计算脉冲在非线性耦合器中演化的Matlab 程序 f 3\w99\o 8*"rZh}' % This Matlab script file solves the coupled nonlinear Schrodinger equations of
q
w"e0q% ) % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
6l=M;B7:i % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
OHQ3+WJ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
)8\Z=uC X ^9t %fid=fopen('e21.dat','w');
jeyaT^F(
N = 128; % Number of Fourier modes (Time domain sampling points)
Z|f^nH #-C M1 =3000; % Total number of space steps
!/[AQ{**T! J =100; % Steps between output of space
g9! d pP T =10; % length of time windows:T*T0
pvI&-D #} T0=0.1; % input pulse width
w 2 s, MN1=0; % initial value for the space output location
"F04c|oR<X dt = T/N; % time step
9n-RXVL+ n = [-N/2:1:N/2-1]'; % Index
fdvi}SS8 t = n.*dt;
]q@rGD85K u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
`z5v}T u20=u10.*0.0; % input to waveguide 2
X/K| WOO6 u1=u10; u2=u20;
9? v) U1 = u1;
I*%&)H j~ U2 = u2; % Compute initial condition; save it in U
oM m/ !Dc ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
6eV e}V4W w=2*pi*n./T;
&fh .w]\ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
+*]SP@|IYI L=4; % length of evoluation to compare with S. Trillo's paper
g=)U_D PRi dz=L/M1; % space step, make sure nonlinear<0.05
)GQ D*b for m1 = 1:1:M1 % Start space evolution
e=|F(iW u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
)yfOrs M u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
`=WzG" ca1 = fftshift(fft(u1)); % Take Fourier transform
mvxc[ ca2 = fftshift(fft(u2));
L+` }euu5 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
}d$vcEI$3 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
Zm?G'06 u2 = ifft(fftshift(c2)); % Return to physical space
C _ k_D u1 = ifft(fftshift(c1));
\v B9f A:* if rem(m1,J) == 0 % Save output every J steps.
!!\ 4'Q[ U1 = [U1 u1]; % put solutions in U array
m|g$'vjk U2=[U2 u2];
1mkQ"E4 MN1=[MN1 m1];
G N8`xR{J* z1=dz*MN1'; % output location
h= m I{w* end
E9
:|8#b end
y$"~^8"z hg=abs(U1').*abs(U1'); % for data write to excel
9. ]Cy8 ha=[z1 hg]; % for data write to excel
?3e!A9x t1=[0 t'];
cJ 1{2R hh=[t1' ha']; % for data write to excel file
\ltE rd- %dlmwrite('aa',hh,'\t'); % save data in the excel format
Qt)7mf figure(1)
X,Q 6 waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
bDcWb2 lqs figure(2)
S@l
a.0HDA waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
f^>lObvd rmAP&Gw I 非线性超快脉冲耦合的数值方法的Matlab程序 '{1W )X gGceK^# 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。
mDe+ M {/ 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
Yn?2,^?N a93d' ZE-X P,LXZ }*{\)7g % This Matlab script file solves the nonlinear Schrodinger equations
U(=f5|- % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
r A&#>R ` % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
0*'`%W+5 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
p3'mJ3MA J,& `iL - C=1;
G$cq M1=120, % integer for amplitude
H tS1N}@ M3=5000; % integer for length of coupler
p'9
V. _h N = 512; % Number of Fourier modes (Time domain sampling points)
9# .NPfMF dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
FK/ro91L T =40; % length of time:T*T0.
ADJ5Z D<Q dt = T/N; % time step
K. sj" #D n = [-N/2:1:N/2-1]'; % Index
~6Ee=NaLzP t = n.*dt;
2e D\_IW ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
:@z5& h w=2*pi*n./T;
:)3$&QdHT g1=-i*ww./2;
[b\lcQ8O g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
vY TPZ@RL g3=-i*ww./2;
.\hib. n3 P1=0;
.w*{=x 0k P2=0;
&t =>:C$1Y P3=1;
>?uH#%C5 P=0;
iTtAj~dfZ for m1=1:M1
XiZ Zo p=0.032*m1; %input amplitude
qS[p|*BL s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
cq+ M
*1; s1=s10;
t h>yi)m s20=0.*s10; %input in waveguide 2
>t6' 8g"T s30=0.*s10; %input in waveguide 3
\Lh<E5@] s2=s20;
1rzq$, O s3=s30;
K]=>F p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
|jC E9Ve# %energy in waveguide 1
]mGsNQ ].H p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
=Q8^@i4[&D %energy in waveguide 2
} k%\ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
N#6A> %energy in waveguide 3
:J)l C = for m3 = 1:1:M3 % Start space evolution
qh'f,#dI} s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
F|3FvxA s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
N<i Vs s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
A?Hjz%EcW sca1 = fftshift(fft(s1)); % Take Fourier transform
{G*:N[pJp sca2 = fftshift(fft(s2));
PXQ9P<m sca3 = fftshift(fft(s3));
TB3T:A>2 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
cB"F1~z sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
bz,cfc;?$ sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
2b&;Y /z s3 = ifft(fftshift(sc3));
{XUfxNDf s2 = ifft(fftshift(sc2)); % Return to physical space
0 Vgn N s1 = ifft(fftshift(sc1));
SJu f` end
So]FDd p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
Q24:G p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
$ Q7E# p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
y&I|m P1=[P1 p1/p10];
M6d w~0e P2=[P2 p2/p10];
rM?Dp2 P3=[P3 p3/p10];
r.G/f{=<@ P=[P p*p];
71 m-W#zyA end
}oxaB9r figure(1)
{q>4:lsS plot(P,P1, P,P2, P,P3);
OL9C #er u0H`%m 转自：
http://blog.163.com/opto_wang/
