计算脉冲在非线性耦合器中演化的Matlab 程序 7 0EH~ S,Q(,e ^& % This Matlab script file solves the coupled nonlinear Schrodinger equations of
8idI Jm%y % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
c2L\m* ^o % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
d (9-T@J % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
;f= .SJF PDLps[a %fid=fopen('e21.dat','w');
:B\ $7+$v N = 128; % Number of Fourier modes (Time domain sampling points)
/2MZH M1 =3000; % Total number of space steps
aj=-^i GG J =100; % Steps between output of space
5 0a';!H T =10; % length of time windows:T*T0
Mb45UG#2 T0=0.1; % input pulse width
jy_4W !4a MN1=0; % initial value for the space output location
b5ul|p dt = T/N; % time step
ux, eY n = [-N/2:1:N/2-1]'; % Index
GkI{7GD:z t = n.*dt;
) 1$H 7| u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
yo% Nz" u20=u10.*0.0; % input to waveguide 2
`b%^_@Fb u1=u10; u2=u20;
N8=-=]0G U1 = u1;
U* uMMb}$ U2 = u2; % Compute initial condition; save it in U
l}k'ZX 4 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
LI^D\ w=2*pi*n./T;
o/[Ks;l g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
=NSunW ! L=4; % length of evoluation to compare with S. Trillo's paper
EQX<<x" dz=L/M1; % space step, make sure nonlinear<0.05
}:QoY Nq for m1 = 1:1:M1 % Start space evolution
BuUM~k&SY u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
^:,wk7 u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
W|(<z'S ca1 = fftshift(fft(u1)); % Take Fourier transform
}*O8] lG ca2 = fftshift(fft(u2));
UMT}2d% c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
Ndyo)11z c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
L3 KJ~LI u2 = ifft(fftshift(c2)); % Return to physical space
] mK{E~Zll u1 = ifft(fftshift(c1));
K<%8.mZ7 if rem(m1,J) == 0 % Save output every J steps.
Kaaz,C.$^ U1 = [U1 u1]; % put solutions in U array
LabI5+g U2=[U2 u2];
l.Z+.<@ MN1=[MN1 m1];
Wg<o %6` z1=dz*MN1'; % output location
. ~a~(| end
pbIVj3-lY end
hlz/TIP^N3 hg=abs(U1').*abs(U1'); % for data write to excel
d`% 7Pk ha=[z1 hg]; % for data write to excel
+_QcLuV, t1=[0 t'];
5 PP^w~n hh=[t1' ha']; % for data write to excel file
8@|{n`n] %dlmwrite('aa',hh,'\t'); % save data in the excel format
2=%]Ax"R figure(1)
mS49l waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
madb l0[y. figure(2)
q'IMt7} waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
H+@?K6{h DF-.|-^9I 非线性超快脉冲耦合的数值方法的Matlab程序 Xg\u nUHa %?F$3YN, 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。
6&L;Sw#Dg 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
$vn )(zn+ y{~tMpo< =WEDQ\ c |`fuu2W! % This Matlab script file solves the nonlinear Schrodinger equations
{Z
Ld_VGW % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
yS3o r(K % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
W@zu N)U % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Z|)1 ftcC c>Ri6=C C=1;
{<#b@=G M1=120, % integer for amplitude
+8"P*z, M3=5000; % integer for length of coupler
u D[T l N = 512; % Number of Fourier modes (Time domain sampling points)
H\a \xCP3 dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
2 ^nws T =40; % length of time:T*T0.
N^k&
8 dt = T/N; % time step
ikb77 ? . n = [-N/2:1:N/2-1]'; % Index
tx Qr|\4k t = n.*dt;
ZF8`= D`:R ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
Y##lFEt w=2*pi*n./T;
Uv~|Xj 4. g1=-i*ww./2;
4$U^)\06W g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
pd.unEWwF g3=-i*ww./2;
kjXwVGK=P< P1=0;
/x_AWnU P2=0;
$ @L2zl1 P3=1;
q!~DCv df P=0;
V ZtFgN$J for m1=1:M1
Y^ ;izM} p=0.032*m1; %input amplitude
,}9
tJY@ E s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
@gM}&G08 s1=s10;
q|r*4={^!* s20=0.*s10; %input in waveguide 2
{kb7u5- s30=0.*s10; %input in waveguide 3
CC3M7 |eO3 s2=s20;
] ;CJ6gM~ s3=s30;
zJ:%iL@ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
z2!4w +2 %energy in waveguide 1
<(yAat$H p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
%?[0G,JG %energy in waveguide 2
/FC(d5I p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
TmM~uc7mj %energy in waveguide 3
7r.~L for m3 = 1:1:M3 % Start space evolution
r:4]:NKCi s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
DF
gM7if s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
@D `j s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
dJdOh#8+Xi sca1 = fftshift(fft(s1)); % Take Fourier transform
X\i;j!;d sca2 = fftshift(fft(s2));
_+~&t9A! sca3 = fftshift(fft(s3));
)r)ZmS5O sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
!, ]c}Y{i sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
[,MK)7DU sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
`U >2H4P s3 = ifft(fftshift(sc3));
u`Y~r<?P( s2 = ifft(fftshift(sc2)); % Return to physical space
ELG9ts+5Uj s1 = ifft(fftshift(sc1));
BMV\@Sg end
/<%L& p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
vF>]9sMv p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
C ?'s p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
.b ^!f<j P1=[P1 p1/p10];
joZd P2=[P2 p2/p10];
PAx R?2m{ P3=[P3 p3/p10];
b *{U O P=[P p*p];
)%f]P<kq6 end
)UVe kkq>Q figure(1)
|YfJ#Agm+ plot(P,P1, P,P2, P,P3);
W
)Ps2 e#k)F.TZ:% 转自：
http://blog.163.com/opto_wang/
