计算脉冲在非线性耦合器中演化的Matlab 程序 h D/b O Do|`wpR % This Matlab script file solves the coupled nonlinear Schrodinger equations of
YtrM J" % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
:q4 Mnr % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
^ ffh % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
LHWh-h(s !lF|90= %fid=fopen('e21.dat','w');
Om0S^4y]x N = 128; % Number of Fourier modes (Time domain sampling points)
y*6r&989 M1 =3000; % Total number of space steps
dR_h PBn/@ J =100; % Steps between output of space
QE5
85s5
T =10; % length of time windows:T*T0
g5t o0 T0=0.1; % input pulse width
$sO}l MN1=0; % initial value for the space output location
2Xgw7`
!L dt = T/N; % time step
* #;rp~ n = [-N/2:1:N/2-1]'; % Index
^dP@QMly6 t = n.*dt;
z@ A5t4+3 u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
)[)-.{q u20=u10.*0.0; % input to waveguide 2
+Z[%+x92 u1=u10; u2=u20;
/kVy#sT| U1 = u1;
9ffRY,1@ U2 = u2; % Compute initial condition; save it in U
<S0!$.Kg*< ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
-zz9k= q w=2*pi*n./T;
zT~ GBC-IX g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
i\rI j0+ L=4; % length of evoluation to compare with S. Trillo's paper
M42D5|tZc dz=L/M1; % space step, make sure nonlinear<0.05
*(d^ k; for m1 = 1:1:M1 % Start space evolution
tO?*x/XC{ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
m= fmf( u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
S-yd-MtQp ca1 = fftshift(fft(u1)); % Take Fourier transform
ld[] f*RuW ca2 = fftshift(fft(u2));
$Y aL3n c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
=W ! m` c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
A Sy7 ")5 u2 = ifft(fftshift(c2)); % Return to physical space
fC%;|V'Nd u1 = ifft(fftshift(c1));
rf1nC$Sop if rem(m1,J) == 0 % Save output every J steps.
4 '9h^C& U1 = [U1 u1]; % put solutions in U array
h2aJa@;S U2=[U2 u2];
Zml9 ndzT MN1=[MN1 m1];
x)vYc36H z1=dz*MN1'; % output location
JEBo!9 end
G68N@g end
rmQGzQnun hg=abs(U1').*abs(U1'); % for data write to excel
hY'"^?OP ha=[z1 hg]; % for data write to excel
5'V'~Q% t1=[0 t'];
>o>'@)I?e6 hh=[t1' ha']; % for data write to excel file
~w[zX4@ %dlmwrite('aa',hh,'\t'); % save data in the excel format
:@b>,{*4zS figure(1)
9f,HjRP waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
F<-Pbtw figure(2)
' Dk(jpYB waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
-R7f/a8 ~? b(2gn 非线性超快脉冲耦合的数值方法的Matlab程序 D|-]"(2i u{p\8v%7 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。
/e{Oqhf[n 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
R!pV`N <O\z`aA'q tg8VFH2q.z XcfTE
m % This Matlab script file solves the nonlinear Schrodinger equations
"hlIGJ?_= % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
={L:q8v) % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
6lWO8j^BN % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
X?7$JV-: ir,Zc\C C=1;
,$;CII
v M1=120, % integer for amplitude
cF vGpZ M3=5000; % integer for length of coupler
Vj?.' ( N = 512; % Number of Fourier modes (Time domain sampling points)
DD3J2J dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
{8B \-LUR T =40; % length of time:T*T0.
Z p__ dt = T/N; % time step
^jmnE.8R n = [-N/2:1:N/2-1]'; % Index
b0t];Gc%b t = n.*dt;
<
m9O0 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
IG9Q~7@ w=2*pi*n./T;
09 %eaoW g1=-i*ww./2;
uqO51V ~ g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
ZA9']u%EJ g3=-i*ww./2;
x(=kh%\; P1=0;
Bgs~1E @8V P2=0;
!w)Mm P Xb P3=1;
>$Fc=~;Ba P=0;
T:!sfhrZ~< for m1=1:M1
r
2 p=0.032*m1; %input amplitude
s)M2Z3>+ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
nO|S+S_9 s1=s10;
g3Xz- s20=0.*s10; %input in waveguide 2
A| > C 3S s30=0.*s10; %input in waveguide 3
*UyV@ s2=s20;
ToMX7x z6 s3=s30;
%*19S.=l p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
ASYUKh,h %energy in waveguide 1
Zi[)(agAT p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
H|TzD "2N %energy in waveguide 2
3 x=F p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
] nQ$:%HP %energy in waveguide 3
x1}q!)e for m3 = 1:1:M3 % Start space evolution
cL Yc" "= s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
Zgg 7pL)#c s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
" pWdz}! s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
V.-?aXQ * sca1 = fftshift(fft(s1)); % Take Fourier transform
no/]Me!j= sca2 = fftshift(fft(s2));
<#s-hQ sca3 = fftshift(fft(s3));
i
L m1l sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
"FXS;Jf sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
0}^-, Q, sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
Fhsmpe~ s3 = ifft(fftshift(sc3));
b?bYPN+ s2 = ifft(fftshift(sc2)); % Return to physical space
gP`!Ml Y@ s1 = ifft(fftshift(sc1));
Ffxk] o&%c end
,m"ztu- p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
f C^l9CRY p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
FSQ&J|O p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
v|/3Mi9mz P1=[P1 p1/p10];
o6y,M!p@ P2=[P2 p2/p10];
&=?`; K P3=[P3 p3/p10];
7 IHD?pnZ P=[P p*p];
_ kx end
w7Pe< vT figure(1)
Q r<%rU^{. plot(P,P1, P,P2, P,P3);
/-hF<oNQ vV[dJ% 转自：
http://blog.163.com/opto_wang/
