计算脉冲在非线性耦合器中演化的Matlab 程序 U|QLc 3 f=_F % This Matlab script file solves the coupled nonlinear Schrodinger equations of
z^z_!@7v
% soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
n $RhD93 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
P ,-f]k[_ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
sdF;H [ k%|7H,7 %fid=fopen('e21.dat','w');
5+*MqO> N = 128; % Number of Fourier modes (Time domain sampling points)
;i*<HNQ M1 =3000; % Total number of space steps
QOA7#H-m9 J =100; % Steps between output of space
2F k4jHj T =10; % length of time windows:T*T0
ol QT r T0=0.1; % input pulse width
oc+TsVt MN1=0; % initial value for the space output location
hK F*{,' dt = T/N; % time step
#=mLQSiQ n = [-N/2:1:N/2-1]'; % Index
p4QQ5O$; t = n.*dt;
-j1?l Y u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
:.wR *E u20=u10.*0.0; % input to waveguide 2
eT33&:n4 u1=u10; u2=u20;
`|maf=SnY5 U1 = u1;
h3 -y}.VjG U2 = u2; % Compute initial condition; save it in U
!nh7<VJ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
\1Tu
P}P w=2*pi*n./T;
GCaiogiBg g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
[B<htD& L=4; % length of evoluation to compare with S. Trillo's paper
z,pKy Inw dz=L/M1; % space step, make sure nonlinear<0.05
oasp/Y.p for m1 = 1:1:M1 % Start space evolution
1vKAJ<4W u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
nn[OC=cDN u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
i\~@2 ca1 = fftshift(fft(u1)); % Take Fourier transform
MIa#\tJj ca2 = fftshift(fft(u2));
X{cFq W7 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
D d['e c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
1dDK(RBbQ u2 = ifft(fftshift(c2)); % Return to physical space
^n Gj 7b u1 = ifft(fftshift(c1));
SI_u0j4%* if rem(m1,J) == 0 % Save output every J steps.
og0su U1 = [U1 u1]; % put solutions in U array
S7i,oP7 U2=[U2 u2];
u!4i+7} MN1=[MN1 m1];
yN- o?[o z1=dz*MN1'; % output location
N_jpCCG~ end
jQ>~ end
:g&9v_}&K{ hg=abs(U1').*abs(U1'); % for data write to excel
\
@XvEx% ha=[z1 hg]; % for data write to excel
}eKY%WU>O t1=[0 t'];
qPal'c 0 hh=[t1' ha']; % for data write to excel file
g$X4ZRSel %dlmwrite('aa',hh,'\t'); % save data in the excel format
ZC7Zl L _ figure(1)
.J=<E waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
}4$k-,1S figure(2)
N{b ;kiZq waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
)gNS%t c*K Z+p'3 非线性超快脉冲耦合的数值方法的Matlab程序 4~8!3JH39 9):h
%o 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。
<!qN<#$y Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
2!@ER i J}zN] |bz ~F)[H'$A +K2p2Dw(k % This Matlab script file solves the nonlinear Schrodinger equations
d d?ZQ:n % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
`1xJ1 z# % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
_;z IH5 H % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
L0^rw|Z%' S/?!ESW6 C=1;
Z'Uc}M 'U M1=120, % integer for amplitude
G q& [T: M3=5000; % integer for length of coupler
c]Z@L~WW N = 512; % Number of Fourier modes (Time domain sampling points)
Nbyc,a[o dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
s?Wkh `b T =40; % length of time:T*T0.
K>a@AXC dt = T/N; % time step
QmiS/`AAv n = [-N/2:1:N/2-1]'; % Index
%D Q!#Nl* t = n.*dt;
w?JR Y ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
pnTuYT^%) w=2*pi*n./T;
(Ts#^qC g1=-i*ww./2;
Jxo#s V-
g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
"| ,;~k1 g3=-i*ww./2;
A_pcv7=@ P1=0;
v)c[-:"z P2=0;
BN]{o(EB P3=1;
>Hd Pcsl L P=0;
AQ<2 "s for m1=1:M1
#Y_v0.N p=0.032*m1; %input amplitude
o[Gp * o\ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
5f}GV0=n s1=s10;
9JtPP s20=0.*s10; %input in waveguide 2
&sA@! s30=0.*s10; %input in waveguide 3
=@\Li)Y s2=s20;
a +lTAe s3=s30;
&al\8 p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
znq/
%7 %energy in waveguide 1
2EAY`}Rl6. p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
b%_[\(( %energy in waveguide 2
k6 2KZ5| D p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
5^0K5R6GQf %energy in waveguide 3
A5q %yt I for m3 = 1:1:M3 % Start space evolution
`21$ e s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
_ /pdZM,V s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
6Gj69Lr s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
+cf. In,{ sca1 = fftshift(fft(s1)); % Take Fourier transform
kf -/rC)> sca2 = fftshift(fft(s2));
q% pjY sca3 = fftshift(fft(s3));
L=v"5)m2R sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
,!I'0x1OR sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
&{=`g+4n sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
\f-HfYG s3 = ifft(fftshift(sc3));
o c0z1u s2 = ifft(fftshift(sc2)); % Return to physical space
$ 0 Up. s1 = ifft(fftshift(sc1));
@7z_f!'u end
EG
oe<. p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
k<.VR"I
p p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
*#&s+h,^ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
Z.{r%W{ 2 P1=[P1 p1/p10];
R2B0?fu P2=[P2 p2/p10];
jHx)q|2\ P3=[P3 p3/p10];
1 GB P=[P p*p];
\CK f/:" end
> Du>vlT Y figure(1)
<uL0 M`u3 plot(P,P1, P,P2, P,P3);
$8t\|O3 ~'3hK4 转自：
http://blog.163.com/opto_wang/
