计算脉冲在非线性耦合器中演化的Matlab 程序 *Z; r
B IytDvz*| % This Matlab script file solves the coupled nonlinear Schrodinger equations of
Yt pRy%
R % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
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% Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
#~S>K3( % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
=HS4I.@c_5 \ADLMj`F| %fid=fopen('e21.dat','w');
T{tn.sT N = 128; % Number of Fourier modes (Time domain sampling points)
Q(e{~
]* M1 =3000; % Total number of space steps
tvGlp)?. J =100; % Steps between output of space
x}|+sS,g T =10; % length of time windows:T*T0
YQYX, b T0=0.1; % input pulse width
JCD?qeTg MN1=0; % initial value for the space output location
IT18v[-G dt = T/N; % time step
l#$TYJi n = [-N/2:1:N/2-1]'; % Index
>azEed<B t = n.*dt;
t!:)L+$3 u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
lH6 fvz u20=u10.*0.0; % input to waveguide 2
lm*g Gy1i u1=u10; u2=u20;
5B?i(2&# U1 = u1;
?!y"OrHg U2 = u2; % Compute initial condition; save it in U
) b0];&hw] ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
BPewc9RxV w=2*pi*n./T;
`7\H41%\pp g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
Z9VR ]cf? L=4; % length of evoluation to compare with S. Trillo's paper
?A&%Cwj dz=L/M1; % space step, make sure nonlinear<0.05
n]iyFZ`9 for m1 = 1:1:M1 % Start space evolution
7]Rk+q2: u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
N 2Ssf$ u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
'fn$ 'CeM( ca1 = fftshift(fft(u1)); % Take Fourier transform
z SXA=
ca2 = fftshift(fft(u2));
)NIv "Q c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
ke]Yfwk c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
Cfv]VQQE u2 = ifft(fftshift(c2)); % Return to physical space
|vz9Hs$@l u1 = ifft(fftshift(c1));
0X>T+A[E if rem(m1,J) == 0 % Save output every J steps.
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}nLS3t U1 = [U1 u1]; % put solutions in U array
hl]S'yr U2=[U2 u2];
ve fU' MN1=[MN1 m1];
Nbk K&bz z1=dz*MN1'; % output location
PJK9704 6 end
:j,}{)5 = end
RB;BQoGX hg=abs(U1').*abs(U1'); % for data write to excel
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c:Zx! ha=[z1 hg]; % for data write to excel
+?AW>&68y t1=[0 t'];
qrE0H hh=[t1' ha']; % for data write to excel file
x<>YUw8` %dlmwrite('aa',hh,'\t'); % save data in the excel format
N}mh} figure(1)
WFDCPQ@ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
p[qg&VKB figure(2)
Ao"C<.gUYP waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
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?@ y/tSGkMv 非线性超快脉冲耦合的数值方法的Matlab程序 12O lrU oKa>.e7. 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
;==j|/ERe Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
vQHpf>o mNDuwDd$S %*K;np-q{ iRve) % This Matlab script file solves the nonlinear Schrodinger equations
?1w"IjUS % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
f^e&hyC
% Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
+|&0fGv;d9 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
GTAf g~)3WfC$[ C=1;
DFy1 bg M1=120, % integer for amplitude
-N# #w= M3=5000; % integer for length of coupler
^P$7A ]! N = 512; % Number of Fourier modes (Time domain sampling points)
moG~S] dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
X"<|Z]w T =40; % length of time:T*T0.
WcEt%mGQ, dt = T/N; % time step
~kb{K; n = [-N/2:1:N/2-1]'; % Index
{7X~!e|w t = n.*dt;
A[JM4 x
ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
kEP<[K w=2*pi*n./T;
h<N RE0- g1=-i*ww./2;
,YB1 y)x g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
zy>}L # g3=-i*ww./2;
"%
Y u
wMY P1=0;
u)~s4tP4 P2=0;
vYnftJK& P3=1;
A*i_|]Q P=0;
]sL45k2W for m1=1:M1
uJ8{HB p=0.032*m1; %input amplitude
h (N=V|0 s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
+tU Q s1=s10;
S #2[%o s20=0.*s10; %input in waveguide 2
'5 rU e\k s30=0.*s10; %input in waveguide 3
Gru ALx7 s2=s20;
X| <yq s3=s30;
; k}H(QI p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
mx}E$b$<CY %energy in waveguide 1
L|\Diap p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
E {>`MNj %energy in waveguide 2
KlO(o#&N p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
Ekjf^Uo %energy in waveguide 3
= DMbz`t for m3 = 1:1:M3 % Start space evolution
&t_h'JX& s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
7>,rvW:] s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
TB#N k5 s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
PA oX$q sca1 = fftshift(fft(s1)); % Take Fourier transform
Ef,Cd[]b sca2 = fftshift(fft(s2));
k?j Fh6% sca3 = fftshift(fft(s3));
j04/[V) sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
%g w{[
/[A sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
TSQh X~RN sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
VQ< 5%+ s3 = ifft(fftshift(sc3));
}\Z5{OA s2 = ifft(fftshift(sc2)); % Return to physical space
f:vD`Fz1 s1 = ifft(fftshift(sc1));
aQ|hi F} end
ps+:</;Z p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
[`nY2[A$ p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
F$yeF^\g p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
9p*-?kPb P1=[P1 p1/p10];
9L HuS P2=[P2 p2/p10];
:e2X/ tl# P3=[P3 p3/p10];
5-w: c> P=[P p*p];
l% <c6 ; end
=P]GPEz_ figure(1)
@vAFfYU9<. plot(P,P1, P,P2, P,P3);
7\%$>< K `bqzg 转自：
http://blog.163.com/opto_wang/
