计算脉冲在非线性耦合器中演化的Matlab 程序 9:RV5Dt e^~d x }X % This Matlab script file solves the coupled nonlinear Schrodinger equations of
rC|nE =i % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
-}T7F+ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
1S(oi % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
n7ZJ< ~wl Gl{'a1 %fid=fopen('e21.dat','w');
YG*<jKcX N = 128; % Number of Fourier modes (Time domain sampling points)
n)a/pO_ M1 =3000; % Total number of space steps
)ZLj2H < J =100; % Steps between output of space
V WdTnu T =10; % length of time windows:T*T0
fuHNsrNlm T0=0.1; % input pulse width
K($+ILZ MN1=0; % initial value for the space output location
dMjQ V& dt = T/N; % time step
Vo{
~D:) n = [-N/2:1:N/2-1]'; % Index
) xV>Va8) t = n.*dt;
$N vox<d0 u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
7 ?k3jDK
u20=u10.*0.0; % input to waveguide 2
V3*@n *"N; u1=u10; u2=u20;
aW|=|K U1 = u1;
9b-4BON{P U2 = u2; % Compute initial condition; save it in U
Y=s v
ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
Su,<id S w=2*pi*n./T;
tD}{/`{_t g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
kd&~_=Q L=4; % length of evoluation to compare with S. Trillo's paper
t`}=~/#`X dz=L/M1; % space step, make sure nonlinear<0.05
OBlQ for m1 = 1:1:M1 % Start space evolution
2|exY>`w u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
L28wT)D- u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
v%`k*n ': ca1 = fftshift(fft(u1)); % Take Fourier transform
!F6rcDK I ca2 = fftshift(fft(u2));
[=. iJ5,{2 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
j1Sjw6}GCH c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
B "4A1! u2 = ifft(fftshift(c2)); % Return to physical space
\N? lG q u1 = ifft(fftshift(c1));
#>C Wee; if rem(m1,J) == 0 % Save output every J steps.
qS}{O0 U1 = [U1 u1]; % put solutions in U array
j" ;L { U2=[U2 u2];
^Bw"+ 6d MN1=[MN1 m1];
U[yA`7Zs} z1=dz*MN1'; % output location
fK@UlMC] 7 end
33}p02# end
^N ;TCn hg=abs(U1').*abs(U1'); % for data write to excel
Q-s5-&h ( ha=[z1 hg]; % for data write to excel
HC ktgL:E= t1=[0 t'];
+m}D. u*cp hh=[t1' ha']; % for data write to excel file
/NPx9cLW^ %dlmwrite('aa',hh,'\t'); % save data in the excel format
W>x.*K figure(1)
Bq4@I_b waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
Q}lY1LT` figure(2)
gHL:X W^ waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
p*zTuB~e < '|tmmoY6a: 非线性超快脉冲耦合的数值方法的Matlab程序 VL\Ah3+ }D vT6 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。
- t 4F 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
8-L -W[ (S=CxK _!vuDv% "0>AefFd# % This Matlab script file solves the nonlinear Schrodinger equations
aJs! bx>K % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
h^H)p`[Gme % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
'|% \QWuZ
% pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
U;
#v-'Z : 9>U+)% C=1;
aNICSxDN M1=120, % integer for amplitude
@%MGLR{pH M3=5000; % integer for length of coupler
L[+4/a!HQ N = 512; % Number of Fourier modes (Time domain sampling points)
+OI nf_O dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
&xC5Mecb* T =40; % length of time:T*T0.
-ebyW# dt = T/N; % time step
Ni ;jMc n = [-N/2:1:N/2-1]'; % Index
6% c]{eTd9 t = n.*dt;
| mw3v> ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
8X\":l: w=2*pi*n./T;
PMj!T \B| g1=-i*ww./2;
\%W"KLP g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
_4lKd` g3=-i*ww./2;
/dR:\ffz2 P1=0;
(x[z=_I%` P2=0;
``h* A P3=1;
2tp95E`(O P=0;
eN TKX for m1=1:M1
>/-Bg: p=0.032*m1; %input amplitude
c5eimA%` s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
2 ) Q/cH\g s1=s10;
x)kp*^/ s20=0.*s10; %input in waveguide 2
99Nm? $ g s30=0.*s10; %input in waveguide 3
I^ ``x+a s2=s20;
r;zG
s3=s30;
7*Gg#XQ>( p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
T' ) l %energy in waveguide 1
FbD9G6h5 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
phcY QqR %energy in waveguide 2
N/B-u)?\: p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
Cj6$W5I m %energy in waveguide 3
5.U|CL for m3 = 1:1:M3 % Start space evolution
=kW7|c5Z s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
[Al} GM s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
+39p5O! s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
#ChF{mh sca1 = fftshift(fft(s1)); % Take Fourier transform
s";9G^: sca2 = fftshift(fft(s2));
SivJaY% sca3 = fftshift(fft(s3));
_s0;mvz' sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
]n4G]ybK% sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
MF5o\-&dN sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
M+M\3U s3 = ifft(fftshift(sc3));
0 SDyE s2 = ifft(fftshift(sc2)); % Return to physical space
GUvEOD=p s1 = ifft(fftshift(sc1));
{ =IAS} end
S),acc(d p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
$_W kI^ p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
e6' y S81 p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
C.VU"= - P1=[P1 p1/p10];
|#O>DdKHT P2=[P2 p2/p10];
Cfst)[j P3=[P3 p3/p10];
? wZ`U
Oi P=[P p*p];
=D^R,Q end
v6'k`HnK figure(1)
*)qxrBc0 plot(P,P1, P,P2, P,P3);
k4~2hD<| 89%#;C 转自：
http://blog.163.com/opto_wang/
