计算脉冲在非线性耦合器中演化的Matlab 程序 S\g7wXH X]MM7hMuR % This Matlab script file solves the coupled nonlinear Schrodinger equations of
F>kn:I"X) % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
\w[ZY$/ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
H0 n@kKr % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
8sF0]J [g{ b%f2"e0g %fid=fopen('e21.dat','w');
N vHy' N = 128; % Number of Fourier modes (Time domain sampling points)
>m6,xxTR M1 =3000; % Total number of space steps
{C0^D*U: J =100; % Steps between output of space
u|>U`[Zpj T =10; % length of time windows:T*T0
MQH8Q$5D T0=0.1; % input pulse width
|ezO@ MN1=0; % initial value for the space output location
ajW$d! dt = T/N; % time step
FJ,\?ooGf n = [-N/2:1:N/2-1]'; % Index
S%s|P=u t = n.*dt;
'A(-MTd% u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
m\ Fb , u20=u10.*0.0; % input to waveguide 2
Ldj^O9 p( u1=u10; u2=u20;
&R FM
d= U1 = u1;
+6)kX4 U2 = u2; % Compute initial condition; save it in U
%%,hR' +| ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
p F *~)e w=2*pi*n./T;
hPi
:31-0 g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
i
=fOdp L=4; % length of evoluation to compare with S. Trillo's paper
hOL y*% dz=L/M1; % space step, make sure nonlinear<0.05
l)PFzIz=V for m1 = 1:1:M1 % Start space evolution
h:Mn$VR, u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
($ B ]9* u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
`MYK XBM ca1 = fftshift(fft(u1)); % Take Fourier transform
~v(M6dz~vk ca2 = fftshift(fft(u2));
OK2/k_jXN' c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
8j +:s\ c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
19w,'}CGk u2 = ifft(fftshift(c2)); % Return to physical space
9k+ &fyy u1 = ifft(fftshift(c1));
J (&M<<% if rem(m1,J) == 0 % Save output every J steps.
ny_ kr`$42 U1 = [U1 u1]; % put solutions in U array
S}p&\w H U2=[U2 u2];
-f;j1bQ MN1=[MN1 m1];
vb. Y8[ z1=dz*MN1'; % output location
L!b0y7yR end
{{[jC"4AY end
k1Mxsd hg=abs(U1').*abs(U1'); % for data write to excel
GKsL~;8" ha=[z1 hg]; % for data write to excel
B/9<b{6 t1=[0 t'];
JXRf4QmG hh=[t1' ha']; % for data write to excel file
0@e}hv; %dlmwrite('aa',hh,'\t'); % save data in the excel format
am'p^Z @ figure(1)
)4F/T, {;m waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
0O['-x figure(2)
qfP"UAc{/ waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
d,J<SG&L& B[/['sD 非线性超快脉冲耦合的数值方法的Matlab程序 ,ORG"]_F >]XaUQ- 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。
7MuK/q. 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
vPl6Das r xlPcg7 < ;,S"e N} x/&e % This Matlab script file solves the nonlinear Schrodinger equations
&b@!DAwAJ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
qvfAG 0p % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
Ubw!/|mi % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
?<yq 2`\4O Puth8 $ C=1;
[>M *_1F M1=120, % integer for amplitude
4z0R\tjT M3=5000; % integer for length of coupler
;/)Mcx] n N = 512; % Number of Fourier modes (Time domain sampling points)
),y!<\oQ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
5Du>-.r T =40; % length of time:T*T0.
|p8"9jN@}c dt = T/N; % time step
10l1 a4 n = [-N/2:1:N/2-1]'; % Index
X~)V )'R t = n.*dt;
6Er0o{iI ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
ghJ,s|lH w=2*pi*n./T;
d[>N6?JA/ g1=-i*ww./2;
ReB(T7Vk= g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
rz[uuY7 g3=-i*ww./2;
f?>-yMR| P1=0;
@^:7UI_ P2=0;
5;K-,"UQ P3=1;
BudWbZ5>Ep P=0;
JW % /^' for m1=1:M1
z"s%# /# p=0.032*m1; %input amplitude
1W}nYU s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
%];h|[ax] s1=s10;
.cH{WZ s20=0.*s10; %input in waveguide 2
q(jkit~`A s30=0.*s10; %input in waveguide 3
9#EHXgz s2=s20;
?LV -W s3=s30;
< 9d-Hz p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
!}L~@[v,uL %energy in waveguide 1
S`W'G&bCj
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
VT5cxB< %energy in waveguide 2
#A|D\IhF p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
lZS_n9Sc %energy in waveguide 3
Xew1LPI for m3 = 1:1:M3 % Start space evolution
Hlt8al3 s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
n2jvXLJq s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
MR?*GI's s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
'Ffy8z{& 3 sca1 = fftshift(fft(s1)); % Take Fourier transform
'd2qa`H'}B sca2 = fftshift(fft(s2));
D 8@n kSP sca3 = fftshift(fft(s3));
{XDY:`vZ} sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
{w |dM # sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
hr_9;,EPh sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
E,<\T6/%q s3 = ifft(fftshift(sc3));
7|+ |\ 7l# s2 = ifft(fftshift(sc2)); % Return to physical space
mX<Fuu}E*Z s1 = ifft(fftshift(sc1));
+&7[lsD*
end
7 g A08M[O p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
s.R-<Y 3 p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
>op:0on]} p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
z_:eM7]jv P1=[P1 p1/p10];
}XGMa?WR P2=[P2 p2/p10];
96"yNqBf P3=[P3 p3/p10];
!cEb z b P=[P p*p];
H{\.g=01 end
` j&0VIU>> figure(1)
M('s|>\l plot(P,P1, P,P2, P,P3);
,]PyDq6 eK Z@ FEZ 转自：
http://blog.163.com/opto_wang/
