计算脉冲在非线性耦合器中演化的Matlab 程序 MLDuo|? Io X(Pa % This Matlab script file solves the coupled nonlinear Schrodinger equations of
4
qnQF] 4 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
8177x7UG2[ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
V$@2:@8mo % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
u,C-U!A ,To ED %fid=fopen('e21.dat','w');
=:b/z1-v N = 128; % Number of Fourier modes (Time domain sampling points)
}"T:z{n M1 =3000; % Total number of space steps
5mV'k"Om#" J =100; % Steps between output of space
6QV/8IX T =10; % length of time windows:T*T0
O~D}&M@/R T0=0.1; % input pulse width
]
=D+a& MN1=0; % initial value for the space output location
P)H%dJ ^l dt = T/N; % time step
QEVjXJOt0 n = [-N/2:1:N/2-1]'; % Index
HG^8&uh] t = n.*dt;
-{< %Wt9 u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
|`|b&Rhu u20=u10.*0.0; % input to waveguide 2
~5|a9HV: u1=u10; u2=u20;
>!$4nx q2> U1 = u1;
HCP Be2 U2 = u2; % Compute initial condition; save it in U
eY-$h nUe ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
8'YL!moG| w=2*pi*n./T;
v|hi;l@7E g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
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;g0 ?M\ L=4; % length of evoluation to compare with S. Trillo's paper
O-7 \qz dz=L/M1; % space step, make sure nonlinear<0.05
xW09k6 for m1 = 1:1:M1 % Start space evolution
6(z.(eT u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
"}!vYr u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
b/ynCf8X ca1 = fftshift(fft(u1)); % Take Fourier transform
rUyT5Vf ca2 = fftshift(fft(u2));
iCH Z{<k c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
l"- D@]" c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
~(^[TuJC u2 = ifft(fftshift(c2)); % Return to physical space
/eE P^)h u1 = ifft(fftshift(c1));
NO<myN+N if rem(m1,J) == 0 % Save output every J steps.
9uq|
VU5 U1 = [U1 u1]; % put solutions in U array
| zA ey\ U2=[U2 u2];
)TWf/L cp MN1=[MN1 m1];
$q+7 , ," z1=dz*MN1'; % output location
.OjJK? end
|[qI2-e l? end
( R0 hg=abs(U1').*abs(U1'); % for data write to excel
S`-z$ph} ha=[z1 hg]; % for data write to excel
iX,Qh2(ig t1=[0 t'];
mX#T< _=d hh=[t1' ha']; % for data write to excel file
<l\FHJhjq %dlmwrite('aa',hh,'\t'); % save data in the excel format
qaUHcdH figure(1)
9/'j<v6M waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
:s4CWE d figure(2)
J3$ihH. waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
/qz( ra 2n@"|\ uHD 非线性超快脉冲耦合的数值方法的Matlab程序 E 1> 3 [3 UqA vFCy 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
0D\FFfs Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
s2tEyR+gW _x:K%1_[ dx~F [ Wl*\kQ}U % This Matlab script file solves the nonlinear Schrodinger equations
6=zme6D % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
R; I B o % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
jW6@U%[!b % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
5tf/VT ch-GmA j
9 C=1;
yeW| Ux: M1=120, % integer for amplitude
C|>#|5XaF M3=5000; % integer for length of coupler
Y!SD^Ie7! N = 512; % Number of Fourier modes (Time domain sampling points)
Y X~H!6l dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
_{A($/~c? T =40; % length of time:T*T0.
Hv%a\WNS1 dt = T/N; % time step
\zKVgywR n = [-N/2:1:N/2-1]'; % Index
} wiq?dr t = n.*dt;
W}EO]A%f.\ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
h[ t OY w=2*pi*n./T;
(;s \Ip0 g1=-i*ww./2;
K r 9 @ g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
SQEXC*0 8 g3=-i*ww./2;
]CTu | P1=0;
al^ yCoB P2=0;
-
@ P3=1;
wK ,t q P=0;
9 'T(Fc for m1=1:M1
]ao]?=q C p=0.032*m1; %input amplitude
y<5s)OehG s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
GSMP)8 W s1=s10;
}U8H4B~UtY s20=0.*s10; %input in waveguide 2
."MBKyg6 s30=0.*s10; %input in waveguide 3
$#0%gs/x s2=s20;
d`2VbZC` s3=s30;
n0EKNMO p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
yvVs9"|0 %energy in waveguide 1
Ex~OT p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
oW-luC+ %energy in waveguide 2
D
F0~A p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
&oAuh?kTq %energy in waveguide 3
!QYqRH~ 5 for m3 = 1:1:M3 % Start space evolution
N<?RN;M s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
5~ jGF s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
F n 6>n04v s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
u< ):gI sca1 = fftshift(fft(s1)); % Take Fourier transform
{At1]> sca2 = fftshift(fft(s2));
aLP 2p] sca3 = fftshift(fft(s3));
TG'A'wXxy sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
8p PAEf sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
^gNAGQYA sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
'?q|7[SU s3 = ifft(fftshift(sc3));
3{
`fT5]U s2 = ifft(fftshift(sc2)); % Return to physical space
"4I`.$F%O( s1 = ifft(fftshift(sc1));
{ Rbc end
rU (N@i% p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
;@Ls "+g p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
u TO L p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
GX a-g-d P1=[P1 p1/p10];
*-g S u P2=[P2 p2/p10];
U+nwLxe' P3=[P3 p3/p10];
HSyohP8 7 P=[P p*p];
Y]ZOvA5W end
xUj[ d(q figure(1)
5. idC-\ plot(P,P1, P,P2, P,P3);
xpUaFb UiW( /L 转自：
http://blog.163.com/opto_wang/
