计算脉冲在非线性耦合器中演化的Matlab 程序 %-!ruc "} W8j)2nKD % This Matlab script file solves the coupled nonlinear Schrodinger equations of
euO!+ 9p % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
/ w0l7N % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
Qhb].V{utV % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
/Fej)WQp O7|0t\) %fid=fopen('e21.dat','w');
4Y5Q>2D} N = 128; % Number of Fourier modes (Time domain sampling points)
l$D]*_ jc, M1 =3000; % Total number of space steps
.8hB <G J =100; % Steps between output of space
3+_? /}< T =10; % length of time windows:T*T0
6Clxe Lk T0=0.1; % input pulse width
Mi&,64< MN1=0; % initial value for the space output location
%m]9"; dt = T/N; % time step
K 0RY2Hiw n = [-N/2:1:N/2-1]'; % Index
Cdl#LVqs t = n.*dt;
$lmbeW[0 u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
S0nBX"$u u20=u10.*0.0; % input to waveguide 2
[8AGW7_ u1=u10; u2=u20;
az@{O4 U1 = u1;
B
Jp\a7`; U2 = u2; % Compute initial condition; save it in U
<@xp. Y ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
u9 rlNmf$ w=2*pi*n./T;
= M^4T?{T g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
7 ET^, 6 L=4; % length of evoluation to compare with S. Trillo's paper
Qrjo@_+w! dz=L/M1; % space step, make sure nonlinear<0.05
@ROMHMd} for m1 = 1:1:M1 % Start space evolution
1lZl 10M:f u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
MkZm
=Sf u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
Cw]& B ca1 = fftshift(fft(u1)); % Take Fourier transform
.VN "j ca2 = fftshift(fft(u2));
ez_qG=J . c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
s@sRdoTdF c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
4]O{Nko) u2 = ifft(fftshift(c2)); % Return to physical space
62K 7afH u1 = ifft(fftshift(c1));
_2+}_ >d if rem(m1,J) == 0 % Save output every J steps.
V.5gxr3QqW U1 = [U1 u1]; % put solutions in U array
AFO g*{1 U2=[U2 u2];
I*_@WoI* MN1=[MN1 m1];
8B ;wn<O z1=dz*MN1'; % output location
T6MlKcw,t end
'&,$"QXwE end
%cMX]U hg=abs(U1').*abs(U1'); % for data write to excel
FOiwB^$ > ha=[z1 hg]; % for data write to excel
nsF OtOdd t1=[0 t'];
IMLk{y%6 hh=[t1' ha']; % for data write to excel file
{h/[!I ` %dlmwrite('aa',hh,'\t'); % save data in the excel format
{pMbkA Q@ figure(1)
XB,
2+ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
(&R /ns~
figure(2)
J '9hzag waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
~ *RG|4# j*@^O`^v 非线性超快脉冲耦合的数值方法的Matlab程序 $j*%}x~[ xayo{l=uGv 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。
XB* )d
9'8 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
Cm g(# $ X Zyxr#:Qm lPyGL-Q c }GmS@ % This Matlab script file solves the nonlinear Schrodinger equations
P3X;&i T % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
$Kgw6 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
eS(\E0% QI % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
p2 u*{k{ 7Y T% .ID C=1;
zhtNL_ M1=120, % integer for amplitude
/.r|ron:e M3=5000; % integer for length of coupler
m xk :P N = 512; % Number of Fourier modes (Time domain sampling points)
gSQq dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
_7r<RZ T =40; % length of time:T*T0.
Ik2y If5d dt = T/N; % time step
qYF OHu n = [-N/2:1:N/2-1]'; % Index
6lw) L t = n.*dt;
.lnyn|MVb ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
u;p.:{' w=2*pi*n./T;
^=:e9i3u g1=-i*ww./2;
;sd[Q01 g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
HwTb753 g3=-i*ww./2;
!h3 $C\ P1=0;
<$bM*5sHF> P2=0;
9jq}`$S{ P3=1;
&n kYJi(! P=0;
~<
%%n'xmm for m1=1:M1
Nn<TPT[, p=0.032*m1; %input amplitude
R6l`IlG` s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
iJ n< s1=s10;
xR;>n[6 s20=0.*s10; %input in waveguide 2
JDPn
s30=0.*s10; %input in waveguide 3
EH{m~x[Ei s2=s20;
BSt^QH-' s3=s30;
j"6r]nc& p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
ybLl[K(D= %energy in waveguide 1
KMC] < p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
V4I5PPz~ %energy in waveguide 2
"(bnr0 p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
pQv`fr= %energy in waveguide 3
k4:$LFw@ for m3 = 1:1:M3 % Start space evolution
Fy:CG6@X s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
RO cI.tL s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
IoO t n s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
n
N.6?a sca1 = fftshift(fft(s1)); % Take Fourier transform
x(oL\I_Z sca2 = fftshift(fft(s2));
,z<J`n sca3 = fftshift(fft(s3));
LsaE-l sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
n E.w sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
6S]K@C=r sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
SOE 5` s3 = ifft(fftshift(sc3));
) CgKZ" s2 = ifft(fftshift(sc2)); % Return to physical space
W^j;"qj s1 = ifft(fftshift(sc1));
j9Qd
45 end
m? 3! p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
S,ZlS<Z# p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
4lrF{S8 p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
L#U-d zy\ P1=[P1 p1/p10];
Gy}WZ9{ P2=[P2 p2/p10];
h-r\ 1{Q1] P3=[P3 p3/p10];
s<3 cvF< P=[P p*p];
Xwz9E!m end
aumWU{j= figure(1)
+x oh=m plot(P,P1, P,P2, P,P3);
K1y] !O|d,)$q 转自：
http://blog.163.com/opto_wang/
