计算脉冲在非线性耦合器中演化的Matlab 程序 bh+ R9~ %tQIKjsVaY % This Matlab script file solves the coupled nonlinear Schrodinger equations of
2hU4g
e?6 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
sU+~#K$ b % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
eZ
]6 Q % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
i<=@ 7W |wK)(s %fid=fopen('e21.dat','w');
qn4Dm ^ N = 128; % Number of Fourier modes (Time domain sampling points)
<_42h|- M1 =3000; % Total number of space steps
/dWuHS J =100; % Steps between output of space
_KD(V2 W T =10; % length of time windows:T*T0
S93N srBbY T0=0.1; % input pulse width
vz@QGgQ9~2 MN1=0; % initial value for the space output location
lG jdDqi dt = T/N; % time step
=YPWt>\a} n = [-N/2:1:N/2-1]'; % Index
S:^Q( w7 t = n.*dt;
pRt )B`# u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
RsrZ1dhPvV u20=u10.*0.0; % input to waveguide 2
_V Y ] u1=u10; u2=u20;
sy>P n U1 = u1;
p&ow\A O U2 = u2; % Compute initial condition; save it in U
^!kv gm<{$ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
cl)MI,/> w=2*pi*n./T;
JTz1M~ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
B5tJ|3! L=4; % length of evoluation to compare with S. Trillo's paper
%iJ6;V 4 dz=L/M1; % space step, make sure nonlinear<0.05
h ]MSjC.X for m1 = 1:1:M1 % Start space evolution
IP{Cj= u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
dIM:U :c u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
#2cH.`ty ca1 = fftshift(fft(u1)); % Take Fourier transform
^P{'l ^CVX ca2 = fftshift(fft(u2));
o8Bo %OjE c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
$F/&/Aa c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
EDnmYaa)dZ u2 = ifft(fftshift(c2)); % Return to physical space
;g W~+hW ^ u1 = ifft(fftshift(c1));
;7 IVg[f if rem(m1,J) == 0 % Save output every J steps.
6] <?+#uQ U1 = [U1 u1]; % put solutions in U array
/Ee0S8!Z!1 U2=[U2 u2];
Odbjl[>k MN1=[MN1 m1];
U *6-Y %7 z1=dz*MN1'; % output location
1noFXzeU3 end
4)XN1r: end
jh g!K.A hg=abs(U1').*abs(U1'); % for data write to excel
G& 3j/5V ha=[z1 hg]; % for data write to excel
=U,;/f t1=[0 t'];
! ;R{- hh=[t1' ha']; % for data write to excel file
*DG*&Me %dlmwrite('aa',hh,'\t'); % save data in the excel format
?BWWb
figure(1)
lgnF\) waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
*riGi figure(2)
T /] ayc: waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
`
0\hm` mTs[3opg 非线性超快脉冲耦合的数值方法的Matlab程序 ShSh/0
.Hgiru& 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。
qrt+{5/t 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
MhJ`> .z1
,'ndQ{\9 <|m"Q!f e?f[t*td % This Matlab script file solves the nonlinear Schrodinger equations
I E ,g % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
1TbKnmTx % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
jj.yB#T % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
aC%0jJ<eo pq4+n'uO C=1;
c)$/Uu M1=120, % integer for amplitude
:$9 4y{ M3=5000; % integer for length of coupler
&"L3U N = 512; % Number of Fourier modes (Time domain sampling points)
bk>M4l61 dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
G1P m!CM= T =40; % length of time:T*T0.
moc_}( dt = T/N; % time step
?=PQQx2_*u n = [-N/2:1:N/2-1]'; % Index
MJ7!f+!5
t = n.*dt;
rc;| ,\ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
$jw!Dr E w=2*pi*n./T;
g8v N^nQf[ g1=-i*ww./2;
u' r ;-|7 g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
DU[UGJg g3=-i*ww./2;
?m~;*wn% P1=0;
6.By)L P2=0;
QY{f= P3=1;
C6/, -?%) P=0;
2&=;$2?} for m1=1:M1
40 :YJ_n p=0.032*m1; %input amplitude
b"f 4}b s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
b$B5sKQ s1=s10;
\!631FcQ s20=0.*s10; %input in waveguide 2
35c9 c(A s30=0.*s10; %input in waveguide 3
6*]Kow? s2=s20;
zlXkD~GV s3=s30;
"+ )ey> _ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
s2d;601*b %energy in waveguide 1
YjsaTdZ!& p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
#b{ otc) %energy in waveguide 2
.JH3,L"S^ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
a?D\H5TF- %energy in waveguide 3
Z9! goI for m3 = 1:1:M3 % Start space evolution
us5`?XeX] s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
S"}FsS;k<? s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
,ciNoP*-~% s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
t#<q O6& B sca1 = fftshift(fft(s1)); % Take Fourier transform
fTH?t_e sca2 = fftshift(fft(s2));
qdcCX:Z< sca3 = fftshift(fft(s3));
/] R]7 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
FiI N \ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
U2SxRFs >
sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
d B?I ( s3 = ifft(fftshift(sc3));
9{>m04888 s2 = ifft(fftshift(sc2)); % Return to physical space
dnN " s1 = ifft(fftshift(sc1));
VF 6@;5p
end
R;,&CQUl p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
OBj .-jL p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
X|8Y z3:o p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
b@5bN\"x$ P1=[P1 p1/p10];
W'6*$Ron P2=[P2 p2/p10];
o 'yR^` P3=[P3 p3/p10];
J .El& Dev P=[P p*p];
K=!J=R; end
Q&n|tQ*4 figure(1)
+z9; BPw % plot(P,P1, P,P2, P,P3);
g fO.Ky6 <Q szmE 转自：
http://blog.163.com/opto_wang/
