计算脉冲在非线性耦合器中演化的Matlab 程序 SFHa(JOS N^ )OlH % This Matlab script file solves the coupled nonlinear Schrodinger equations of
01J.XfCd6 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
d 9|u~3 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
ty ~U~ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
< M=K!k {,m!%FDL %fid=fopen('e21.dat','w');
_<8n]0lX3 N = 128; % Number of Fourier modes (Time domain sampling points)
VH/_0 M1 =3000; % Total number of space steps
"- 9YvB# J =100; % Steps between output of space
e> [QF+e)y T =10; % length of time windows:T*T0
W;1H yk T0=0.1; % input pulse width
Z1&8 U=pax MN1=0; % initial value for the space output location
x|Dj dt = T/N; % time step
&wJ"9pQ~6E n = [-N/2:1:N/2-1]'; % Index
<B)lV'!Bd t = n.*dt;
F~m tE8 B: u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
MxY CMe4S[ u20=u10.*0.0; % input to waveguide 2
Ut<_D8Tzx u1=u10; u2=u20;
j%lW+ [% U1 = u1;
W!{uEH{%l U2 = u2; % Compute initial condition; save it in U
/<@oUv ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
rl4-nA w=2*pi*n./T;
OHB!ec6W g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
"|hmiMdGB L=4; % length of evoluation to compare with S. Trillo's paper
! !9V0[ dz=L/M1; % space step, make sure nonlinear<0.05
`T ab'7 for m1 = 1:1:M1 % Start space evolution
mesR )fTI u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
>y1/*)O9~ u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
h5~tsd}OU ca1 = fftshift(fft(u1)); % Take Fourier transform
yY!jkRq%w ca2 = fftshift(fft(u2));
V r y# c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
'1 d-N[ c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
SQ@@79A u2 = ifft(fftshift(c2)); % Return to physical space
DY1o!thz) u1 = ifft(fftshift(c1));
$Uzc if rem(m1,J) == 0 % Save output every J steps.
X{)M}WO+r U1 = [U1 u1]; % put solutions in U array
^uYxeQY[ U2=[U2 u2];
)%*uMuF MN1=[MN1 m1];
-IP c;`< z1=dz*MN1'; % output location
KN V$9&Z end
uvT]MgT end
6 ,k} v: hg=abs(U1').*abs(U1'); % for data write to excel
>J4_/p>Qs ha=[z1 hg]; % for data write to excel
=!7yX ;| t1=[0 t'];
Z cc6E2 hh=[t1' ha']; % for data write to excel file
`74A'(u_ %dlmwrite('aa',hh,'\t'); % save data in the excel format
bY#> figure(1)
,#<"VU2 bC waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
yH CBf)N7\ figure(2)
t&n gOF waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
tvP"t{C6, &0M^UvO 非线性超快脉冲耦合的数值方法的Matlab程序 @L`t/OD m~# O
~) 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
= \tg$ 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
QQqWJ q~ "}EydG"= ++ x EMP) ZYg="q0x& % This Matlab script file solves the nonlinear Schrodinger equations
^ G15]Pyw % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
P\SE_ *& % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
`6UW?1_Z5 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
aVd{XVE 2OEO b,` C=1;
q W) ,)i M1=120, % integer for amplitude
--y .q~d M3=5000; % integer for length of coupler
R:=i/P/ N = 512; % Number of Fourier modes (Time domain sampling points)
lepgmQ| oY dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
%A?Ym33 T =40; % length of time:T*T0.
Dg \fjuK9 dt = T/N; % time step
jh9^5"vQ n = [-N/2:1:N/2-1]'; % Index
RoP z?,u t = n.*dt;
74QWGw`, ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
Ip|7JL0Z w=2*pi*n./T;
(eHvp g1=-i*ww./2;
4u A ;--j g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
s(F^ P g3=-i*ww./2;
8xlj:5;(w P1=0;
?$9C[Kw` P2=0;
LDO@$jg P3=1;
DqbN=[!X~n P=0;
J7$5< for m1=1:M1
W +C\/ p=0.032*m1; %input amplitude
!\^c9Pg|v s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
-4 9OE*uF s1=s10;
v$lP?\P;}X s20=0.*s10; %input in waveguide 2
dX` _Y s30=0.*s10; %input in waveguide 3
rJ K~kKG s2=s20;
sJ25<2/ s3=s30;
EPW
Iu)A p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
P6dIU/w %energy in waveguide 1
!ZH PR:k| p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
}fUV*U:3 %energy in waveguide 2
-fn["R] p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
H;%a1 %energy in waveguide 3
>(p "! for m3 = 1:1:M3 % Start space evolution
^!!@O91T s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
q#F ;GD s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
_"Y; E s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
WADNr8. sca1 = fftshift(fft(s1)); % Take Fourier transform
UPA))Iv> sca2 = fftshift(fft(s2));
Y <I/y sca3 = fftshift(fft(s3));
E XEae ? sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
{])F%Q_#cD sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
Q];+?Pu. sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
aa8W Rf s3 = ifft(fftshift(sc3));
3;@t {rIin s2 = ifft(fftshift(sc2)); % Return to physical space
jI[:` s1 = ifft(fftshift(sc1));
C
3 b end
^;!A`t p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
vH9/}w 2 p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
>n{(2bcFs p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
:TxfkicN\ P1=[P1 p1/p10];
eZk
[6H P2=[P2 p2/p10];
X2/ `EN\ P3=[P3 p3/p10];
K zG8K 6wZ P=[P p*p];
/k l0(=' end
p (:\)HP)R figure(1)
H@.j@l plot(P,P1, P,P2, P,P3);
VrrCW/ o : DCj2" 转自：
http://blog.163.com/opto_wang/
