计算脉冲在非线性耦合器中演化的Matlab 程序 Zlv`yC*r vJQ_mz % This Matlab script file solves the coupled nonlinear Schrodinger equations of
j,1cb,}=^ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
Vp8!-[R % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
z:08;}t % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
("=B,%F_ n ,@ ge %fid=fopen('e21.dat','w');
3)l<'~"z< N = 128; % Number of Fourier modes (Time domain sampling points)
n]K {-C; M1 =3000; % Total number of space steps
9 vNz
yh\ J =100; % Steps between output of space
y )7;"3Q< T =10; % length of time windows:T*T0
;v ~xL!uQ T0=0.1; % input pulse width
Ujvk*~: MN1=0; % initial value for the space output location
9"dZ4{\! dt = T/N; % time step
C-(O*hK n = [-N/2:1:N/2-1]'; % Index
3I oN. t = n.*dt;
h 3p~\%^ u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
!6J+# u20=u10.*0.0; % input to waveguide 2
* [b ~2 u1=u10; u2=u20;
h~#. s*0.F U1 = u1;
:|=Xh"l" U2 = u2; % Compute initial condition; save it in U
*{=q:E$ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
]w !=1( w=2*pi*n./T;
k[1w] l8 g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
}5u; '>$ L=4; % length of evoluation to compare with S. Trillo's paper
= Fwz m^}6 dz=L/M1; % space step, make sure nonlinear<0.05
"gXvnl for m1 = 1:1:M1 % Start space evolution
%:Zp7O2UB' u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
tSiQr I u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
ASr3P5/ ca1 = fftshift(fft(u1)); % Take Fourier transform
92^Dn`g ca2 = fftshift(fft(u2));
* C(q{|f c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
XE;aJ'kt c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
l,
-q:8 u2 = ifft(fftshift(c2)); % Return to physical space
.j`8E^7< u1 = ifft(fftshift(c1));
oN(F$Nvk if rem(m1,J) == 0 % Save output every J steps.
f /i[?
gw U1 = [U1 u1]; % put solutions in U array
JL?|NV- U2=[U2 u2];
p49 T3V MN1=[MN1 m1];
*35o$P46 z1=dz*MN1'; % output location
Bh6lK}9 end
q/3co86c end
N| |s# hg=abs(U1').*abs(U1'); % for data write to excel
}ct*<zj[~u ha=[z1 hg]; % for data write to excel
^NO;A=9b[ t1=[0 t'];
:LD+B1$y hh=[t1' ha']; % for data write to excel file
P~@I`r567 %dlmwrite('aa',hh,'\t'); % save data in the excel format
R)9FXz$). figure(1)
4$4n9`odE waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
Q0TKM > figure(2)
62>/0_m 5 waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
/ gE9 W `R o>?H 非线性超快脉冲耦合的数值方法的Matlab程序 {A LOs^ _- |bjLmGb 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。
w%f51Ex 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
oX[I4i%G V(n3W=#kky E>qe hs,g `wNJ*` % This Matlab script file solves the nonlinear Schrodinger equations
OC2%9Igx0 % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
su Z` % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
[, mcvO; % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
$I90KQB\_ t Ow[ C=1;
"QV1G' M1=120, % integer for amplitude
Bq b3[^;~ M3=5000; % integer for length of coupler
U,nQnD"!t& N = 512; % Number of Fourier modes (Time domain sampling points)
`O}bPwa{> dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
) "y]_} T =40; % length of time:T*T0.
B4;P)\ 2 dt = T/N; % time step
2pAshw1G n = [-N/2:1:N/2-1]'; % Index
L&~>(/*7U t = n.*dt;
]\:l>< ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
)jN f Q!?/ w=2*pi*n./T;
x:IY6 l g1=-i*ww./2;
ZQrgYeQ l" g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
?a-}1A{
g3=-i*ww./2;
+4Lj}8, P1=0;
zy[|4Q(? P2=0;
s&qr2'F+z P3=1;
,5Tw5<S P=0;
}ilX
2s?> for m1=1:M1
r#K" d p=0.032*m1; %input amplitude
.s<tQU s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
, MU9p* s1=s10;
SQx:`{O s20=0.*s10; %input in waveguide 2
BGVy
\F< s30=0.*s10; %input in waveguide 3
9 i#K{CkC| s2=s20;
]lzOz<0q s3=s30;
.A Z+|?d p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
XY`2>7 %energy in waveguide 1
(Zu V5|N p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
WjMP]ND#c %energy in waveguide 2
=6+j
Po{F p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
w 'Q2Czso %energy in waveguide 3
; V3d"@R, for m3 = 1:1:M3 % Start space evolution
+ )K yG s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
We*c_;@< s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
?GK m_b]JC s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
p h=[|P ) sca1 = fftshift(fft(s1)); % Take Fourier transform
yj{:%Km :` sca2 = fftshift(fft(s2));
5Ai$1'*p sca3 = fftshift(fft(s3));
<0I=XsE1iX sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
j\8'P9~% sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
tc<t%]c sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
_ a,XL<9 I s3 = ifft(fftshift(sc3));
YJ^TO\4WM s2 = ifft(fftshift(sc2)); % Return to physical space
dbLxm!;( s1 = ifft(fftshift(sc1));
S~DY1e54GF end
~j2=hk S
p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
n; Etn!4M p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
)hai?v~g p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
-d6*M*{| P1=[P1 p1/p10];
bwA L: P2=[P2 p2/p10];
Bh,LJawE P3=[P3 p3/p10];
0,`$ KbV\ P=[P p*p];
I3V>VLv end
i <Be)Y-' figure(1)
/1q] D8 plot(P,P1, P,P2, P,P3);
}ZWeb#\ <=,KP) 转自：
http://blog.163.com/opto_wang/
