计算脉冲在非线性耦合器中演化的Matlab 程序 l&(l$@t S6 i@"h5 % This Matlab script file solves the coupled nonlinear Schrodinger equations of
2a =sm1? % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
qv2!grp]*W % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
1+kE!2b;b % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
; @mRo`D` t;qP ']2
%fid=fopen('e21.dat','w');
h) (* q+a N = 128; % Number of Fourier modes (Time domain sampling points)
\}*k )$r M1 =3000; % Total number of space steps
P7 y q^| J =100; % Steps between output of space
$9!D\N,}]C T =10; % length of time windows:T*T0
w`HI]{hE~N T0=0.1; % input pulse width
ub :ly0;t MN1=0; % initial value for the space output location
/%rq
hHs dt = T/N; % time step
0DPxW8Y -` n = [-N/2:1:N/2-1]'; % Index
\FmKJ\ t = n.*dt;
,?cH"@ RJ u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
#$ thPZ u20=u10.*0.0; % input to waveguide 2
w|Cx>8P8@ u1=u10; u2=u20;
.giz=* q+ U1 = u1;
]c)_&{:V U2 = u2; % Compute initial condition; save it in U
_c(4o : ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
R3.*dqo$ w=2*pi*n./T;
(K..k-o`. g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
B}?IEpYp L=4; % length of evoluation to compare with S. Trillo's paper
L5fuM]G` dz=L/M1; % space step, make sure nonlinear<0.05
IND ]j72 for m1 = 1:1:M1 % Start space evolution
1eS_
nLFw~ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
T )~9Wac u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
aG`;OgrH ca1 = fftshift(fft(u1)); % Take Fourier transform
.3qu9eP ca2 = fftshift(fft(u2));
KP"%Rm`XN c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
}CGSEr4'w~ c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
95W?{>
@ u2 = ifft(fftshift(c2)); % Return to physical space
~g ;
u1 = ifft(fftshift(c1));
K{ fsn4rk if rem(m1,J) == 0 % Save output every J steps.
6i@\5}m= U1 = [U1 u1]; % put solutions in U array
s,]%dG! U2=[U2 u2];
x *XH]&V MN1=[MN1 m1];
t ~7V { xk z1=dz*MN1'; % output location
Zi\['2CG end
Q4* -wF-P end
L5YnG _M& hg=abs(U1').*abs(U1'); % for data write to excel
/'.=sH ha=[z1 hg]; % for data write to excel
2;3f =$3 t1=[0 t'];
G bP!9I hh=[t1' ha']; % for data write to excel file
" Dcs] )7Q %dlmwrite('aa',hh,'\t'); % save data in the excel format
arK_oh0B figure(1)
Lv[OUW#S waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
Y5q3T`x E figure(2)
0IkM waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
0C%W&;r0 ef! XV7 P 非线性超快脉冲耦合的数值方法的Matlab程序 0U/,aHvhP nKr9#JebRC 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。
siDh="{s 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
58xnB !h\} ti5HrKIw @F* wg |R/.r_x,V? % This Matlab script file solves the nonlinear Schrodinger equations
I`(l *U % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
ykg# {9+ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
(h-*_a}F4 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
m #/_x 1nknSw# C=1;
$!@\ M1=120, % integer for amplitude
>ydRSr^ M3=5000; % integer for length of coupler
`Hx~UH) N = 512; % Number of Fourier modes (Time domain sampling points)
T\s)le dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
RC#C\S6 T =40; % length of time:T*T0.
:wqC8&V dt = T/N; % time step
6M.;@t,Y n = [-N/2:1:N/2-1]'; % Index
I&|f'pn^< t = n.*dt;
Q?t^ @ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
qo6y %[ w=2*pi*n./T;
&hIRd,1# g1=-i*ww./2;
S"m cUU}} g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
-D^A: }$ g3=-i*ww./2;
3-Dt[0%{ P1=0;
h&3YGCl P2=0;
o\otgyoh P3=1;
>kZ57, P=0;
$*a'84-5G- for m1=1:M1
cXMhq<GkAA p=0.032*m1; %input amplitude
rx"s!y{!- s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
b
IW'c_
, s1=s10;
w9RS)l2FQ s20=0.*s10; %input in waveguide 2
E`H$YS3o s30=0.*s10; %input in waveguide 3
d x*qb s2=s20;
)py{\r9X s3=s30;
%%ae^*[!n p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
4F3x@H' %energy in waveguide 1
^ &/G| p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
o'<^LYSnB %energy in waveguide 2
)&{K~i ;: p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
~9\WF F/ %energy in waveguide 3
6pOx'u>h+ for m3 = 1:1:M3 % Start space evolution
)QagS.L{z s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
z\s s4 s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
88"Sai s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
X;F?:Iw \ sca1 = fftshift(fft(s1)); % Take Fourier transform
tc r// sca2 = fftshift(fft(s2));
`cQo0{xK sca3 = fftshift(fft(s3));
M~*u;vA/ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
Z4$cyL'$P sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
7`IpBm< sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
/"H`.LD.? s3 = ifft(fftshift(sc3));
)Rat0$6 s2 = ifft(fftshift(sc2)); % Return to physical space
=$8nUX` s1 = ifft(fftshift(sc1));
kPBV6+d~ end
L\{IljA p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
Cd 79 tu| p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
d%I" /8-J p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
$ N']TN P1=[P1 p1/p10];
wfvU0]wk} P2=[P2 p2/p10];
I\?9+3 XnQ P3=[P3 p3/p10];
\k `n[{ P=[P p*p];
BG^C9*ZuP end
qa(>wR"mT figure(1)
CxhY$%C (L plot(P,P1, P,P2, P,P3);
:M{Y,~cP ^ 5VK> 转自：
http://blog.163.com/opto_wang/
