计算脉冲在非线性耦合器中演化的Matlab 程序 *'=JT# J+IQ vOn_| % This Matlab script file solves the coupled nonlinear Schrodinger equations of
x]|8 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
p.,o@GcL~ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
|5|^ [v % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
E yu]0+ g#0h{%3A
\ %fid=fopen('e21.dat','w');
qa
'YZE` N = 128; % Number of Fourier modes (Time domain sampling points)
pE( \q+1< M1 =3000; % Total number of space steps
'vKB] /e; J =100; % Steps between output of space
Q7oJ4rIP T =10; % length of time windows:T*T0
K r $R " T0=0.1; % input pulse width
!l!^` c MN1=0; % initial value for the space output location
WJvD,VMz dt = T/N; % time step
b(wzn`Z%Et n = [-N/2:1:N/2-1]'; % Index
b6%T[B B t = n.*dt;
cn1CM'Ru u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
$ c4Q6w u20=u10.*0.0; % input to waveguide 2
csZ IBi u1=u10; u2=u20;
MJ^NRT0?b U1 = u1;
, |SO'dG U2 = u2; % Compute initial condition; save it in U
ZC+F* :$ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
oK1"8k|Z w=2*pi*n./T;
- '& 4No g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
;!U`GN,tH L=4; % length of evoluation to compare with S. Trillo's paper
'~i;g.n=}- dz=L/M1; % space step, make sure nonlinear<0.05
p] kpDx[9 for m1 = 1:1:M1 % Start space evolution
&Npv~Iy u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
It,m %5
Py u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
-N`j` zb| ca1 = fftshift(fft(u1)); % Take Fourier transform
B EM_y:# ca2 = fftshift(fft(u2));
ZAe>MNtW c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
3\FPW1$i|[ c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
n\k6UD u2 = ifft(fftshift(c2)); % Return to physical space
Am 3^3> u1 = ifft(fftshift(c1));
DArEIt6Q if rem(m1,J) == 0 % Save output every J steps.
{ ?*3Ou U1 = [U1 u1]; % put solutions in U array
oL0Q%_9hW U2=[U2 u2];
5Gm,lNQ Av MN1=[MN1 m1];
pjr,X+6o z1=dz*MN1'; % output location
UEm NT9 V end
pnin;;D* end
SpbOv Y=> hg=abs(U1').*abs(U1'); % for data write to excel
-.ITcD g ha=[z1 hg]; % for data write to excel
fhqc[@Y[ t1=[0 t'];
=&?}qa(P hh=[t1' ha']; % for data write to excel file
/C"dwh"`` %dlmwrite('aa',hh,'\t'); % save data in the excel format
l<
8RG@ figure(1)
4~-"k{Xt waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
XE);oL2xP figure(2)
9M o(3M waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
oj*5m+:>a TA; 非线性超快脉冲耦合的数值方法的Matlab程序 !
7,rz1s73 |__\Vn 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。
U085qKyCw 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
`-!t 8BH 3DRbCKNL VyK]:n<5Q lVY`^pw? % This Matlab script file solves the nonlinear Schrodinger equations
Y%!3/ 3T % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
HrQBzS % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
]0P-?O: % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
w^tNYN,i ,aS6|~ac4 C=1;
m@o/ W M1=120, % integer for amplitude
@f442@_4 M3=5000; % integer for length of coupler
c;DWSgIw N = 512; % Number of Fourier modes (Time domain sampling points)
WP&P#ju& dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
s>d@=P>R T =40; % length of time:T*T0.
?H8w/{J dt = T/N; % time step
? 2h oY n = [-N/2:1:N/2-1]'; % Index
HU ]Yv+3 t = n.*dt;
tWL3F?wd ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
cA%70Y:AV w=2*pi*n./T;
+r[u4? g1=-i*ww./2;
zOA{S ~> g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
2ILM f?} g3=-i*ww./2;
0eq="|n^| P1=0;
kzPHPERA] P2=0;
K(RG:e~R0i P3=1;
n%PHHu
P=0;
/CX_@%m}e= for m1=1:M1
xe} d& p=0.032*m1; %input amplitude
i/;Ql, gm s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
],ioY*4G s1=s10;
vU&I,:72
H s20=0.*s10; %input in waveguide 2
=YlsJ={h s30=0.*s10; %input in waveguide 3
M@@l>"g@ s2=s20;
xV HZZ?e s3=s30;
to~Ap=E p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
'5zolp%St %energy in waveguide 1
PR?Ls{}p\ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
e m`z=JGG %energy in waveguide 2
x aQ]Vjw p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
b%<-(o/ %energy in waveguide 3
SS O F\ for m3 = 1:1:M3 % Start space evolution
$%!'c#
F s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
O#}T .5 t s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
dWV.5cViP s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
FbB^$ ]* sca1 = fftshift(fft(s1)); % Take Fourier transform
]kUF>W p sca2 = fftshift(fft(s2));
c!l=09a~a+ sca3 = fftshift(fft(s3));
{HP Kp&kl sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
y]$%>N0vLX sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
gj {2" tE sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
Xy[ O s3 = ifft(fftshift(sc3));
EJ7}h?a]U_ s2 = ifft(fftshift(sc2)); % Return to physical space
0<"4W: s1 = ifft(fftshift(sc1));
Hq'mv_}qG end
ximW!y7 p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
E0QrByr_ p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
\fG?j@Qx p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
${\iHg[vZ P1=[P1 p1/p10];
:tclY X P2=[P2 p2/p10];
@-y.Y}k#$~ P3=[P3 p3/p10];
^hPREbD+f P=[P p*p];
4DaLt&1 end
>jxo,xz figure(1)
}gw
\w?/ plot(P,P1, P,P2, P,P3);
V'TBt= !=] +\ ~.cP7 [ 转自：
http://blog.163.com/opto_wang/
