计算脉冲在非线性耦合器中演化的Matlab 程序 7o!t/WEEq ph!h8@e % This Matlab script file solves the coupled nonlinear Schrodinger equations of
:h3U ^ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
v AeVQ~ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
e(b$LUV % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
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$ ` ' %fid=fopen('e21.dat','w');
U-,s/VQ? N = 128; % Number of Fourier modes (Time domain sampling points)
P&t w!B M1 =3000; % Total number of space steps
4:b'VHW. J =100; % Steps between output of space
SXJjagAoML T =10; % length of time windows:T*T0
|_+l D|' T0=0.1; % input pulse width
.i|nn[H & MN1=0; % initial value for the space output location
N0\<B-8+,> dt = T/N; % time step
4N7|LxNNl_ n = [-N/2:1:N/2-1]'; % Index
%i?v)EW t = n.*dt;
{KEmGHC4R u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
o :4#Ak S u20=u10.*0.0; % input to waveguide 2
}rs>B,=*k u1=u10; u2=u20;
n8T'}d+mm U1 = u1;
^4<&"ao o U2 = u2; % Compute initial condition; save it in U
>$r o\ / ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
A
=&`TfXu w=2*pi*n./T;
e$`hRZ%
g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
wPcEvGBN= L=4; % length of evoluation to compare with S. Trillo's paper
\&Bdi6xAy dz=L/M1; % space step, make sure nonlinear<0.05
}&6:0l$4! for m1 = 1:1:M1 % Start space evolution
%AWc`D
u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
f3>DmH# u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
yO7#n0q ca1 = fftshift(fft(u1)); % Take Fourier transform
4)'U!jSb ca2 = fftshift(fft(u2));
7+X~i@#rU c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
0&2` )W?9 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
Xi\c>eALO u2 = ifft(fftshift(c2)); % Return to physical space
SdnO#J}{ u1 = ifft(fftshift(c1));
0B}2~}# if rem(m1,J) == 0 % Save output every J steps.
}*qj,8-9 U1 = [U1 u1]; % put solutions in U array
+~y>22Zfg U2=[U2 u2];
=1
S%E MN1=[MN1 m1];
|~18MW z1=dz*MN1'; % output location
d:#tN4y7( end
! gfd! R end
DpT$19 Q+ hg=abs(U1').*abs(U1'); % for data write to excel
p:0X3 ?IG3 ha=[z1 hg]; % for data write to excel
zf^|H%
~^ t1=[0 t'];
fYh <S hh=[t1' ha']; % for data write to excel file
x5/&,&m`% %dlmwrite('aa',hh,'\t'); % save data in the excel format
?gjx7TQ ? figure(1)
%9S0!h\ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
A%^7D.j figure(2)
)%n $_N n waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
[9NrPm3d ?`O^;f 非线性超快脉冲耦合的数值方法的Matlab程序 27$,D XD &,{YfAxQ` 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。
O.xtY @'" 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
I:UDEoQo iy]?j$B$ $p$p C/:% ?~yJ7~3TS< % This Matlab script file solves the nonlinear Schrodinger equations
YV@efPy}n % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
x7G*xHJ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
o[+t}hC[ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
mF jM6pmo 0\@oqw]6hv C=1;
b >k 2@ M1=120, % integer for amplitude
&Vgpv#&Cfx M3=5000; % integer for length of coupler
6q T- N = 512; % Number of Fourier modes (Time domain sampling points)
v+SdjFAY dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
~ oT*@ T =40; % length of time:T*T0.
jh`[ Y7RJO dt = T/N; % time step
=]/<Kd}A. n = [-N/2:1:N/2-1]'; % Index
MOnTp8 t = n.*dt;
{ w sT ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
q(~|roKA( w=2*pi*n./T;
BpYxH#4 g1=-i*ww./2;
n&?)gKL0g g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
t*)mX2R, g3=-i*ww./2;
&o y')\H P1=0;
K{"hf:k P2=0;
)4c?BCgy P3=1;
EUQtl_h/H P=0;
o;
U!{G(X for m1=1:M1
;^E_BJm p=0.032*m1; %input amplitude
kLU-4W 5t s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
$60`Hh 4/ s1=s10;
Vf P\)Rl s20=0.*s10; %input in waveguide 2
JEMc _ngR! s30=0.*s10; %input in waveguide 3
DX+zK'34 s2=s20;
[ ;sTl~gC s3=s30;
b(Tvc p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
cGdYfi %energy in waveguide 1
d%-/U !z? p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
w-LENdw %energy in waveguide 2
Ot:}Ncq^\O p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
z0SF2L H %energy in waveguide 3
uZ\+{j= for m3 = 1:1:M3 % Start space evolution
Vp|?R65S* s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
h& }i H s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
TO"Md["GI s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
y) CvlI sca1 = fftshift(fft(s1)); % Take Fourier transform
_*Z3,*~"X sca2 = fftshift(fft(s2));
A>2 _I) sca3 = fftshift(fft(s3));
`8RKpZv& sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
()O&O+R|) sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
,u PcQ sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
nw%`CnzT s3 = ifft(fftshift(sc3));
[0]A-#J s2 = ifft(fftshift(sc2)); % Return to physical space
`& OX|mL^w s1 = ifft(fftshift(sc1));
> $E;."a end
0Bh cXH t p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
_ezRE"F5 p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
$/;K<*O$ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
'@ Rk#=85Z P1=[P1 p1/p10];
BI %XF
9{ P2=[P2 p2/p10];
vB{i w}Hi! P3=[P3 p3/p10];
~?HK,` 0h> P=[P p*p];
{B4qeG5 end
Sp:w _;{# figure(1)
3Ke6lV)uq plot(P,P1, P,P2, P,P3);
1PUZB`"3 F@f4-NR> 转自：
http://blog.163.com/opto_wang/
