计算脉冲在非线性耦合器中演化的Matlab 程序 I9y.e++/ @R2at % This Matlab script file solves the coupled nonlinear Schrodinger equations of
kCP$I732 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
W{" XJt_ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
bE\, }DTy % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
b"j|Bb 7"v$- W y %fid=fopen('e21.dat','w');
u5E]t9~Pq N = 128; % Number of Fourier modes (Time domain sampling points)
S"2qJ!.u M1 =3000; % Total number of space steps
dZ(|uC!? J =100; % Steps between output of space
;?L\Fz(< T =10; % length of time windows:T*T0
6XV<?
9q T0=0.1; % input pulse width
5\4g>5PD MN1=0; % initial value for the space output location
:`,3h% dt = T/N; % time step
SW? p?< n = [-N/2:1:N/2-1]'; % Index
2XSHZ|; t = n.*dt;
\ FzM4- u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
a}nbo4jK u20=u10.*0.0; % input to waveguide 2
X" R<J#4 u1=u10; u2=u20;
r.3KP iYK U1 = u1;
:
mGAt[Cc U2 = u2; % Compute initial condition; save it in U
_D!g4" ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
)ZR+lX } w=2*pi*n./T;
V6a` `i] g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
JhK/']R L=4; % length of evoluation to compare with S. Trillo's paper
6j9)/ H P dz=L/M1; % space step, make sure nonlinear<0.05
pK&I^r for m1 = 1:1:M1 % Start space evolution
[J#1Ff; u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
H=MCjh&$q u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
(k "_># % ca1 = fftshift(fft(u1)); % Take Fourier transform
j2n,f7hl. ca2 = fftshift(fft(u2));
">jwh. c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
qoU3"8 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
30cd|
S? u2 = ifft(fftshift(c2)); % Return to physical space
MBr:?PE7 u1 = ifft(fftshift(c1));
y9HK | if rem(m1,J) == 0 % Save output every J steps.
Es5p}uh.[Y U1 = [U1 u1]; % put solutions in U array
Ka_S n U2=[U2 u2];
j ) vlM+ MN1=[MN1 m1];
ZU&"73 z1=dz*MN1'; % output location
FH5ql~ end
y }2F9= end
j
-O2aL hg=abs(U1').*abs(U1'); % for data write to excel
gPC@Yy ha=[z1 hg]; % for data write to excel
~%y @Xsot> t1=[0 t'];
]dPZ .r hh=[t1' ha']; % for data write to excel file
Owv +1+B %dlmwrite('aa',hh,'\t'); % save data in the excel format
'_0]vupvY figure(1)
wo^Sy41bF waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
W 0[N0c figure(2)
JqU ADm waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
U HO_Z VV_l$E$ 非线性超快脉冲耦合的数值方法的Matlab程序 9l/E jF^ vP-M,4c 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。
Pt< s* ( 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
\>/M .2 i, n D5 @# 6)gd^{ Z0,~ V % This Matlab script file solves the nonlinear Schrodinger equations
LxN*)[ Wb % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
`cB_.& % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
xl4=++pu) % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
BNGe
exs@ 4jm K]. C=1;
}o dV_WT M1=120, % integer for amplitude
TW&DFKK` M3=5000; % integer for length of coupler
n]CbDbNw7) N = 512; % Number of Fourier modes (Time domain sampling points)
(zo^Nn9VJ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
%i{;r35M;9 T =40; % length of time:T*T0.
%,*$D} H dt = T/N; % time step
F_;tT%ywfx n = [-N/2:1:N/2-1]'; % Index
':
F}3At t = n.*dt;
B)SLG]72f ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
M@UVpQwgv w=2*pi*n./T;
nY? g1=-i*ww./2;
{OMg d3%14 g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
#TJk-1XM*q g3=-i*ww./2;
rjA@U<o P1=0;
N> Jw P2=0;
25{ uz P3=1;
}2>"<) P=0;
tV;% J4E' for m1=1:M1
cSP*f0n,eo p=0.032*m1; %input amplitude
L wJ0 s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
8|1^|B( l s1=s10;
h+UnZfm s20=0.*s10; %input in waveguide 2
R""%F#4XJ2 s30=0.*s10; %input in waveguide 3
=ZYThfAEw s2=s20;
,lN5,zI=S s3=s30;
A]`:VC=IU p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
DtCEm(b0 %energy in waveguide 1
{i{xo2<1" p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
{kB `>VS %energy in waveguide 2
2i=H"('G)+ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
3SG?W_
%energy in waveguide 3
^y.UbI for m3 = 1:1:M3 % Start space evolution
8}p8r|d!ls s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
haSM=;uPM s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
[`fI:ao| s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
Iq5pAHm>M6 sca1 = fftshift(fft(s1)); % Take Fourier transform
w:=V@-S 8 sca2 = fftshift(fft(s2));
F}?<v8#z0 sca3 = fftshift(fft(s3));
NC 23Z0y sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
+JdZPb sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
T3J'f jY sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
$K}.
+`vVO s3 = ifft(fftshift(sc3));
oY9FK{ s2 = ifft(fftshift(sc2)); % Return to physical space
5fjd{Y[k s1 = ifft(fftshift(sc1));
mNmUUj9z end
* dE^-dm# p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
ZXiRw)rM p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
3 x *z\VJ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
XJ\hd, R P1=[P1 p1/p10];
E0f{iO ;} P2=[P2 p2/p10];
93%{scrm P3=[P3 p3/p10];
r s8\)\ z P=[P p*p];
Csst[3V end
HD`>-E# figure(1)
l[h'6+o plot(P,P1, P,P2, P,P3);
)najO *n 7!V @/S}7 转自：
http://blog.163.com/opto_wang/
