计算脉冲在非线性耦合器中演化的Matlab 程序 e6T?2`5P aH50 0 % This Matlab script file solves the coupled nonlinear Schrodinger equations of
`\BBdQ#bH % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
&(x>J:b % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
hNp.%XnnZ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
c Ct5m HE2t0sAYX %fid=fopen('e21.dat','w');
Z\) P|#L$ N = 128; % Number of Fourier modes (Time domain sampling points)
] HG> O g M1 =3000; % Total number of space steps
,z Bc-Cm J =100; % Steps between output of space
WCI'Kh
T =10; % length of time windows:T*T0
8Tc:TaL T0=0.1; % input pulse width
(i@(ZG]/ MN1=0; % initial value for the space output location
,fm{
krE dt = T/N; % time step
Q6[h;lzGV n = [-N/2:1:N/2-1]'; % Index
=D 5!Xq'| t = n.*dt;
.d4&s7n0 u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
D sBZ% u20=u10.*0.0; % input to waveguide 2
+ k u1=u10; u2=u20;
V F"c} U1 = u1;
2
t]=-@ U2 = u2; % Compute initial condition; save it in U
6<n+p'+n ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
& #]||T- w=2*pi*n./T;
Nn5sD3z# g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
baf@"P9@\A L=4; % length of evoluation to compare with S. Trillo's paper
{JcMJZ3 dz=L/M1; % space step, make sure nonlinear<0.05
KH[Oqd for m1 = 1:1:M1 % Start space evolution
E{}eYU u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
".fnx 8v, u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
&gvX<X4e ca1 = fftshift(fft(u1)); % Take Fourier transform
UWBR5 ca2 = fftshift(fft(u2));
|Gb~[6u c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
.-p?skm =a c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
t\<*Q3rl- u2 = ifft(fftshift(c2)); % Return to physical space
c5HW.3" u1 = ifft(fftshift(c1));
Fz_8 m4 if rem(m1,J) == 0 % Save output every J steps.
?vP }#N!=d U1 = [U1 u1]; % put solutions in U array
& =vi]z:[ U2=[U2 u2];
gf|&u4D MN1=[MN1 m1];
,<Cz S,( z1=dz*MN1'; % output location
55x. Q end
p:|p ? end
< ZeZq hg=abs(U1').*abs(U1'); % for data write to excel
7(5 wP( ha=[z1 hg]; % for data write to excel
]<E\J+5K t1=[0 t'];
t*!Q9GC_ hh=[t1' ha']; % for data write to excel file
9uY$@7qH %dlmwrite('aa',hh,'\t'); % save data in the excel format
, @6_sl figure(1)
/57)y_ \ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
p \,PY figure(2)
mv9@Az9 waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
WAh{*$Rpl ljj}X JQ 非线性超快脉冲耦合的数值方法的Matlab程序 uTUkRqtD! ?s {Pp 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。
80O[pf*? 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
6imQjtI '[Ch8Yf\ >c8EgSZJ 9m_Hm')VG % This Matlab script file solves the nonlinear Schrodinger equations
I =yy
I % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
PF/eQZ *4 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
sBu- \P# % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
'd=B{ 7k@ 5a yH5=(t C=1;
e? !A]2 M1=120, % integer for amplitude
^T/d34A;SP M3=5000; % integer for length of coupler
UPJ3YpK N = 512; % Number of Fourier modes (Time domain sampling points)
|< 1 dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
FFqqA T5 T =40; % length of time:T*T0.
GbZqLZ0 dt = T/N; % time step
rQPV@J]: n = [-N/2:1:N/2-1]'; % Index
XQL]I$? t = n.*dt;
IirXF?&t ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
A\7qPfpG w=2*pi*n./T;
IMDGinHAy g1=-i*ww./2;
_Hn-bp[?> g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
m:,S1V_jl g3=-i*ww./2;
q' %-8t P1=0;
d)&}%
2k u P2=0;
& A%*sD6 P3=1;
>H q)1o P=0;
HTz&h#)JQ for m1=1:M1
prx)Cfv p=0.032*m1; %input amplitude
w{1DwCLKq s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
`}YCUm[SI s1=s10;
1 \_S1ZS s20=0.*s10; %input in waveguide 2
&nk[gb
o\ s30=0.*s10; %input in waveguide 3
2O^7zW s2=s20;
? L A>5 s3=s30;
{>E` Zf: p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
GDgq
4vfj %energy in waveguide 1
ySLa4DQf p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
1 U|IN= %energy in waveguide 2
V uqJ&U.- p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
!vB8Pk" %energy in waveguide 3
+p:#$R)MW for m3 = 1:1:M3 % Start space evolution
T(E$0a)# s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
FCu0)\ s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
GoK[tjb s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
y( )7m/ sca1 = fftshift(fft(s1)); % Take Fourier transform
<lj;}@qQ< sca2 = fftshift(fft(s2));
i1"4z tZ sca3 = fftshift(fft(s3));
A3VXh^y+ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
Hvto]~=GQ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
^x8yW b rE sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
Bn 5]{Df s3 = ifft(fftshift(sc3));
gn>qd6P s2 = ifft(fftshift(sc2)); % Return to physical space
J_]B,'
6 s1 = ifft(fftshift(sc1));
2cy: l03 end
e^?0uVxS1 p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
FvpI\%#~ p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
^a6c/ 2K p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
p<w2e P1=[P1 p1/p10];
%QW1?VVP P2=[P2 p2/p10];
DdY89R 6 P3=[P3 p3/p10];
Z Sj[GI P=[P p*p];
&\Es \qVSf end
qHT_,\l2 figure(1)
dD
Qx [ plot(P,P1, P,P2, P,P3);
b '1n1L kf3 u',}R 转自：
http://blog.163.com/opto_wang/
