计算脉冲在非线性耦合器中演化的Matlab 程序 vK'9{q|g pP
oxVvG{ % This Matlab script file solves the coupled nonlinear Schrodinger equations of
Zih5 /I % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
wLSjXpP 8 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
Ei~] iZ} % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
hs,5LV)|y FLEg0/m0 %fid=fopen('e21.dat','w');
5Q ;dnC N = 128; % Number of Fourier modes (Time domain sampling points)
hgif]?:C< M1 =3000; % Total number of space steps
lYdQB[l J =100; % Steps between output of space
z =%IcSx; T =10; % length of time windows:T*T0
CH#kvR2 T0=0.1; % input pulse width
yI *M[0 MN1=0; % initial value for the space output location
@|]iSD&T
# dt = T/N; % time step
(Z 'WR n = [-N/2:1:N/2-1]'; % Index
_we3jzMW t = n.*dt;
'iGM n_& u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
P69>gBZYD u20=u10.*0.0; % input to waveguide 2
D~7%};D[ u1=u10; u2=u20;
ew/KZE U1 = u1;
-
Ra \^uz U2 = u2; % Compute initial condition; save it in U
V 3%Krn1' ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
p0?o<AA%O w=2*pi*n./T;
6J]~A0vsi} g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
@V7;TJk L=4; % length of evoluation to compare with S. Trillo's paper
e ^-3etx dz=L/M1; % space step, make sure nonlinear<0.05
:Z ]/Q/$ for m1 = 1:1:M1 % Start space evolution
CARq^xI- u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
J1& A,Gb u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
Kl!DKeF ca1 = fftshift(fft(u1)); % Take Fourier transform
XZ!cW=bqS ca2 = fftshift(fft(u2));
|\rSa^:5 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
%oMWcgsdJi c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
+6wx58.B& u2 = ifft(fftshift(c2)); % Return to physical space
=nw,*q + u1 = ifft(fftshift(c1));
u;QH8 LK if rem(m1,J) == 0 % Save output every J steps.
<)=3XEcb U1 = [U1 u1]; % put solutions in U array
,d3Q+9/ U2=[U2 u2];
hw 7~i MN1=[MN1 m1];
' "'D.,[W2 z1=dz*MN1'; % output location
m]Hb+Y=;h end
,,zd.9n end
ttTI#Fr2 hg=abs(U1').*abs(U1'); % for data write to excel
<e$5~Spc ha=[z1 hg]; % for data write to excel
f&+XPd % t1=[0 t'];
\=$EmH F hh=[t1' ha']; % for data write to excel file
G%y>:$rw[O %dlmwrite('aa',hh,'\t'); % save data in the excel format
.Gjr`6R figure(1)
>2 FAi., waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
4o)(d= q figure(2)
BYkVg2D( waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
m*Q[lr= 0EcC 非线性超快脉冲耦合的数值方法的Matlab程序 (R9Q BZP5 Ty g$`\# 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。
[u,hc/PL 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
TXZ(mj? ^ =aml >_|Z{:z]d. |)
x' % This Matlab script file solves the nonlinear Schrodinger equations
~| 4U@ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
Aqx3!
% Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
%AzPAWcN % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
)< &B &Hp ,eZ;8W{G C=1;
{QIS411 M1=120, % integer for amplitude
^.ZSpc}< M3=5000; % integer for length of coupler
"#_)G7W+e N = 512; % Number of Fourier modes (Time domain sampling points)
94Kuy@0:+ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
ZX~>uf\n T =40; % length of time:T*T0.
OpWC2t) dt = T/N; % time step
g&oc =f` n = [-N/2:1:N/2-1]'; % Index
)x_W & *oZ t = n.*dt;
^KaqvG$ed ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
J dk3)
\ w=2*pi*n./T;
]C t`4pA g1=-i*ww./2;
mq|A8>g g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
Wto@u4 g3=-i*ww./2;
3D 4]yR5 P1=0;
b Q|#_/? P2=0;
:,xyVb+ P3=1;
CS^ oiV%{s P=0;
\] L::"![? for m1=1:M1
c<JM1 p=0.032*m1; %input amplitude
e]dPF[?7 s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
P;HVL flu s1=s10;
5WtQwN~ s20=0.*s10; %input in waveguide 2
{UV<=R,E s30=0.*s10; %input in waveguide 3
4U LJtM3 s2=s20;
@1J51< x s3=s30;
ZTgAZ5_cz p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
$ DABR %energy in waveguide 1
]noP p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
n6}E4E no %energy in waveguide 2
'0])7jq p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
q >D4ma^ %energy in waveguide 3
,N) )=/ for m3 = 1:1:M3 % Start space evolution
Kd ryl s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
&2P: A s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
Hm.&f2|( s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
"2vNkO## sca1 = fftshift(fft(s1)); % Take Fourier transform
)DklOEO sca2 = fftshift(fft(s2));
.NNcc4+ sca3 = fftshift(fft(s3));
hX'z]Am< sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
n !CP_ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
/q*Qx )y+1 sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
c|R3,<Q] s3 = ifft(fftshift(sc3));
U l7 pxzj s2 = ifft(fftshift(sc2)); % Return to physical space
r+V(1<`2X s1 = ifft(fftshift(sc1));
iaaH9X
% end
eK =m0 2 p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
Mi %1+ p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
ki*79d"$ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
f/IRO33 P1=[P1 p1/p10];
L8?Z!0D/h P2=[P2 p2/p10];
,,wyydG P3=[P3 p3/p10];
5w,YBUp P=[P p*p];
Rrs`h `'- end
'^.=gTk figure(1)
:(S/$^ U plot(P,P1, P,P2, P,P3);
$Kw"5cm XCqfAcNQ 转自：
http://blog.163.com/opto_wang/
