计算脉冲在非线性耦合器中演化的Matlab 程序 b`lLqV<[cB (}1:]D{)@V % This Matlab script file solves the coupled nonlinear Schrodinger equations of
e[Tu.$f-
% soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
+b9gP\Hke % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
h()Ok9] % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
p#]D-?CM) *2?-6 %fid=fopen('e21.dat','w');
v$P<:M M N = 128; % Number of Fourier modes (Time domain sampling points)
hS( )OY M1 =3000; % Total number of space steps
E1=WH-iA0 J =100; % Steps between output of space
kF1Tg KSd T =10; % length of time windows:T*T0
}o'WR'LX T0=0.1; % input pulse width
~]d3
f MN1=0; % initial value for the space output location
~6<'cun@x dt = T/N; % time step
BE#s@-zR=p n = [-N/2:1:N/2-1]'; % Index
|4slG t = n.*dt;
jMpV c
E# u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
LU7ia[T u20=u10.*0.0; % input to waveguide 2
l{2Y[&% u1=u10; u2=u20;
hxXl0egI U1 = u1;
2b[R^O} U2 = u2; % Compute initial condition; save it in U
8Hdm(> ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
vFz#A/1 w=2*pi*n./T;
"%mu~&Ga g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
}#b[@3/T L=4; % length of evoluation to compare with S. Trillo's paper
gsSUm f1 dz=L/M1; % space step, make sure nonlinear<0.05
hB!>*AsG for m1 = 1:1:M1 % Start space evolution
Xcy Xju#"p u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
6JCq?:#ab u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
:vsF4 ca1 = fftshift(fft(u1)); % Take Fourier transform
oZ/z{` ca2 = fftshift(fft(u2));
[?=Vqd c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
zL%ruWNG c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
HW@r1[Y u2 = ifft(fftshift(c2)); % Return to physical space
ik;S!S\v u1 = ifft(fftshift(c1));
u>K(m))5W3 if rem(m1,J) == 0 % Save output every J steps.
# },4m U1 = [U1 u1]; % put solutions in U array
|e]2 >NjQa U2=[U2 u2];
"u H VX|` MN1=[MN1 m1];
&nRbI:R z1=dz*MN1'; % output location
cl'#nLPz; end
=B/Ac0Y end
8+?|4'\` hg=abs(U1').*abs(U1'); % for data write to excel
@[s+5_9nk ha=[z1 hg]; % for data write to excel
8F;r$i2 t1=[0 t'];
Jtv~n hh=[t1' ha']; % for data write to excel file
*!wBn %dlmwrite('aa',hh,'\t'); % save data in the excel format
Hy*_4r figure(1)
k>'c4ay290 waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
IHrG!owf figure(2)
TA~FP#. waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
-Y{=bZS u $#HPwmd 非线性超快脉冲耦合的数值方法的Matlab程序 &|LP>'H; T\
cJn>kCn 在研究脉冲在非线性耦合器中的演变时,我们需要求解非线性偏微分方程组。在如下的
论文中,我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
ZDhl$m[m 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
CZ~%qPwDw "UVqHW1%K [%1 87dz:D s (hJ * % This Matlab script file solves the nonlinear Schrodinger equations
CkHifmc(u- % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
0o>l+c % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
c:@lR/oe" % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
F.DRGi.i E[nJ'h<h C=1;
v!~ ;QO M1=120, % integer for amplitude
5>nbA8 M3=5000; % integer for length of coupler
&3:U&}I N = 512; % Number of Fourier modes (Time domain sampling points)
fPj*qi dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
?S~@Ea8/M T =40; % length of time:T*T0.
kzb%=EI dt = T/N; % time step
k/`WfSM\. n = [-N/2:1:N/2-1]'; % Index
+YNN$i t = n.*dt;
(v2.8zrJ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
pAY[XN w=2*pi*n./T;
UD+r{s/% g1=-i*ww./2;
$.g)%#h: g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
sT;:V
g3=-i*ww./2;
Tl%n|pc P1=0;
h=7eOK] P2=0;
H*H=a P3=1;
>(9"D8 P=0;
@Q%g#N for m1=1:M1
R3<2Z0lqy p=0.032*m1; %input amplitude
X^%E"{!nU s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
)2YZ [~3 s1=s10;
ZQ_&HmgRy s20=0.*s10; %input in waveguide 2
f'-)
3T s30=0.*s10; %input in waveguide 3
V1
:aR3*! s2=s20;
<8?jn*$;\ s3=s30;
6tDCaB p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
ss4<s
5:y %energy in waveguide 1
|E7)s;}D p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
d=$1Z.] %energy in waveguide 2
M,WC+")Z= p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
yrgb6)]nm@ %energy in waveguide 3
/qeSR3WC for m3 = 1:1:M3 % Start space evolution
`(dRb s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
%CaUC' s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
M9J^;3Lrh s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
F#
a)"$j; sca1 = fftshift(fft(s1)); % Take Fourier transform
L74Sx0nk= sca2 = fftshift(fft(s2));
zB@@Gs> sca3 = fftshift(fft(s3));
BGSqfr1F sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
D,)^l@UP sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
xdV $dDCT sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
{R{Io| s3 = ifft(fftshift(sc3));
LqOjVQxz s2 = ifft(fftshift(sc2)); % Return to physical space
\~{b;$N} s1 = ifft(fftshift(sc1));
S^/:O.X)c, end
{zj<nu p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
zr1,A#BV p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
X"z!52*3] p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
;^cc-bLvF P1=[P1 p1/p10];
P: 3%#d~q P2=[P2 p2/p10];
50Kv4a" P3=[P3 p3/p10];
uJX(s6["= P=[P p*p];
320g!r end
UB7H`)C} figure(1)
Pp9nilb_( plot(P,P1, P,P2, P,P3);
Pqc+p E 4[$D3,A 转自:
http://blog.163.com/opto_wang/