计算脉冲在非线性耦合器中演化的Matlab 程序 biV NZdA 5fRr d; % This Matlab script file solves the coupled nonlinear Schrodinger equations of
0rvBjlFT % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
\/b[V3<" % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
{yDQncq'^ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
8tVSai8[ DTa!vg %fid=fopen('e21.dat','w');
K0D|p $v N = 128; % Number of Fourier modes (Time domain sampling points)
1OV] W
f M1 =3000; % Total number of space steps
6s'n
r7'0 J =100; % Steps between output of space
q[ 9N4nj$< T =10; % length of time windows:T*T0
bGkLa/?S T0=0.1; % input pulse width
`z$P,^g` MN1=0; % initial value for the space output location
.PV(MV dt = T/N; % time step
qOIVuzi* n = [-N/2:1:N/2-1]'; % Index
7!wc'~; t = n.*dt;
8nWPt!U: u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
5 D=r7 u20=u10.*0.0; % input to waveguide 2
;WAa4r> u1=u10; u2=u20;
!2>@:CKX U1 = u1;
LzD Ry L U2 = u2; % Compute initial condition; save it in U
/8!n7a7 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
+v$W$s&b-h w=2*pi*n./T;
Gpi_p g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
[!MS1v c; L=4; % length of evoluation to compare with S. Trillo's paper
yFS{8yrRUU dz=L/M1; % space step, make sure nonlinear<0.05
,SNt*t1 " for m1 = 1:1:M1 % Start space evolution
78r0K 5= u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
}h1eB~6M u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
Bl^ BtE?-b ca1 = fftshift(fft(u1)); % Take Fourier transform
8I Ip,#%v ca2 = fftshift(fft(u2));
n`@dk_%yI c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
f( Dtv c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
z`.<dNg u2 = ifft(fftshift(c2)); % Return to physical space
, fqM>Q u1 = ifft(fftshift(c1));
6kMkFZ}+ if rem(m1,J) == 0 % Save output every J steps.
xR8.1T?8 U1 = [U1 u1]; % put solutions in U array
>2=
Y 35j U2=[U2 u2];
RWX!d54& MN1=[MN1 m1];
<1B+@ z1=dz*MN1'; % output location
~mwI r end
8!HB$vdw7 end
E m^Dg9 hg=abs(U1').*abs(U1'); % for data write to excel
|) C *i ha=[z1 hg]; % for data write to excel
HVhP |+ t1=[0 t'];
"RM\<) IF hh=[t1' ha']; % for data write to excel file
OZd
(~E %dlmwrite('aa',hh,'\t'); % save data in the excel format
dsj}GgG?Z figure(1)
W/b)OlG"2 waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
Jgg< u# figure(2)
||.Hv[
]V* waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
4=EA3`l ``I[1cC 非线性超快脉冲耦合的数值方法的Matlab程序 ?L0k |7 -(>Ch>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。
co1aG,>"q 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
VIN0k RQ# >fth
iA FvG?%IFM 0xO*8aKT % This Matlab script file solves the nonlinear Schrodinger equations
M_-L#FHX % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
eB=&(ZT % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
X,#~[%h$-= % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
f$n5$hJ lQ PHEQG]H S C=1;
}ijQ*ECdl M1=120, % integer for amplitude
UqyW8TCf? M3=5000; % integer for length of coupler
p\F%Nj, N = 512; % Number of Fourier modes (Time domain sampling points)
{: #nrD" dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
<<E 9MIn_ T =40; % length of time:T*T0.
-u4")V> dt = T/N; % time step
R dwt4A+ n = [-N/2:1:N/2-1]'; % Index
y22DBB8 t = n.*dt;
bk;uKV+< ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
#.[eZ[ w=2*pi*n./T;
_H@ATut g1=-i*ww./2;
5ya^k{`+ZO g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
|2@*?o"ll g3=-i*ww./2;
AO]cnh C P1=0;
9xhc:@B1J P2=0;
S4[ #[w`= P3=1;
k4hk*
0Jq P=0;
3Jt #
Mp for m1=1:M1
(_<,Oj#*S p=0.032*m1; %input amplitude
S*|/txE'~Y s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
=-X-${/ s1=s10;
M@<9/x PS s20=0.*s10; %input in waveguide 2
/*k_`3L s30=0.*s10; %input in waveguide 3
VN `fZ5*d~ s2=s20;
e0(aRN{W s3=s30;
+egwZ$5I p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
m%apGp'=1 %energy in waveguide 1
6hv.;n}; p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
g#^MO]pY %energy in waveguide 2
Bf;_~1+vLG p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
&KAe+~aPm %energy in waveguide 3
/]5*;kO` for m3 = 1:1:M3 % Start space evolution
Owi/e s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
uf9&o# s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
5Gy#$' kdf s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
Ly baE~=
sca1 = fftshift(fft(s1)); % Take Fourier transform
%K-8D L8|( sca2 = fftshift(fft(s2));
h_S>Q sca3 = fftshift(fft(s3));
la_c:#ho sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
'ScvteQ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
< Nqbp sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
5TB6QLPEwY s3 = ifft(fftshift(sc3));
p^ k0Rad s2 = ifft(fftshift(sc2)); % Return to physical space
X(MS!R V s1 = ifft(fftshift(sc1));
y32$b,%Xi, end
xlu4 p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
=g M@[2 p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
3oMHy5 p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
^N|8
B ?Vg P1=[P1 p1/p10];
_W _< bI34 P2=[P2 p2/p10];
kDWEgnXK,v P3=[P3 p3/p10];
S#y[_ C?H P=[P p*p];
OM&GypP6& end
vQK/xg figure(1)
!e~[U- plot(P,P1, P,P2, P,P3);
3u$ 1W@T( =
a60Xv 转自：
http://blog.163.com/opto_wang/
