计算脉冲在非线性耦合器中演化的Matlab 程序 1I*b7t <lj;}@qQ< % This Matlab script file solves the coupled nonlinear Schrodinger equations of
?n 9<PMo % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
-Q6njt & % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
+O 2H":$ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
F|t3%dpj 2`XG"[@ %fid=fopen('e21.dat','w');
gn>qd6P N = 128; % Number of Fourier modes (Time domain sampling points)
J_]B,'
6 M1 =3000; % Total number of space steps
2cy: l03 J =100; % Steps between output of space
e^?0uVxS1 T =10; % length of time windows:T*T0
FvpI\%#~ T0=0.1; % input pulse width
^a6c/ 2K MN1=0; % initial value for the space output location
p<w2e dt = T/N; % time step
xWv@ PqXD n = [-N/2:1:N/2-1]'; % Index
dvWQ?1l_ t = n.*dt;
@ pcmVsIp u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
'gDhi!h% u20=u10.*0.0; % input to waveguide 2
gZI8 8Q u1=u10; u2=u20;
&&/2oP+z U1 = u1;
L 1FT h U2 = u2; % Compute initial condition; save it in U
dX4"o?KD> ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
fO+$`r>9 w=2*pi*n./T;
Fc{X$hh< g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
n2NxO0 L=4; % length of evoluation to compare with S. Trillo's paper
8ug\GlZc dz=L/M1; % space step, make sure nonlinear<0.05
g]sc)4 for m1 = 1:1:M1 % Start space evolution
\OV><|Lkh u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
8<gYB$* S u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
u|v2J/_5Y ca1 = fftshift(fft(u1)); % Take Fourier transform
$IZ02ZM$ ca2 = fftshift(fft(u2));
K"%_q$[YQ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
g%P6 f c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
z+R A u2 = ifft(fftshift(c2)); % Return to physical space
n-/ {H4\ u1 = ifft(fftshift(c1));
+K6j p if rem(m1,J) == 0 % Save output every J steps.
vkFq/+'U U1 = [U1 u1]; % put solutions in U array
k
E^%w?C U2=[U2 u2];
gLyXe,Jp MN1=[MN1 m1];
D %CKkQ<u2 z1=dz*MN1'; % output location
oCw>b]S end
O#j&8hQ> end
k,p:!S(bl hg=abs(U1').*abs(U1'); % for data write to excel
=0Z^ q0. ha=[z1 hg]; % for data write to excel
|\PI" rW t1=[0 t'];
{h < V^r hh=[t1' ha']; % for data write to excel file
l :e&w(1H %dlmwrite('aa',hh,'\t'); % save data in the excel format
ID /=YG@ figure(1)
g j(|#n5C waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
<OQn |zU\ figure(2)
sqtMhUQ?>w waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
2pKkg>/ S cPFs K*w 非线性超快脉冲耦合的数值方法的Matlab程序 7Nu.2q E 5G
>{*K/ 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。
g4Y1*`}2f 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
] LcCom:] b0QC91
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OX|F_ Q L 0 % This Matlab script file solves the nonlinear Schrodinger equations
{5% u G2g % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
FTVV+9.l: % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
s7"NK" % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Pv- i. /2%6 46 C=1;
w"A.*8Iu M1=120, % integer for amplitude
~ AqFLv/% M3=5000; % integer for length of coupler
AQx:}PO N = 512; % Number of Fourier modes (Time domain sampling points)
oGtz*AP% dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
e}xx4mYo T =40; % length of time:T*T0.
J@ CKgE dt = T/N; % time step
RgB5 '$x} n = [-N/2:1:N/2-1]'; % Index
]0Y5 Z)3:z t = n.*dt;
GkOZ =ej ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
F
gi&CJ8Q w=2*pi*n./T;
v (|Arm? g1=-i*ww./2;
No|T#=BZ[ g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
I34|<3t$ g3=-i*ww./2;
!HV<2q() P1=0;
^x BQ#p P2=0;
i[IOR 0 P3=1;
|\# ~ P=0;
kYW>o}J| for m1=1:M1
~AvB5 p=0.032*m1; %input amplitude
W@b Z~Q9 s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
[w1 4hHnq s1=s10;
})V^t 3 s20=0.*s10; %input in waveguide 2
IqA'Vz,lL s30=0.*s10; %input in waveguide 3
?:sk [f6 s2=s20;
S S)9+0$ s3=s30;
eYpK!9 p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
r pB0?h!$ %energy in waveguide 1
o)V@|i0Js p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
k1.h |&JJN %energy in waveguide 2
n|p(Cb#G p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
V_x8
Q+~? %energy in waveguide 3
;4%Co)Rw for m3 = 1:1:M3 % Start space evolution
H;1_" s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
`X8wnD s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
_
SuW86 s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
Bn4wr sca1 = fftshift(fft(s1)); % Take Fourier transform
?@>PKUv{ sca2 = fftshift(fft(s2));
j;7:aM"BQW sca3 = fftshift(fft(s3));
+u[^@>_I0 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
]jB`"to*} sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
]B2%\}c sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
vW s#4JoG s3 = ifft(fftshift(sc3));
|7$Q'3V s2 = ifft(fftshift(sc2)); % Return to physical space
qexnsL s1 = ifft(fftshift(sc1));
: Yb_ end
+{r~-Rn3 p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
2+oS'nL p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
>d9b"T p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
5qL ;@Y P1=[P1 p1/p10];
)8JfBzR P2=[P2 p2/p10];
75"&"*R/*G P3=[P3 p3/p10];
"XB6k 0.# P=[P p*p];
M(|6YF7u end
-U BH,U figure(1)
2{6%+>jB plot(P,P1, P,P2, P,P3);
M669G;w(K u [<ij 转自：
http://blog.163.com/opto_wang/
