计算脉冲在非线性耦合器中演化的Matlab 程序 ym]12PAU5 7_=7 ;PQ< % This Matlab script file solves the coupled nonlinear Schrodinger equations of
]* #k|>Fl % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
9s.x% m, % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
T?DX|?2X % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Yn ~N;VUA CnXl 7" %fid=fopen('e21.dat','w');
- &7\do< N = 128; % Number of Fourier modes (Time domain sampling points)
~Z{IdE M1 =3000; % Total number of space steps
]Qu.-F#g J =100; % Steps between output of space
g?9IS,Gp T =10; % length of time windows:T*T0
I6.!0.G T0=0.1; % input pulse width
AZ HZUd4 MN1=0; % initial value for the space output location
#W]4aZ 1 dt = T/N; % time step
Uo~-^w} n = [-N/2:1:N/2-1]'; % Index
dF`\ewRFn t = n.*dt;
e@`"V,i u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
US.7:S-r" u20=u10.*0.0; % input to waveguide 2
&*e( u1=u10; u2=u20;
CyWMr/' U1 = u1;
2 #XYR>[ U2 = u2; % Compute initial condition; save it in U
`Z' h[-2` ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
b3vPGR w=2*pi*n./T;
2_i9
q>I g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
6Hh\y s L=4; % length of evoluation to compare with S. Trillo's paper
gZg5O n dz=L/M1; % space step, make sure nonlinear<0.05
/uNg ftj for m1 = 1:1:M1 % Start space evolution
#+Pk_? u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
(b*PDhl`+ u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
3=
q,k<=L ca1 = fftshift(fft(u1)); % Take Fourier transform
'G#T 6B! ca2 = fftshift(fft(u2));
fPA5]a9 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
C&1()U c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
^z^zsNx u2 = ifft(fftshift(c2)); % Return to physical space
ov9+6'zya u1 = ifft(fftshift(c1));
r](%9Y if rem(m1,J) == 0 % Save output every J steps.
P@xb U1 = [U1 u1]; % put solutions in U array
8NUVHcB6 U2=[U2 u2];
z2
m(<zb MN1=[MN1 m1];
HT%
=o}y z1=dz*MN1'; % output location
2C & G' @> end
lG>, &( end
h,palP6^ hg=abs(U1').*abs(U1'); % for data write to excel
j MAZ4M ha=[z1 hg]; % for data write to excel
X9S` #N t1=[0 t'];
~CRd0T[^ hh=[t1' ha']; % for data write to excel file
*Bm 7>g6 %dlmwrite('aa',hh,'\t'); % save data in the excel format
w Jr5[p*M figure(1)
kLfk2A;' i waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
YTk "'q- figure(2)
oR1H J2>Z1 waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
6 o!*bWh dln1JZ! 非线性超快脉冲耦合的数值方法的Matlab程序 ;WqWD-C d OYEl<!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。
})#SjFq<V 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
fK?/o]vq c(j|xQ\pE Af`qe+0E +5k^- % This Matlab script file solves the nonlinear Schrodinger equations
7%0V ?+]P % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
%p(!7FDE2n % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
#sRkKl| % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
ih[! v"bv <=g{E- C=1;
L#>^R M1=120, % integer for amplitude
6A ;,Ph2 M3=5000; % integer for length of coupler
{}A1[ Y| N = 512; % Number of Fourier modes (Time domain sampling points)
xaw)iC[gI{ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
hUo}n>Aa T =40; % length of time:T*T0.
u;/5@ADW dt = T/N; % time step
}NgevsV>; n = [-N/2:1:N/2-1]'; % Index
9()d7Y#d/` t = n.*dt;
v *[oe ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
|vUjoa'.7E w=2*pi*n./T;
Zai:?%^ g1=-i*ww./2;
1I#]OY#> g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
8 rE UZk g3=-i*ww./2;
\v]esIP5R' P1=0;
5IJm_oy P2=0;
+~{Honj[ P3=1;
|3SM P=0;
d&x #9ka for m1=1:M1
gT&s &0_7 p=0.032*m1; %input amplitude
t"Tv(W?_ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
" R5! VV s1=s10;
.gP}/dj s20=0.*s10; %input in waveguide 2
sWKe5@-o0 s30=0.*s10; %input in waveguide 3
HVLj(_
A s2=s20;
AS-%I+ A s3=s30;
< u Kd)l p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
O>tz;RU %energy in waveguide 1
g-8D1.U p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
cqSo%a2 %energy in waveguide 2
(l_/ HQ32 p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
vP. ^j7wB %energy in waveguide 3
A(84cmq!q for m3 = 1:1:M3 % Start space evolution
Py^fWQ5I~% s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
Ss$/Bh>hN s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
6!T9VL\=H s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
" IuHSjP sca1 = fftshift(fft(s1)); % Take Fourier transform
A}l+BIt sca2 = fftshift(fft(s2));
|1/UC"f sca3 = fftshift(fft(s3));
SF. Is=b sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
ZT
d)4f sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
3I.0jA#T&/ sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
G}V5PEF]` s3 = ifft(fftshift(sc3));
L}hc|(: s2 = ifft(fftshift(sc2)); % Return to physical space
>X58 zlxk s1 = ifft(fftshift(sc1));
NfsF'v end
@ i*It Hk p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
?qJt 4Om p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
, #nYH D p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
jnzOTS P1=[P1 p1/p10];
J-U5_>S P2=[P2 p2/p10];
!l|fzS8g P3=[P3 p3/p10];
ZFFKv P=[P p*p];
.EB'n{zxd end
4^3lG1^YY figure(1)
duq(K9S plot(P,P1, P,P2, P,P3);
N% !TFQf ;_iDiL C; 转自：
http://blog.163.com/opto_wang/
