计算脉冲在非线性耦合器中演化的Matlab 程序 P-ri=E}> +-E~6^> % This Matlab script file solves the coupled nonlinear Schrodinger equations of
2Ry1b+\ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
D@!=d@V. % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
i;!H!-sM % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
IpP~Uz ^h{)Gf,+\ %fid=fopen('e21.dat','w');
1KjU ]
r2 N = 128; % Number of Fourier modes (Time domain sampling points)
rk)##) M1 =3000; % Total number of space steps
sg+uBCGB J =100; % Steps between output of space
Z!U)I-x& T =10; % length of time windows:T*T0
>3c@x T0=0.1; % input pulse width
ezPz<iZ\N MN1=0; % initial value for the space output location
~#kT_*sw) dt = T/N; % time step
UKM2AZ0lb n = [-N/2:1:N/2-1]'; % Index
uL[.ND2._& t = n.*dt;
qL,tYJ<m% u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
dDF
.qXq. u20=u10.*0.0; % input to waveguide 2
AE} )o)B u1=u10; u2=u20;
OK\A</8r U1 = u1;
sP ls
zC[ U2 = u2; % Compute initial condition; save it in U
H"qOSf{ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
yz0zFfiX w=2*pi*n./T;
Yot?=T};3{ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
R58-wUto L=4; % length of evoluation to compare with S. Trillo's paper
'Y]mOD^p dz=L/M1; % space step, make sure nonlinear<0.05
)HX|S-qRU= for m1 = 1:1:M1 % Start space evolution
TC<@e<-%Sq u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
1AU#%wIEP u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
R+Y4| ca1 = fftshift(fft(u1)); % Take Fourier transform
{l |E:>Q2 ca2 = fftshift(fft(u2));
!E T~KL! c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
fJ ,1Ef;Z c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
",!1m7[wF u2 = ifft(fftshift(c2)); % Return to physical space
J9=m]R8T u1 = ifft(fftshift(c1));
9]e V?yoA8 if rem(m1,J) == 0 % Save output every J steps.
yrR1[aT U1 = [U1 u1]; % put solutions in U array
Q:5KZm[ [ U2=[U2 u2];
l&[;rh MN1=[MN1 m1];
B9wPU1 z1=dz*MN1'; % output location
vBog0KD);s end
A\#iXOd end
$ibuWb"a hg=abs(U1').*abs(U1'); % for data write to excel
hEw-
O;T0 ha=[z1 hg]; % for data write to excel
CP6LHkM9 t1=[0 t'];
v'BZs hh=[t1' ha']; % for data write to excel file
,u/aT5\_ %dlmwrite('aa',hh,'\t'); % save data in the excel format
f aLtdQi figure(1)
-N"&/) waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
yR4|S2D3xn figure(2)
lv]hTH 4T waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
:hM/f &-mX , 非线性超快脉冲耦合的数值方法的Matlab程序 SI=yI- 3K_A<j: 在研究脉冲在非线性耦合器中的演变时,我们需要求解非线性偏微分方程组。在如下的
论文中,我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
A*um{E+ Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
qkC/\![@ ,dx3zBI C?2'+K #b~JDO( % This Matlab script file solves the nonlinear Schrodinger equations
46 PoM % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
,13Lq- % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
/FIE:Io % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
W]nSR RWco A$w4PVS C=1;
PnoPbk[< M1=120, % integer for amplitude
|M+<m">E M3=5000; % integer for length of coupler
)LyojwY_g N = 512; % Number of Fourier modes (Time domain sampling points)
o";Z$tAJkC dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
rSJ9v: T =40; % length of time:T*T0.
WH= EPOR, dt = T/N; % time step
+gLPhX:` n = [-N/2:1:N/2-1]'; % Index
`+uhy, t = n.*dt;
$k2*[sn, ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
3#TV5+x*"` w=2*pi*n./T;
AU$Uxwz4 g1=-i*ww./2;
<^lRUw g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
K5XK%Gl" g3=-i*ww./2;
=|YxDas P1=0;
+9")KQT P2=0;
t8dm)s[r8 P3=1;
sx`O8t P=0;
QI3Nc8t_2 for m1=1:M1
pi
,eIm p=0.032*m1; %input amplitude
qk;{cfzHA s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
E8~}PQW:I s1=s10;
>mjNmh7 s20=0.*s10; %input in waveguide 2
_C`K*u
6Z< s30=0.*s10; %input in waveguide 3
l'TWkQ- s2=s20;
Yk5}`d!: s3=s30;
r}jGUe}d p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
n;:rf 7hGY %energy in waveguide 1
aG92ay p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
6#Q K%[1!> %energy in waveguide 2
J;f!!<l\ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
|lkNi %energy in waveguide 3
7Ddaf> for m3 = 1:1:M3 % Start space evolution
yn/rW$ s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
1Q.\s_2 s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
E,f>1meN= s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
a!u
rew# sca1 = fftshift(fft(s1)); % Take Fourier transform
%C=]1Q=T) sca2 = fftshift(fft(s2));
pe{;~-|6 sca3 = fftshift(fft(s3));
NwZ@#D#[ Y sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
cJL'$`gWf sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
~mR'Q-hi< sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
npNB{J[ s3 = ifft(fftshift(sc3));
6A=8+R'`F s2 = ifft(fftshift(sc2)); % Return to physical space
4M^G`WA}t9 s1 = ifft(fftshift(sc1));
HVC>9_:] end
(1NA p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
44F`$.v96 p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
\R3H+W p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
mb!9&&2-t P1=[P1 p1/p10];
r{rQu-|. P2=[P2 p2/p10];
^*fxR]Y P3=[P3 p3/p10];
,-OCc!7K P=[P p*p];
3hK#'."`N end
W[}s o6 figure(1)
T0]*{k(FR plot(P,P1, P,P2, P,P3);
w&x!,yd; {je-I9%OK 转自:
http://blog.163.com/opto_wang/