 3C7o= dz=L/M1; % space step, make sure nonlinear<0.05
;f7;U=gl, for m1 = 1:1:M1 % Start space evolution
Z;#Ei.7p| u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
`Vqp o / u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
)m Uc
!TP ca1 = fftshift(fft(u1)); % Take Fourier transform
:5`BhFAd ca2 = fftshift(fft(u2));
A+lP]Oy0S c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
-S"$S16D c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
@i[z4)"S u2 = ifft(fftshift(c2)); % Return to physical space
JS<4%@ u1 = ifft(fftshift(c1));
1wpeYn7>W if rem(m1,J) == 0 % Save output every J steps.
$MEK t}S U1 = [U1 u1]; % put solutions in U array
zp2IpYQ,3 U2=[U2 u2];
"38ya2* MN1=[MN1 m1];
wcT0XXh z1=dz*MN1'; % output location
D{aN_0mT end
8U07]=Bt< end
D $RQ D{* hg=abs(U1').*abs(U1'); % for data write to excel
G,8LF/sR ha=[z1 hg]; % for data write to excel
Ta38/v;S t1=[0 t'];
iraO/KhD*3 hh=[t1' ha']; % for data write to excel file
IZ;%lV7t %dlmwrite('aa',hh,'\t'); % save data in the excel format
EQkv&k5X figure(1)
. ` OdnLGy waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
U.
1Vpfy figure(2)
/?jAG3" waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
P!{
O<P /2 & jId 非线性超快脉冲耦合的数值方法的Matlab程序 3JiDi
X"| zhDmZ 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。
rZDlPp>BPZ 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
s e9X f.`noZN lbv9 kk[ AWP CJmr % This Matlab script file solves the nonlinear Schrodinger equations
'Dq!o[2 y % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
r`|/qP:T[ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
;K:) R_H % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
)jK"\'cK {ZH9W C=1;
)POuH*j M1=120, % integer for amplitude
Y#_,Ig5. M3=5000; % integer for length of coupler
J 3fcnI N = 512; % Number of Fourier modes (Time domain sampling points)
D 5]sf>~ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
9d4 PH T =40; % length of time:T*T0.
e`#c[lbAAM dt = T/N; % time step
n\}!'>d' n = [-N/2:1:N/2-1]'; % Index
|\ j'Z0 t = n.*dt;
SLL%XF~/Sb ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
H'E > QT w=2*pi*n./T;
> _1*/o
JO g1=-i*ww./2;
<h2WM (n g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
0+0+%#? g3=-i*ww./2;
DKCPi 0 P1=0;
s% "MaDz P2=0;
|~bl%g8xP P3=1;
h5&l#>8& P=0;
UfEF>@0 for m1=1:M1
tm~V+t!mj p=0.032*m1; %input amplitude
@eN x :} s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
dF*@G/p>V s1=s10;
mu2r#I s20=0.*s10; %input in waveguide 2
}u&.n
pc s30=0.*s10; %input in waveguide 3
"_JGe#= s2=s20;
FW: x XK s3=s30;
F
kp; G p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
;}{%|UAsx %energy in waveguide 1
| eIN<RY5 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
(b Q1,y %energy in waveguide 2
%^m6Q! p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
p6]4YGw*^ %energy in waveguide 3
<k'=_mC_ for m3 = 1:1:M3 % Start space evolution
cA1" Nek s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
6~sb8pK.= s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
{[PoLOCI s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
Z9s tB>? sca1 = fftshift(fft(s1)); % Take Fourier transform
!Ac <A. sca2 = fftshift(fft(s2));
$
+;`[b sca3 = fftshift(fft(s3));
7=t4;8|j; sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
]:JoGGE a0 sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
p q7G[ sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
BEyg 63= s3 = ifft(fftshift(sc3));
^!-*xH.dK s2 = ifft(fftshift(sc2)); % Return to physical space
n4+l, ~ s1 = ifft(fftshift(sc1));
jEsP: H(0^ end
Y@N} XH<4R p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
9D:p~_"g p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
"o/:LCE p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
q-gN0"z^6$ P1=[P1 p1/p10];
\5 IB/ * P2=[P2 p2/p10];
XKB)++Q= P3=[P3 p3/p10];
m5SJB]a/ P=[P p*p];
quHq?oX V, end
<\GP\G figure(1)
7y:%^sl plot(P,P1, P,P2, P,P3);
~U#afGH$ *{8K b>D 转自：
http://blog.163.com/opto_wang/
