计算脉冲在非线性耦合器中演化的Matlab 程序 VsIDd}~C% ~m`j=ot % This Matlab script file solves the coupled nonlinear Schrodinger equations of
Mk-zeq<2z % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
3MqyHOOv % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
o8uak*"{ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
5?] Dn k.o 5~,usA * %fid=fopen('e21.dat','w');
Veeuw N = 128; % Number of Fourier modes (Time domain sampling points)
},eV?eGj M1 =3000; % Total number of space steps
_ tba:a( J =100; % Steps between output of space
>#u9W'@| T =10; % length of time windows:T*T0
(:|g"8mQm T0=0.1; % input pulse width
qcV mt1" MN1=0; % initial value for the space output location
j Wpm "C
dt = T/N; % time step
H6o_*Y n = [-N/2:1:N/2-1]'; % Index
3UR'*5|' t = n.*dt;
CdZS"I u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
M9C
v00& u20=u10.*0.0; % input to waveguide 2
zG^|W8um_ u1=u10; u2=u20;
,8Eg/ U1 = u1;
?^}
z U2 = u2; % Compute initial condition; save it in U
^*g= 65!1 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
2E 0A` w=2*pi*n./T;
|K. J@zW g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
u W 7Yem& L=4; % length of evoluation to compare with S. Trillo's paper
>;^t) 6 dz=L/M1; % space step, make sure nonlinear<0.05
jjJvyZi~J for m1 = 1:1:M1 % Start space evolution
xj<
K6 u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
Xtk3~@ u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
#MyF 1 E ca1 = fftshift(fft(u1)); % Take Fourier transform
zg}#X6\G<_ ca2 = fftshift(fft(u2));
u.yjk/jF c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
k a c -@ c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
3[*x'"Q;H u2 = ifft(fftshift(c2)); % Return to physical space
9EFQo^
E u1 = ifft(fftshift(c1));
]broU%#" if rem(m1,J) == 0 % Save output every J steps.
^1w<wB\B U1 = [U1 u1]; % put solutions in U array
MkK6.qV\z
U2=[U2 u2];
qsG}A MN1=[MN1 m1];
HrK7qLw7 z1=dz*MN1'; % output location
16-1&WuY@ end
QHHj.ZY end
*KYh_i hg=abs(U1').*abs(U1'); % for data write to excel
]^>RBegJBO ha=[z1 hg]; % for data write to excel
tBjMm8lgb t1=[0 t'];
=Sjf-o1 V hh=[t1' ha']; % for data write to excel file
hd>_K*oH %dlmwrite('aa',hh,'\t'); % save data in the excel format
49!(Sa_]j figure(1)
,>3b|-C- waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
p!/ *(TT figure(2)
eW\C@>K e waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
J;5G]$s :"Gd;~p. 非线性超快脉冲耦合的数值方法的Matlab程序 Ue&I]/?; $ pP)> x*1 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。
*| B5,Ey 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
j
V'~ > D6fGr$(N% dF+R
q|n{ GLiD,QX< % This Matlab script file solves the nonlinear Schrodinger equations
Hd $ {I", % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
[A'9sxG % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
vSv:!5* % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
1SG^g*mf LTZ~Id-)P C=1;
zlhU[J}"1| M1=120, % integer for amplitude
i Qa=4'9; M3=5000; % integer for length of coupler
2# _ i_j N = 512; % Number of Fourier modes (Time domain sampling points)
NOQSL T= dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
S{S.H?{F
T =40; % length of time:T*T0.
1Gp| _8 dt = T/N; % time step
xX~;
/e&, n = [-N/2:1:N/2-1]'; % Index
l0BYv&tu t = n.*dt;
rrrn8b6
ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
? oQ_qleuo w=2*pi*n./T;
t-Zk)*d/0 g1=-i*ww./2;
ia*Bcx_RW+ g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
K*aGz8N g3=-i*ww./2;
nC@UK{tVa P1=0;
' p!\[* e P2=0;
`{+aJ0<S P3=1;
fctVJ{? P=0;
p Igjo>K for m1=1:M1
PS/00F/Ak p=0.032*m1; %input amplitude
PbIi r= s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
+8 }p-<a s1=s10;
^~DClZ s20=0.*s10; %input in waveguide 2
*3h!&.zm s30=0.*s10; %input in waveguide 3
s}Q*zy s2=s20;
]-8yZWal s3=s30;
r !)jxIL\ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
@YI- @ %energy in waveguide 1
kWxcB7)uk p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
5@`DS-7h %energy in waveguide 2
a3B^RbDP&8 p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
8gXf4A(N %energy in waveguide 3
x0ICpt{; for m3 = 1:1:M3 % Start space evolution
W XX08" s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
(k<__W c_t s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
xf 4`+[ s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
o0FVVS l sca1 = fftshift(fft(s1)); % Take Fourier transform
4L/8Hj#g sca2 = fftshift(fft(s2));
Na>?1F"KHk sca3 = fftshift(fft(s3));
5tcJ T z sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
i1-wzI
sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
C^9bur/ sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
4qg]
oiT s3 = ifft(fftshift(sc3));
zf?U q s2 = ifft(fftshift(sc2)); % Return to physical space
^<v]x;
3 s1 = ifft(fftshift(sc1));
L<O" 36R end
ky{-NrK p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
#RVN 7-x p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
DS>qth p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
9p%8VDF= P1=[P1 p1/p10];
O_[]+5.TX P2=[P2 p2/p10];
=(]||1 . P3=[P3 p3/p10];
|emZZj P=[P p*p];
ZfSAXr "( end
c@)}zcw* figure(1)
@ >Ul0&Mf? plot(P,P1, P,P2, P,P3);
p WLFJH}N 8L,i}hIo. 转自：
http://blog.163.com/opto_wang/
