计算脉冲在非线性耦合器中演化的Matlab 程序 ZcX%:ebKS UuT>qWxQ8 % This Matlab script file solves the coupled nonlinear Schrodinger equations of
4cJ^L < % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
8NeP7.U<w % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
ci5ERv` % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
D u$kDCU H` Q_gy5Z( %fid=fopen('e21.dat','w');
xm~ff+(&@S N = 128; % Number of Fourier modes (Time domain sampling points)
60~{sk~E M1 =3000; % Total number of space steps
(W3R3>; J =100; % Steps between output of space
yhQo1e> T =10; % length of time windows:T*T0
wias ]u| T0=0.1; % input pulse width
Ym& _IOx MN1=0; % initial value for the space output location
4,FkA_k dt = T/N; % time step
zo@>~G3$9 n = [-N/2:1:N/2-1]'; % Index
w[PW-m^` t = n.*dt;
/ c/!13| u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
L7n->8Qk u20=u10.*0.0; % input to waveguide 2
B_`A[0H u1=u10; u2=u20;
@[zPN[z . U1 = u1;
BAm H2" U2 = u2; % Compute initial condition; save it in U
QEUg=*3W= ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
:Iwe> ;} w=2*pi*n./T;
y+Q!4A g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
HtY\!_ Ea L=4; % length of evoluation to compare with S. Trillo's paper
"5XD+qi dz=L/M1; % space step, make sure nonlinear<0.05
!Si ZA " for m1 = 1:1:M1 % Start space evolution
TKoO\\ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
tDEpR u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
sF_.9G)S0 ca1 = fftshift(fft(u1)); % Take Fourier transform
,PRM( n - ca2 = fftshift(fft(u2));
^fnRzX c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
?ZlwRjB\ c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
X~GZI*P u2 = ifft(fftshift(c2)); % Return to physical space
yKZ ~ ^ u1 = ifft(fftshift(c1));
O|7q,bEm^ if rem(m1,J) == 0 % Save output every J steps.
]N1$ioC# U1 = [U1 u1]; % put solutions in U array
DKIDL f U2=[U2 u2];
0%F C;v0 MN1=[MN1 m1];
S)g5T u) z1=dz*MN1'; % output location
axU!o /m> end
^N Et{]x end
w^R5/#F_r hg=abs(U1').*abs(U1'); % for data write to excel
(jY.S|% ha=[z1 hg]; % for data write to excel
J _rCo4} t1=[0 t'];
22tY%Y9 hh=[t1' ha']; % for data write to excel file
;1{S"UY %dlmwrite('aa',hh,'\t'); % save data in the excel format
IA8kq =W figure(1)
z_JZx]*/ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
4pA<s- figure(2)
Y ;&Cmi waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
,Hys9I 'kW`62AX 非线性超快脉冲耦合的数值方法的Matlab程序 +qsdA#2 8l!S<RA 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。
#" i}wS 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
-iH/~a 6_zL#7E' 1g rrb&K rX;(48Y % This Matlab script file solves the nonlinear Schrodinger equations
dqF--)Nb % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
)}WG` % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
vNE91 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
& rw|fF|] u{6*}6@fi C=1;
9SAyU%mS: M1=120, % integer for amplitude
[&FMVM` M3=5000; % integer for length of coupler
x( mY$l,il N = 512; % Number of Fourier modes (Time domain sampling points)
XHpoaHyx dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
ZV;#ZXch T =40; % length of time:T*T0.
m"U\;Mw? dt = T/N; % time step
l[\[)X3$ n = [-N/2:1:N/2-1]'; % Index
uu#ALB
Jm t = n.*dt;
i"w$D{N ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
,dh*GJ{5 w=2*pi*n./T;
{'d?vm!r g1=-i*ww./2;
P\N`E?lJL g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
2d$hgR#v g3=-i*ww./2;
I[[rVts P1=0;
lfj>]om$ P2=0;
-QZped;?* P3=1;
gvy%`SSW P=0;
[xI@)5Xk for m1=1:M1
(#Y2H p=0.032*m1; %input amplitude
ZB ~D_S s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
cHJ
&a`; s1=s10;
e j!C^ s20=0.*s10; %input in waveguide 2
<'GI<Hc s30=0.*s10; %input in waveguide 3
/1MO ]u\ s2=s20;
w,`x(!& s3=s30;
1L &_3} p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
)*s.AFu]7x %energy in waveguide 1
w
#1l)+ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
lZ_i~;u4@v %energy in waveguide 2
?"sk" { p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
2!" N9Adt %energy in waveguide 3
Keof{>V=CA for m3 = 1:1:M3 % Start space evolution
UTs0=:+,t s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
3s>& h-E s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
umls =i z s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
bR ;H@Fdg? sca1 = fftshift(fft(s1)); % Take Fourier transform
%? RX}37K sca2 = fftshift(fft(s2));
l|N 1u=Z sca3 = fftshift(fft(s3));
\" .3x
PkE sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
iY*Xm, # sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
-{L[Wt{1 sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
$f C = v s3 = ifft(fftshift(sc3));
*AxKV5[H s2 = ifft(fftshift(sc2)); % Return to physical space
4H1s"mP< s1 = ifft(fftshift(sc1));
WVwNjQ2PM end
40q8,M p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
c]xpp;% ] p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
|5![k<o# p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
Xb;CY9 & P1=[P1 p1/p10];
"t\r jFw P2=[P2 p2/p10];
gQ/zk3?k P3=[P3 p3/p10];
jRq>Sz{8 P=[P p*p];
C{Npipd}v end
eKLxNw5 figure(1)
\ =83#*KK plot(P,P1, P,P2, P,P3);
;J?!D x 0BVMLRB 转自：
http://blog.163.com/opto_wang/
