计算脉冲在非线性耦合器中演化的Matlab 程序 Hp
fTuydU ~1{~i B2G % This Matlab script file solves the coupled nonlinear Schrodinger equations of
l o >:S1 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
y+VR D % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
@qsOWx`l$ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
& *& _..5G7%#% %fid=fopen('e21.dat','w');
`,wX&@sN N = 128; % Number of Fourier modes (Time domain sampling points)
l)0yv2[h M1 =3000; % Total number of space steps
{O[ !*+O J =100; % Steps between output of space
fli7Ow?M~ T =10; % length of time windows:T*T0
t2%gS"
[ T0=0.1; % input pulse width
kZ
9n@($B MN1=0; % initial value for the space output location
5YiBw|Z7 " dt = T/N; % time step
W!Rr_'yFe) n = [-N/2:1:N/2-1]'; % Index
9**u\H)P6 t = n.*dt;
vf_pEkx*wD u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
]JHY(H2| u20=u10.*0.0; % input to waveguide 2
xWty2/!h u1=u10; u2=u20;
/^Lo@672 U1 = u1;
xJ|Z]m=d
U2 = u2; % Compute initial condition; save it in U
a% 82I ::t ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
M$LzV}k w=2*pi*n./T;
IRDD
g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
nHF L=4; % length of evoluation to compare with S. Trillo's paper
gq?~*4H dz=L/M1; % space step, make sure nonlinear<0.05
}Qvoms<k for m1 = 1:1:M1 % Start space evolution
;
>>/}Jw\ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
x6*.zo5e u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
s!BZrVM%I` ca1 = fftshift(fft(u1)); % Take Fourier transform
< 'qtqUL\ ca2 = fftshift(fft(u2));
V -9z{ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
y/A<eHLy c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
QmB,~x{j> u2 = ifft(fftshift(c2)); % Return to physical space
C}mWX7<Z. u1 = ifft(fftshift(c1));
9!6yo if rem(m1,J) == 0 % Save output every J steps.
K,GX5c5 U1 = [U1 u1]; % put solutions in U array
b(gcnSzM2 U2=[U2 u2];
kPZ1OSX MN1=[MN1 m1];
s=| &NlO$ z1=dz*MN1'; % output location
\~q cYp end
i(>v~T,( end
^-7{{/ hg=abs(U1').*abs(U1'); % for data write to excel
l{x?i00tAS ha=[z1 hg]; % for data write to excel
fYv{M; t1=[0 t'];
! J@pox-t hh=[t1' ha']; % for data write to excel file
pDx}~IB %dlmwrite('aa',hh,'\t'); % save data in the excel format
/-) |dP figure(1)
kOuQR$9s waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
cY Ee`?* figure(2)
6<A3H$3b waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
_`Sz}Yk h?:Y\DlU' 非线性超快脉冲耦合的数值方法的Matlab程序 0=J69Yd ) N"gW* 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
TS<uB X Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
cB[.ET$ 0#KB.2AP EMejvPnZO
#[#dc]D % This Matlab script file solves the nonlinear Schrodinger equations
>taZw ' % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
yo 0?QRT % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
CSooJ1Ep~' % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
RsDI7v -0doL ^A C=1;
SB[,}h<u1 M1=120, % integer for amplitude
WH$
Ls(' M3=5000; % integer for length of coupler
B1Iq:5nmoS N = 512; % Number of Fourier modes (Time domain sampling points)
t`mLZ
<X dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
$rC`)"t T =40; % length of time:T*T0.
8Lpy `He dt = T/N; % time step
Z vO:!u0+" n = [-N/2:1:N/2-1]'; % Index
9? W38EF t = n.*dt;
.*g;2.-qv& ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
yMa5?]J w=2*pi*n./T;
<cz~q=%v2& g1=-i*ww./2;
G:rM_q9\u g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
~dw l7Qc g3=-i*ww./2;
m"vV=6m| \ P1=0;
*WgP+"h P2=0;
_n{6/ P3=1;
JhDjY8?86 P=0;
Z@8amT;Y for m1=1:M1
qO9_ e p=0.032*m1; %input amplitude
F<w/@ .&m s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
-}juj;IVv s1=s10;
{w^flizY s20=0.*s10; %input in waveguide 2
[P{Xg:0 s30=0.*s10; %input in waveguide 3
\9/n~/{ s2=s20;
es(vWf' s3=s30;
+T^m p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
&/, BFx" %energy in waveguide 1
aV(*BE/@F p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
q#Qr@Jf %energy in waveguide 2
}%R6Su]y p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
CsR~qQ
5 %energy in waveguide 3
uj/le0 for m3 = 1:1:M3 % Start space evolution
]3QQ"HLcp s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
1^Zx-p3J s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
1ck2Gxn s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
6v1#i sca1 = fftshift(fft(s1)); % Take Fourier transform
5#f&WL*U@ sca2 = fftshift(fft(s2));
\aUbBa%! sca3 = fftshift(fft(s3));
}u+R,@l/ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
] @?3,N sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
>k \*NW sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
km<~H w>Z s3 = ifft(fftshift(sc3));
x Hr s2 = ifft(fftshift(sc2)); % Return to physical space
]-fZeyY$ s1 = ifft(fftshift(sc1));
xG}eiUbM` end
cdIy[
1 p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
!P92e1 p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
u%[*;@;9+ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
T)Nis~ P1=[P1 p1/p10];
JrL/LGY P2=[P2 p2/p10];
H[Pb Wy: P3=[P3 p3/p10];
" a"[B' P=[P p*p];
;L rKXp end
nQ(#'9 figure(1)
dF. T6b plot(P,P1, P,P2, P,P3);
VBCj.dw 4GHIRH
C%[ 转自：
http://blog.163.com/opto_wang/
