计算脉冲在非线性耦合器中演化的Matlab 程序 Skz|*n|eY <9sO % This Matlab script file solves the coupled nonlinear Schrodinger equations of
\cLSf= % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
?EX"k+G % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
X w .p % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
``A 0WN Z#.f&K )xX %fid=fopen('e21.dat','w');
Jdy=_88MD
N = 128; % Number of Fourier modes (Time domain sampling points)
|7 Ke R- M1 =3000; % Total number of space steps
* H[Iq !@ J =100; % Steps between output of space
QKE9R-K TE T =10; % length of time windows:T*T0
R<x'l=,D( T0=0.1; % input pulse width
-TZ p
FT" MN1=0; % initial value for the space output location
2Dd|~{% dt = T/N; % time step
*UW=Mdt n = [-N/2:1:N/2-1]'; % Index
Ix|~f1*% t = n.*dt;
8J)xzp`*) u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
}oJAB1'k u20=u10.*0.0; % input to waveguide 2
s`Cy
a` u1=u10; u2=u20;
L^^4=ao0 U1 = u1;
it2 a U2 = u2; % Compute initial condition; save it in U
J1XL<7 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
Eq:2k)BE w=2*pi*n./T;
G4
G5PX i g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
@t1V
o}c L=4; % length of evoluation to compare with S. Trillo's paper
`Bn=?9 dz=L/M1; % space step, make sure nonlinear<0.05
s
s
3 t for m1 = 1:1:M1 % Start space evolution
Q o =Kqv u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
$W;b{H=F u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
I \ | N ca1 = fftshift(fft(u1)); % Take Fourier transform
W9oAjO NE ca2 = fftshift(fft(u2));
+u'I0>)S c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
A>VX*xd c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
p
h[\ ) u2 = ifft(fftshift(c2)); % Return to physical space
MlW 8t[ u1 = ifft(fftshift(c1));
KS*oxZ if rem(m1,J) == 0 % Save output every J steps.
oR p:B & U1 = [U1 u1]; % put solutions in U array
U1 _&gy @y U2=[U2 u2];
N - w(e MN1=[MN1 m1];
3/JyUh? z1=dz*MN1'; % output location
[\ R>Xcu> end
%PJhy 2 end
f f 7 ( hg=abs(U1').*abs(U1'); % for data write to excel
[Vdz^_@Y ha=[z1 hg]; % for data write to excel
oVCmI"' t1=[0 t'];
*V(Fn-6( hh=[t1' ha']; % for data write to excel file
(Vg}Hh?p %dlmwrite('aa',hh,'\t'); % save data in the excel format
(c v!Y=] figure(1)
6D;^uM2N waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
s=Q( C[%I figure(2)
CVXytS?@x waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
_y .]3JNm nW?R"@Zm 非线性超快脉冲耦合的数值方法的Matlab程序 ]I Jv-( G%u9+XV1# 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。
c-j_IN Gm 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
+rWZ|&r% +CM7C%U
P NSMcakD >6Lm9&} % This Matlab script file solves the nonlinear Schrodinger equations
# fhEc;t % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
%~*jae!f % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
1px\K8 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
b]gY~c bI8 uHNpfK nZ C=1;
jw6T j;c M1=120, % integer for amplitude
zGc(Ef5`M6 M3=5000; % integer for length of coupler
Hoz5 6y N = 512; % Number of Fourier modes (Time domain sampling points)
0=v{RQ;W4 dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
TJ6#P <M T =40; % length of time:T*T0.
;+pOP |P= dt = T/N; % time step
M,:Bl} n = [-N/2:1:N/2-1]'; % Index
u~Tg&0V30 t = n.*dt;
[;O^[Iybf: ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
ZEbLL4n w=2*pi*n./T;
`0#H]=$2h g1=-i*ww./2;
U l Mi.;/^ g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
3}&ZOO g3=-i*ww./2;
&~5=K P1=0;
8(X0
: P2=0;
>{Rb 3Z] P3=1;
+yt6(7V* P=0;
yZ}d+ 7T} for m1=1:M1
<M[U#Q~?~e p=0.032*m1; %input amplitude
Uz8hANN0_ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
Tvf~P w s1=s10;
;)! "Ty| s20=0.*s10; %input in waveguide 2
FuP/tTMU1a s30=0.*s10; %input in waveguide 3
Zzd/K^gg s2=s20;
aw}+' (?8] s3=s30;
kRIB<@{ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
#\If]w*j %energy in waveguide 1
: h";c" p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
z REJ#r %energy in waveguide 2
9EF~l9`'U p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
rPq <Xb\ %energy in waveguide 3
g{pQ4jKF for m3 = 1:1:M3 % Start space evolution
r>qA $zD^ s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
ipKG ! s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
#GqTqHNE< s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
JE%A|R<Jl sca1 = fftshift(fft(s1)); % Take Fourier transform
|LYKc.xo sca2 = fftshift(fft(s2));
wFlV=!>, sca3 = fftshift(fft(s3));
P0\eB S sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
DacJ,in_I{ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
xNdID j@ sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
,9/5T : 2 s3 = ifft(fftshift(sc3));
Q2 ~5" s2 = ifft(fftshift(sc2)); % Return to physical space
?=|kC*$/G s1 = ifft(fftshift(sc1));
<lFY7' aY end
dhR( _ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
f?0s & Xo p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
O<,r>b, p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
~y\:iL//E P1=[P1 p1/p10];
-2NwF4VL P2=[P2 p2/p10];
LR$z0rDEM P3=[P3 p3/p10];
t;Wotfc[#0 P=[P p*p];
- 0~I Y end
;A ^K_ w' figure(1)
:Z2tig nL plot(P,P1, P,P2, P,P3);
By)3*<5 a_ !7 ` [ i 转自：
http://blog.163.com/opto_wang/
