计算脉冲在非线性耦合器中演化的Matlab 程序 kbp(
a+5 x+y! P % This Matlab script file solves the coupled nonlinear Schrodinger equations of
y(3c{y@~X % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
. 4C[D{4 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
Lr ? 4Y % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
`KJYm|@ i -wRyMY_ D %fid=fopen('e21.dat','w');
L+~YCat|$U N = 128; % Number of Fourier modes (Time domain sampling points)
7?! Z+r M1 =3000; % Total number of space steps
keQXJ0 J =100; % Steps between output of space
"^
6lvZP( T =10; % length of time windows:T*T0
D R yES i T0=0.1; % input pulse width
XL7;^AE^Wl MN1=0; % initial value for the space output location
Ns!3- Y dt = T/N; % time step
L740s[,`o# n = [-N/2:1:N/2-1]'; % Index
W93JY0Ls9| t = n.*dt;
{~p7*j^0 u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
lO2T/1iMTW u20=u10.*0.0; % input to waveguide 2
JXLWRe u1=u10; u2=u20;
`zzKD2y U1 = u1;
42J';\)oP U2 = u2; % Compute initial condition; save it in U
U.hERe ~ X ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
Vy%
:\p+ w=2*pi*n./T;
}6CXJ+-UR g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
"0H56#eW L=4; % length of evoluation to compare with S. Trillo's paper
b%[ nB dz=L/M1; % space step, make sure nonlinear<0.05
fZ6 fV=HEF for m1 = 1:1:M1 % Start space evolution
u
JQaHL! u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
/K,|k
EE'n u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
5rf H;` ca1 = fftshift(fft(u1)); % Take Fourier transform
ne"?90~ ca2 = fftshift(fft(u2));
zD)IU_GWa c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
ckf<N9 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
eg2U+g4 u2 = ifft(fftshift(c2)); % Return to physical space
2 ]V>J u1 = ifft(fftshift(c1));
i[2bmd !H if rem(m1,J) == 0 % Save output every J steps.
k'@7ZH U1 = [U1 u1]; % put solutions in U array
0;FqX* U2=[U2 u2];
pM&]&Nk MN1=[MN1 m1];
#
cN_ y z1=dz*MN1'; % output location
H}sS4[z end
\o:E La HY end
/UpD$,T|^| hg=abs(U1').*abs(U1'); % for data write to excel
1tc]rC4h ha=[z1 hg]; % for data write to excel
=& q-[JW t1=[0 t'];
e8AjO$49 hh=[t1' ha']; % for data write to excel file
Xq ,UV %dlmwrite('aa',hh,'\t'); % save data in the excel format
>~5 lYD figure(1)
kqKj 7L waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
`dv}a-Q)c figure(2)
't|Un G waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
cBLR#Yu;O5 ceFsGdS 非线性超快脉冲耦合的数值方法的Matlab程序 [lNqT1%] K\IYx|Hm a 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。
&Y54QE". 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
_{LN{iqDv Uvjdx(fY[a %RQ C9! K\{b!Cfr^ % This Matlab script file solves the nonlinear Schrodinger equations
\7Gg2;TA6o % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
] #Vo}CVP % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
bJQ5- *F % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
$J QWfGwR 7P<r`,~k- C=1;
V~(EVF{h M1=120, % integer for amplitude
4 M @ oj M3=5000; % integer for length of coupler
$!YKZ0)B'0 N = 512; % Number of Fourier modes (Time domain sampling points)
7Fmb V/&c dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
0jxO |N 2) T =40; % length of time:T*T0.
I1Hw"G"& dt = T/N; % time step
omM&{ }8 g n = [-N/2:1:N/2-1]'; % Index
W@I
02n2 H t = n.*dt;
yZYK wKG ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
P? 9nTG w=2*pi*n./T;
$; Q$W9+ g1=-i*ww./2;
]2Sfkl0 g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
|@ikx{ W g3=-i*ww./2;
tg.|$n P1=0;
GWF/[ % P2=0;
9z5\*b s P3=1;
k? 3S P=0;
TZ?Os4+ for m1=1:M1
}JRP,YNh p=0.032*m1; %input amplitude
01 U
*_\ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
A2m_q>>
! s1=s10;
j*u XB^ 4 s20=0.*s10; %input in waveguide 2
9 YP*f s30=0.*s10; %input in waveguide 3
`J72+ RA s2=s20;
?h/ x Al s3=s30;
8 YNu< p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
=%!e(N'p %energy in waveguide 1
MaZM%W8Z p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
<,\ `Psa)N %energy in waveguide 2
uxWFM
$ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
q5Fs )B %energy in waveguide 3
bf& }8I$ for m3 = 1:1:M3 % Start space evolution
9 |'
|BC s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
#EJhAJ s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
Aj [?aL s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
!X^Hi=aV sca1 = fftshift(fft(s1)); % Take Fourier transform
{vs 4vS6 sca2 = fftshift(fft(s2));
c\At0.QCA sca3 = fftshift(fft(s3));
w{pUUo:< sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
@.'z* |z sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
XMGx ^mn sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
<"W?<VjO s3 = ifft(fftshift(sc3));
l
:/&E 6 9 s2 = ifft(fftshift(sc2)); % Return to physical space
pD"YNlB^ s1 = ifft(fftshift(sc1));
X*i/A<Y`= end
W+_ R hJ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
WzjL-a( p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
>*I N p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
~
|6dH P1=[P1 p1/p10];
WvujcmOf P2=[P2 p2/p10];
}^9]jSq5 P3=[P3 p3/p10];
#? d Uv# P=[P p*p];
eqq`TT#Z end
!=3Rg-'d1 figure(1)
L'l F/qe^ plot(P,P1, P,P2, P,P3);
*I0Tbc
O PocYFhWQ` 转自：
http://blog.163.com/opto_wang/
