计算脉冲在非线性耦合器中演化的Matlab 程序 >e5q2U $cp16 % This Matlab script file solves the coupled nonlinear Schrodinger equations of
z&6]v N' % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
Cw9@2E'b % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
uyS^W'fF % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
%B*<BgJ;4F EU&6 Tg %fid=fopen('e21.dat','w');
~_/<PIm N = 128; % Number of Fourier modes (Time domain sampling points)
zz+M1n-;o M1 =3000; % Total number of space steps
cQUH %7m J =100; % Steps between output of space
E.WNykF- T =10; % length of time windows:T*T0
wz|Q%.%?[ T0=0.1; % input pulse width
?[NTw./'7A MN1=0; % initial value for the space output location
)U"D4j*p dt = T/N; % time step
!=k* hl0h n = [-N/2:1:N/2-1]'; % Index
&+|jJ{93z t = n.*dt;
ImT+8p a u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
\]~kyy u20=u10.*0.0; % input to waveguide 2
3. GdKP.% u1=u10; u2=u20;
` maN5) U1 = u1;
c)n0 D= U2 = u2; % Compute initial condition; save it in U
p:
Q%Lg_I ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
8as$h*W h w=2*pi*n./T;
5KA
FUR0 g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
P_^ |KEz L=4; % length of evoluation to compare with S. Trillo's paper
2:6Y83 dz=L/M1; % space step, make sure nonlinear<0.05
*1 J #Mdd for m1 = 1:1:M1 % Start space evolution
6@ (k8<3 u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
h~^qG2TYWq u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
Pv/%s) &y& ca1 = fftshift(fft(u1)); % Take Fourier transform
)U/ @J+{{ ca2 = fftshift(fft(u2));
b@Mng6R c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
C4X{Ps \ c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
GFy0R"&d[ u2 = ifft(fftshift(c2)); % Return to physical space
56j/w[&8 u1 = ifft(fftshift(c1));
fs)q7 7g if rem(m1,J) == 0 % Save output every J steps.
Fc{6* wtO U1 = [U1 u1]; % put solutions in U array
WMdz+^ \( U2=[U2 u2];
,sRrV $," MN1=[MN1 m1];
$
uIwRG
< z1=dz*MN1'; % output location
I,`D& end
C6;](rN)N end
(Db*.kd8, hg=abs(U1').*abs(U1'); % for data write to excel
tp,mw24 ha=[z1 hg]; % for data write to excel
STF}~`b:3 t1=[0 t'];
A= YEY n hh=[t1' ha']; % for data write to excel file
Vg C9' "| %dlmwrite('aa',hh,'\t'); % save data in the excel format
[> aoDJ figure(1)
Q e2 /4j4 waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
-+S~1`0 figure(2)
\qK}(xq[ waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
LBiv]3 Nf?,
_Rl 非线性超快脉冲耦合的数值方法的Matlab程序 *M\i4FO8 WriJco<v 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。
*{p& Fy55 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
`QyALcO
=QxE -)v >i#_)th"U! tV}ajs % This Matlab script file solves the nonlinear Schrodinger equations
V
n!az} % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
jP7+s.j> % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
"'p +qbT8 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
eMP Q|
W 7<C~D,x6 C=1;
Lq8Z!AIw> M1=120, % integer for amplitude
; hRpAN M3=5000; % integer for length of coupler
/>j+7ts N = 512; % Number of Fourier modes (Time domain sampling points)
\kJt@ [w% dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
,+5VeRyrV T =40; % length of time:T*T0.
x2IU PM dt = T/N; % time step
Ok{:QA ~# n = [-N/2:1:N/2-1]'; % Index
N\?Az668? t = n.*dt;
r
:Ma AT< ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
kjKpzdbD w=2*pi*n./T;
lO[jf6gB g1=-i*ww./2;
iJj?~\zp g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
+>9^])K| g3=-i*ww./2;
\oZUG P1=0;
=K< I)2
P2=0;
y2hFUq P3=1;
%JH_Nw.P P=0;
UFY~D"% / for m1=1:M1
X]^E:'E! p=0.032*m1; %input amplitude
GWE0 UO} s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
] GP z>k s1=s10;
zxmI/]3+/ s20=0.*s10; %input in waveguide 2
PC(iqL8r s30=0.*s10; %input in waveguide 3
`]I5WTt*X s2=s20;
`h{mj|~ s3=s30;
$Aoqtz d\ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
1^"aR# %energy in waveguide 1
ydFhw}1> p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
dcTM02kEh %energy in waveguide 2
v+_Y72h*a p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
GBOmVQ $Hb %energy in waveguide 3
.p*D[o2 9 for m3 = 1:1:M3 % Start space evolution
$=QO_t)? s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
&Or= _5Y` s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
, ( kXF: s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
7a_n\]t465 sca1 = fftshift(fft(s1)); % Take Fourier transform
fy-Z{ sca2 = fftshift(fft(s2));
v.&*z48 sca3 = fftshift(fft(s3));
zc~xWy+ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
8 q[WfD sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
F?AfB[PM sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
6f9<&dCK s3 = ifft(fftshift(sc3));
1?$ !y s2 = ifft(fftshift(sc2)); % Return to physical space
`Ta(P30
s1 = ifft(fftshift(sc1));
>{) #|pWU end
W%ZU& YBc p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
;Sl0kSu p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
]~ eWr2uG? p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
}Fe{s; P1=[P1 p1/p10];
GoA>sK P2=[P2 p2/p10];
w*kFtNBfU P3=[P3 p3/p10];
={vtfgxl P=[P p*p];
72.IhBNtT end
)KQv4\0y< figure(1)
>w# 3fTJ plot(P,P1, P,P2, P,P3);
dnc!=Z89 _ll aH 转自：
http://blog.163.com/opto_wang/
