计算脉冲在非线性耦合器中演化的Matlab 程序 LmnymcH xsMBC
% This Matlab script file solves the coupled nonlinear Schrodinger equations of
c. 2).Jt, % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
/x1![$oC0 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
U b * wuI % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
9c6gkt9eB 2mGaD \?K %fid=fopen('e21.dat','w');
AQiwugs N = 128; % Number of Fourier modes (Time domain sampling points)
]&pds\ M1 =3000; % Total number of space steps
p ObX42 J =100; % Steps between output of space
O6G0 T =10; % length of time windows:T*T0
-xA2pYz" T0=0.1; % input pulse width
S :<Nc{C MN1=0; % initial value for the space output location
_<OS qE dt = T/N; % time step
p$3sME$L n = [-N/2:1:N/2-1]'; % Index
6 'Worj t = n.*dt;
n@,G8=J? u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
`.Qi?* ^ u20=u10.*0.0; % input to waveguide 2
Evjj"h&0J u1=u10; u2=u20;
\hEN4V[ U1 = u1;
Nu?-0> U2 = u2; % Compute initial condition; save it in U
n4#;k=mA ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
d!
LE{ w=2*pi*n./T;
+y3%3EKs1~ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
d5gR"ja L=4; % length of evoluation to compare with S. Trillo's paper
k+ty>bP= dz=L/M1; % space step, make sure nonlinear<0.05
cZ2kYn 8 for m1 = 1:1:M1 % Start space evolution
L$E{ycn u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
T"DlT/\ u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
-K3^BZ H I ca1 = fftshift(fft(u1)); % Take Fourier transform
*=I}Qh( 1 ca2 = fftshift(fft(u2));
|='z{WS c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
c5D) c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
@8pp EFw u2 = ifft(fftshift(c2)); % Return to physical space
W)f/0QX}W u1 = ifft(fftshift(c1));
r 0iK if rem(m1,J) == 0 % Save output every J steps.
zIu
E9l U1 = [U1 u1]; % put solutions in U array
SX#
e:_ U2=[U2 u2];
a+Kj1ix MN1=[MN1 m1];
yooX$ z1=dz*MN1'; % output location
<BMXCk end
E{Ov>osq end
' DL`Ee\ hg=abs(U1').*abs(U1'); % for data write to excel
xk5@d6Y{r ha=[z1 hg]; % for data write to excel
pw)| |Q t1=[0 t'];
<#u=[_H hh=[t1' ha']; % for data write to excel file
\Ani}qQ%| %dlmwrite('aa',hh,'\t'); % save data in the excel format
dE4L=sTEsy figure(1)
q$B>|y U waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
uYs5f.! ` figure(2)
rzm:Yx waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
ZL&g_jC HiR[(5vnf 非线性超快脉冲耦合的数值方法的Matlab程序 5n9B?T8C &)AVzN+*h 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
eQp4|rf Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
2[O&NdP\Zk PE3vQH=t~ 8{^WY7.' jw^<IMAG\8 % This Matlab script file solves the nonlinear Schrodinger equations
}}\vV} s % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
XH }\15X % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
QSszn`e % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
8TLgNQP QD:{U8YbF$ C=1;
o4 K ~ M1=120, % integer for amplitude
2ZG5<"DQ" M3=5000; % integer for length of coupler
GS a [
oh N = 512; % Number of Fourier modes (Time domain sampling points)
,}EC F> dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
4, CXJ2 T =40; % length of time:T*T0.
XkXHGDEf 1 dt = T/N; % time step
-xEXN[\S n = [-N/2:1:N/2-1]'; % Index
1p/3 !1 t = n.*dt;
ZaV8qAsP ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
kT"Kyd w=2*pi*n./T;
7Z\--=;|[: g1=-i*ww./2;
MHX?@.
v g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
qUob?|
^ g3=-i*ww./2;
X.f> '0i P1=0;
R3;T k^5A P2=0;
ND>r#(_\ P3=1;
ifUGY[ L P=0;
2[ RoxK m for m1=1:M1
$o0 iLFIX/ p=0.032*m1; %input amplitude
1m:XR0 P s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
4W#vP s1=s10;
ER5gmmVP@p s20=0.*s10; %input in waveguide 2
GVYBa_gx s30=0.*s10; %input in waveguide 3
vY${;#~| s2=s20;
qln3 k` s3=s30;
<`B,R*H{ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
gv)P]{%^ %energy in waveguide 1
/H(?
2IHC p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
jV>raCK_ %energy in waveguide 2
j/r]wd"aUS p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
ES.fOdx %energy in waveguide 3
bm?sbE for m3 = 1:1:M3 % Start space evolution
(Pf+0,2 s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
7=TF .TW)
s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
k.vBj~xU s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
K]s[5 sca1 = fftshift(fft(s1)); % Take Fourier transform
TMlP*d# sca2 = fftshift(fft(s2));
Q<^Tl(`/N? sca3 = fftshift(fft(s3));
z(_Ss@ $ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
ur$
_ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
K9$ >Yxe| sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
P"y`A}Bx s3 = ifft(fftshift(sc3));
%C~1^9uq s2 = ifft(fftshift(sc2)); % Return to physical space
+*ZO&yJQ^< s1 = ifft(fftshift(sc1));
@z4*.S&tz end
\ 3wfwu.q p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
tiB_a}5IB p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
4e~A1- p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
\W1,F6&j P1=[P1 p1/p10];
D coX+8 7 P2=[P2 p2/p10];
=j5MFX.-o P3=[P3 p3/p10];
n>+mL"hs P=[P p*p];
Xjo5v*P u end
?s\:hNNY figure(1)
>}`:Ac plot(P,P1, P,P2, P,P3);
! ;i`PPRwk M dZ&A}S 转自：
http://blog.163.com/opto_wang/
