计算脉冲在非线性耦合器中演化的Matlab 程序 {Yq"%n'0 )@lZ~01~d % This Matlab script file solves the coupled nonlinear Schrodinger equations of
2XoFmV),F % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
+c4-7/kE % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
bm/pLC6%. % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
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mI1wV[ %C8p!)Hu %fid=fopen('e21.dat','w');
*B<Ig^c N = 128; % Number of Fourier modes (Time domain sampling points)
H }v.0 R M1 =3000; % Total number of space steps
hF m_`J&" J =100; % Steps between output of space
z}Y23W&sX T =10; % length of time windows:T*T0
hd+(M[C<9 T0=0.1; % input pulse width
bogw /)1 MN1=0; % initial value for the space output location
KmF" Ccc dt = T/N; % time step
>i&"{GZ n = [-N/2:1:N/2-1]'; % Index
Std?p{
i t = n.*dt;
cD^`dn %$ u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
=[A5qwyv u20=u10.*0.0; % input to waveguide 2
RP!!6A6: u1=u10; u2=u20;
4Js2/s U1 = u1;
8&[Lr o9 U2 = u2; % Compute initial condition; save it in U
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ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
9, A(|g w=2*pi*n./T;
7Iz%Jty g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
1P8XVI' L=4; % length of evoluation to compare with S. Trillo's paper
18`Y Y\u( dz=L/M1; % space step, make sure nonlinear<0.05
n8h1S lK08 for m1 = 1:1:M1 % Start space evolution
+#* F"k( u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
V]E# N u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
h=?V)WSM ca1 = fftshift(fft(u1)); % Take Fourier transform
Rgstk/1 ca2 = fftshift(fft(u2));
Z<_"Tk;!', c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
]|H`?L c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
8|]r>L$Wk u2 = ifft(fftshift(c2)); % Return to physical space
c> SFt tbU u1 = ifft(fftshift(c1));
4lM)ZDg if rem(m1,J) == 0 % Save output every J steps.
X667*L^ U1 = [U1 u1]; % put solutions in U array
E&; [E U2=[U2 u2];
[A DSGnw MN1=[MN1 m1];
Np2I*l6W z1=dz*MN1'; % output location
a:q>7V|%$ end
cj[a^ ZH end
g3 V
bP hg=abs(U1').*abs(U1'); % for data write to excel
S['rfD>9 ha=[z1 hg]; % for data write to excel
%-nYK3 t1=[0 t'];
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n,H hh=[t1' ha']; % for data write to excel file
i`nmA-Zj[ %dlmwrite('aa',hh,'\t'); % save data in the excel format
E =*82Y=B figure(1)
-RLY.@'d-M waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
V
yOuw9 figure(2)
w}20l F waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
`j#zwgUs pA%}C mrMq 非线性超快脉冲耦合的数值方法的Matlab程序 l+ ,p= v[7iWBqJ 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。
XBr-UjQ 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
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'A\ (^{tu89ab B|f
=hlY % This Matlab script file solves the nonlinear Schrodinger equations
3-=f@uH! % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
Za110oF % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
C {*' p+f % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
$q$G =8o $ C=1;
^@V; `jsll M1=120, % integer for amplitude
"^froQ{"T M3=5000; % integer for length of coupler
MQ#nP_i N = 512; % Number of Fourier modes (Time domain sampling points)
7^oO
N+=d dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
74w Df T =40; % length of time:T*T0.
ShIJ6L Z dt = T/N; % time step
n%S%a >IQj n = [-N/2:1:N/2-1]'; % Index
,<CFjtelO t = n.*dt;
_Xqa_6+/ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
G (3wI} w=2*pi*n./T;
"y9]>9:$- g1=-i*ww./2;
Vsj1!}X: g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
i8h^~d2" g3=-i*ww./2;
'=WPi_Z5:C P1=0;
Bs3M7z RG P2=0;
@zC p/fo3 P3=1;
$e q *@5B P=0;
/ucS*m:<x for m1=1:M1
Oxp !G7qfo p=0.032*m1; %input amplitude
cr`NHl/XF s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
@ * <`*W s1=s10;
]3\%i2NM s20=0.*s10; %input in waveguide 2
si, )!%b s30=0.*s10; %input in waveguide 3
}> ]`#s s2=s20;
FX
%(<M s3=s30;
;Tec)Fl p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
U^;|as %energy in waveguide 1
B'v ~0Kau p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
~( ;HkT %energy in waveguide 2
uqsVq0H p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
Y2TXWl,Jk %energy in waveguide 3
8+,I(+
for m3 = 1:1:M3 % Start space evolution
Qx_]oz]NY s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
XOoz.GSQ s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
so>jz@!EE s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
xFzaVjjP sca1 = fftshift(fft(s1)); % Take Fourier transform
20
Z/Y\ sca2 = fftshift(fft(s2));
u*m|o8 sca3 = fftshift(fft(s3));
0aqq*e'c sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
0O!A8 FA0 sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
E*vh< C sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
]^0m h[" s3 = ifft(fftshift(sc3));
iOB*K)U1 s2 = ifft(fftshift(sc2)); % Return to physical space
^
A J_
s1 = ifft(fftshift(sc1));
WjsmLb:5 end
*AG01# ZF p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
xq pq|U p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
%%T?LRv p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
{rzvZ0-j} P1=[P1 p1/p10];
Sw.K l
0M P2=[P2 p2/p10];
GO UO P3=[P3 p3/p10];
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1z- P=[P p*p];
~hb; kc3 end
. ^wBv
'Y figure(1)
r@ c!M |m@ plot(P,P1, P,P2, P,P3);
c {3P|O&. cz1 m05E 转自：
http://blog.163.com/opto_wang/
