计算脉冲在非线性耦合器中演化的Matlab 程序 cXx?MF5 @ !0@f'}e % This Matlab script file solves the coupled nonlinear Schrodinger equations of
6/ir("LK % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
TAbd[:2{F % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
o}&TFh T % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
NIcPjo {_0m0
8 %fid=fopen('e21.dat','w');
^nu~q+:+# N = 128; % Number of Fourier modes (Time domain sampling points)
i1]*5;q M1 =3000; % Total number of space steps
T/DKT 1P- J =100; % Steps between output of space
p\]Mf#B T =10; % length of time windows:T*T0
T8&
kxp T0=0.1; % input pulse width
VG*Tdaua~ MN1=0; % initial value for the space output location
$2Y' [Dto\ dt = T/N; % time step
-1Acprr n = [-N/2:1:N/2-1]'; % Index
RG [*:ReB9 t = n.*dt;
)UA$."~O u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
lP *_dt 9 u20=u10.*0.0; % input to waveguide 2
%$/t`'&o- u1=u10; u2=u20;
7%C6hEP/*W U1 = u1;
}J27Y ;Zp9 U2 = u2; % Compute initial condition; save it in U
BsV2Q`(gT ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
}eUeADbC w=2*pi*n./T;
iHoQNog-! g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
S(kj"t*3 L=4; % length of evoluation to compare with S. Trillo's paper
_-a Q.p ?T dz=L/M1; % space step, make sure nonlinear<0.05
iiS^xqSNCt for m1 = 1:1:M1 % Start space evolution
U)~?/s{v u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
uMl.}t2uYu u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
UR|UGldt_T ca1 = fftshift(fft(u1)); % Take Fourier transform
J-t5kU;L{ ca2 = fftshift(fft(u2));
= h,6/cs c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
fHTqLYd- c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
tZlz0BY! u2 = ifft(fftshift(c2)); % Return to physical space
f/t1@d! u1 = ifft(fftshift(c1));
<11 pk if rem(m1,J) == 0 % Save output every J steps.
v a \ 5
U1 = [U1 u1]; % put solutions in U array
H M yw:? U2=[U2 u2];
bF:]MB^VK MN1=[MN1 m1];
.v<c_~y z1=dz*MN1'; % output location
Kbjt CI7 end
<}S1ZEZcQ end
J(+I` hg=abs(U1').*abs(U1'); % for data write to excel
jE!<]
ha=[z1 hg]; % for data write to excel
#g,JNJ} t1=[0 t'];
5MsE oLg hh=[t1' ha']; % for data write to excel file
|_V i8Ly %dlmwrite('aa',hh,'\t'); % save data in the excel format
x
;V7D5 q figure(1)
]Igd< waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
B0Ql1x#x figure(2)
yi`Z(j; waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
eekp&H $'s "Ka2jw, 非线性超快脉冲耦合的数值方法的Matlab程序 E- ,/@4k @T53%v<5 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
j)IXe 0dMC Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
4:\1S ~WW G0p|44_~t '^f,H1oW 2Cd#~ % This Matlab script file solves the nonlinear Schrodinger equations
&6%%_Lw$ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
6.? Ke8iC % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
L}O_1+b % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
<eRE;8C- b e[KNrO C=1;
S ;DqM;Q M1=120, % integer for amplitude
i = $ ## M3=5000; % integer for length of coupler
2 O\p` ,. N = 512; % Number of Fourier modes (Time domain sampling points)
*:r@-=M3= dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
bDI#' F T =40; % length of time:T*T0.
+Bk d dt = T/N; % time step
Mx<V ;GPm n = [-N/2:1:N/2-1]'; % Index
-V@vY42 t = n.*dt;
zbsdK ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
ud]O'@G< w=2*pi*n./T;
,f0|eu> g1=-i*ww./2;
g{K*EL < g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
(jYHaTL6Y' g3=-i*ww./2;
}C1&}h Z P1=0;
Zcq'u
jU P2=0;
R2 k R P3=1;
4DY\Qv W5 P=0;
l UWX[, for m1=1:M1
(. ~#bl p=0.032*m1; %input amplitude
pyA;%vJn s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
{E *dDv s1=s10;
@[ {9B6NlV s20=0.*s10; %input in waveguide 2
b#;%TbDF s30=0.*s10; %input in waveguide 3
r\J"|{)e s2=s20;
5~&9/ ALk5 s3=s30;
;Z]i$Vi_r p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
*?'n A{a)E %energy in waveguide 1
XB p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
tU2 8l. %energy in waveguide 2
-a:+ h\ K p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
3!_X FV %energy in waveguide 3
5U)Ia>p for m3 = 1:1:M3 % Start space evolution
Fd@n#DR ` s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
(V2~txMh s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
dg[ &5D1Q s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
c#'t][Ii sca1 = fftshift(fft(s1)); % Take Fourier transform
ismx evD sca2 = fftshift(fft(s2));
6Y4sv5G sca3 = fftshift(fft(s3));
D:`b61sWi_ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
~ ,[<R sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
f9FJ:? sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
=6FA(R|QU s3 = ifft(fftshift(sc3));
LWG%]m|C s2 = ifft(fftshift(sc2)); % Return to physical space
WGwpryaya s1 = ifft(fftshift(sc1));
ktlI(#\% end
o6 L eC* p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
UI S\t^pJD p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
]PWK^-4P p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
F+yu[Dh: P1=[P1 p1/p10];
\\Ps*HN P2=[P2 p2/p10];
{%g]Ym= P3=[P3 p3/p10];
QWL$F:9: P=[P p*p];
; S
Re` end
gaFOm9y.e figure(1)
\09m
?;^ plot(P,P1, P,P2, P,P3);
N l~' W OV<'v%_& 转自：
http://blog.163.com/opto_wang/
