计算脉冲在非线性耦合器中演化的Matlab 程序 =?hGa;/rb ~~,] b % This Matlab script file solves the coupled nonlinear Schrodinger equations of
o6L\39v_ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
KG7 ~)g % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
oZm)@Vv; % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
~5S[S l /Ilve
U`E %fid=fopen('e21.dat','w');
b?S,% N = 128; % Number of Fourier modes (Time domain sampling points)
=UY)U- M1 =3000; % Total number of space steps
i [,9hp J =100; % Steps between output of space
jNRR=0 T =10; % length of time windows:T*T0
,=!_7'm T0=0.1; % input pulse width
TKJs'%Q7F6 MN1=0; % initial value for the space output location
CWF(OMA dt = T/N; % time step
%@ Mv-A6) n = [-N/2:1:N/2-1]'; % Index
I|&< !{Rq t = n.*dt;
aTXmF1_n u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
& d}1) ? u20=u10.*0.0; % input to waveguide 2
X+6`]] u1=u10; u2=u20;
mm SC0F U1 = u1;
{"f4oK{w U2 = u2; % Compute initial condition; save it in U
Xm#rkF[, ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
|7XPu w=2*pi*n./T;
\M$e#^g g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
o _=t9\: L=4; % length of evoluation to compare with S. Trillo's paper
. tRp dz=L/M1; % space step, make sure nonlinear<0.05
-;T !d for m1 = 1:1:M1 % Start space evolution
ITpo:"X g u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
LdAWCBLS u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
I$yFCd Xr ca1 = fftshift(fft(u1)); % Take Fourier transform
e'"2yA8dh" ca2 = fftshift(fft(u2));
">zK1t5= c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
( x)}k&B; c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
::goqajV u2 = ifft(fftshift(c2)); % Return to physical space
X8m@xFW} u1 = ifft(fftshift(c1));
P_7QZ0k/ if rem(m1,J) == 0 % Save output every J steps.
$qndG,([F U1 = [U1 u1]; % put solutions in U array
M{(g"ha U2=[U2 u2];
'c]Fhe fb MN1=[MN1 m1];
[2~^~ K z1=dz*MN1'; % output location
Ui:WbH<b{ end
VPC7Dh%. end
:`jB1rI hg=abs(U1').*abs(U1'); % for data write to excel
)-jA4!& ha=[z1 hg]; % for data write to excel
<vb%i0+b.^ t1=[0 t'];
1:Sq?=& hh=[t1' ha']; % for data write to excel file
r^g"%nq9/ %dlmwrite('aa',hh,'\t'); % save data in the excel format
U!y GZEU"[ figure(1)
4fR}+[~2 waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
Chso ]N.1 figure(2)
FqWW[Bgd waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
g]$e-X@k 3P,
ul*e 非线性超快脉冲耦合的数值方法的Matlab程序 +Oxw? `I$ NU N~T ( 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。
z*oe ho 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
6y0CEly>3# ]?un'$%e RA_gj lJi R(t1Ei.-? % This Matlab script file solves the nonlinear Schrodinger equations
s!g06F % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
y"I8^CA % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
- f&m4J} E % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
+hZ {/ d~QZc R C=1;
UM(`Oh8 M1=120, % integer for amplitude
H6. M3=5000; % integer for length of coupler
c*!x dK N = 512; % Number of Fourier modes (Time domain sampling points)
E[=# Rw!* dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
$wm.,Vb
T =40; % length of time:T*T0.
>LAhc 7I dt = T/N; % time step
= JW.1 ;
n = [-N/2:1:N/2-1]'; % Index
S %B m4jY t = n.*dt;
n1Z*wMwC ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
=".sCV9"N w=2*pi*n./T;
7*MjQzg-P g1=-i*ww./2;
eaWK 2%v g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
h y}n&h g3=-i*ww./2;
L> \/%x>Wx P1=0;
^[=1J P2=0;
/EvnwYQy P3=1;
N5F+h94z] P=0;
yhsbso,5 a for m1=1:M1
uQmtd p=0.032*m1; %input amplitude
} Q1m s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
Qd"R@+i s1=s10;
c#L. I s20=0.*s10; %input in waveguide 2
K&IH t?vh! s30=0.*s10; %input in waveguide 3
JY0}#FtgV s2=s20;
*eEn8rAr s3=s30;
&0Bs ?oq_ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
Ir?ehA %energy in waveguide 1
E]&t gZ O p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
(GJX[ $@ %energy in waveguide 2
_|C T|q p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
TjWMdoU$J %energy in waveguide 3
0 8W^ for m3 = 1:1:M3 % Start space evolution
Yw6d-5=: s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
s $?u'}G3 s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
aU yJi s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
Fu*Qci1Z sca1 = fftshift(fft(s1)); % Take Fourier transform
3;er.SFu{ sca2 = fftshift(fft(s2));
3f)!RKS9q sca3 = fftshift(fft(s3));
/8[T2Z! sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
0N`'a?x sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
F !MxC sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
{^N 90,! s3 = ifft(fftshift(sc3));
hNL_ e3 s2 = ifft(fftshift(sc2)); % Return to physical space
,0^9VWZV s1 = ifft(fftshift(sc1));
w<m e(!-' end
)%Lgo${[; p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
K-6+fgeB p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
PESJ7/^E p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
:}+m[g P1=[P1 p1/p10];
J?[}h&otQ P2=[P2 p2/p10];
c]3^2Ag, P3=[P3 p3/p10];
f' & P=[P p*p];
&aWY{ ?_ end
qy,X#y'FuE figure(1)
Mw{skK>b plot(P,P1, P,P2, P,P3);
*rmwTD" W}.p, d 转自：
http://blog.163.com/opto_wang/
