计算脉冲在非线性耦合器中演化的Matlab 程序 H+@?K6{h ~PU}==*q % This Matlab script file solves the coupled nonlinear Schrodinger equations of
^+gD;a |t % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
NbCIL8f] % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
Bgp%hK % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
I|;C} lfp K4I/a#S'@6 %fid=fopen('e21.dat','w');
I]3!M`IMG N = 128; % Number of Fourier modes (Time domain sampling points)
Hw6 2'% M1 =3000; % Total number of space steps
H6Gs&y k3 J =100; % Steps between output of space
I :bT"N T =10; % length of time windows:T*T0
V
'fri/ Z T0=0.1; % input pulse width
gv i!|!M= MN1=0; % initial value for the space output location
rV?@Kgxi dt = T/N; % time step
1N5lI97j n = [-N/2:1:N/2-1]'; % Index
qv4r !x t = n.*dt;
-rT#Wi u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
563ExibH u20=u10.*0.0; % input to waveguide 2
@hrIu" '! u1=u10; u2=u20;
fKtlfQG U1 = u1;
L|;sB=$'{ U2 = u2; % Compute initial condition; save it in U
`DM)tm3&m ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
Dd-a*6|x w=2*pi*n./T;
H^vA}F` g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
bQ&%6'ck L=4; % length of evoluation to compare with S. Trillo's paper
C~. T[Mlu dz=L/M1; % space step, make sure nonlinear<0.05
Prc1U)nfo for m1 = 1:1:M1 % Start space evolution
'Z%1Ly^b u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
{.DY \;Q u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
WLta{A? ca1 = fftshift(fft(u1)); % Take Fourier transform
NW*#./WdF8 ca2 = fftshift(fft(u2));
]Zc\si3i& c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
tCPK_Wws?Z c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
4]-7S l, u2 = ifft(fftshift(c2)); % Return to physical space
6Tc! =lk u1 = ifft(fftshift(c1));
2U"2L^oKI if rem(m1,J) == 0 % Save output every J steps.
" " _B3' U1 = [U1 u1]; % put solutions in U array
`0MQL@B U2=[U2 u2];
BHErc \ITP MN1=[MN1 m1];
5PC: 4 z1=dz*MN1'; % output location
]\k&
l
[' end
c 6y>] 8_ end
<P@O{Xi+K hg=abs(U1').*abs(U1'); % for data write to excel
o02G:!gB ha=[z1 hg]; % for data write to excel
vo2G Fo t1=[0 t'];
G)_Zls2 ; hh=[t1' ha']; % for data write to excel file
L]&y[/\E1 %dlmwrite('aa',hh,'\t'); % save data in the excel format
?{5}3a bB` figure(1)
~[~#PO waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
hb
%F"Q figure(2)
{z;4t&5
waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
(Jk[%_b>_ VWzuV&;P 非线性超快脉冲耦合的数值方法的Matlab程序 \w(0k^<7 :2')`xT 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。
|2rOV&@l9 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
LnsYtkb r obPG]*3 (hIo0 . 9]1LwX!M2 % This Matlab script file solves the nonlinear Schrodinger equations
K@
&;f( Y % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
Q:T9&_| % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
]9JH.fF % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
7u 5H o`
o)DO[ C=1;
?5,I`9 M1=120, % integer for amplitude
%Nob B M3=5000; % integer for length of coupler
g-NrxyTBlx N = 512; % Number of Fourier modes (Time domain sampling points)
pK"Z9y& dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
_={mKKoHs T =40; % length of time:T*T0.
y7GgTC/H dt = T/N; % time step
IY
mkZ?cW n = [-N/2:1:N/2-1]'; % Index
qEl PYN*wF t = n.*dt;
jpTk@ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
m&be55M; w=2*pi*n./T;
U}5]Vm$] g1=-i*ww./2;
rls{~ZRl g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
UIS siiG( g3=-i*ww./2;
kc} |L9 P1=0;
x\VP
X P2=0;
hJz]N$@W P3=1;
9U=6l]Np P=0;
0( $On`# for m1=1:M1
*& R|0I{> p=0.032*m1; %input amplitude
j#Lj<jX!xR s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
DnW/q s1=s10;
#T H(:I=[ s20=0.*s10; %input in waveguide 2
wx!2/I> s30=0.*s10; %input in waveguide 3
! T8sWMY s2=s20;
JeA_mtSQ| s3=s30;
lLglF4 p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
&fU48n1Uh %energy in waveguide 1
jR@>~t[}o p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
&n0Ag]$P %energy in waveguide 2
c"t&,OU: p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
T1x67 b
u %energy in waveguide 3
sb?!U"v.' for m3 = 1:1:M3 % Start space evolution
aH8]$e8_,\ s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
t}OzF cyqN s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
yMD0Tj5ZQ s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
Pt-O 1$C[ sca1 = fftshift(fft(s1)); % Take Fourier transform
,Ik~E&Ku2' sca2 = fftshift(fft(s2));
E0DquVrz sca3 = fftshift(fft(s3));
/WK1( B: sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
T, PN6d sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
}Gx@1)?? sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
E]r<t# s3 = ifft(fftshift(sc3));
c>+68<H s2 = ifft(fftshift(sc2)); % Return to physical space
t'.:"H8BI s1 = ifft(fftshift(sc1));
n1PvZ~^3 end
nHp$5|r< p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
'SrDc'? p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
l k
/Ke p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
S 1C#5 = P1=[P1 p1/p10];
\pSRG=` P2=[P2 p2/p10];
* Gj`1# Z$ P3=[P3 p3/p10];
N3oa!PE P=[P p*p];
ZW@cw } end
:2:%
figure(1)
hPCSAo!| plot(P,P1, P,P2, P,P3);
vmo ! c%+uji6 转自：
http://blog.163.com/opto_wang/
