计算脉冲在非线性耦合器中演化的Matlab 程序 N\?iU8w= [% jg;m % This Matlab script file solves the coupled nonlinear Schrodinger equations of
~gc)Ww0(Q % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
o%.cQo=v* % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
rSk $]E ]Z % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
0)NHjKP P
dJ*'@~i %fid=fopen('e21.dat','w');
WJ*DWyd'' N = 128; % Number of Fourier modes (Time domain sampling points)
h:;~)= {"X M1 =3000; % Total number of space steps
QbWD&8T0O J =100; % Steps between output of space
d<Di;5 T =10; % length of time windows:T*T0
]Vsze4>Z[ T0=0.1; % input pulse width
UgP5^3F2 MN1=0; % initial value for the space output location
a
srkuAS dt = T/N; % time step
|&JL6hN n = [-N/2:1:N/2-1]'; % Index
tv2dyC&a t = n.*dt;
OW>U 5 \q u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
_W+TZa@_ u20=u10.*0.0; % input to waveguide 2
" J9+~)e^! u1=u10; u2=u20;
5c#L6 dA) U1 = u1;
,Y!)V U2 = u2; % Compute initial condition; save it in U
'e) t + ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
Oq("E(z+f w=2*pi*n./T;
T^'i+>F!w g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
ZDf9Npe L=4; % length of evoluation to compare with S. Trillo's paper
y Z{YIy~ dz=L/M1; % space step, make sure nonlinear<0.05
O 6pjuhMx for m1 = 1:1:M1 % Start space evolution
Yp L}R# u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
#FcYJH u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
y+PukHY ca1 = fftshift(fft(u1)); % Take Fourier transform
u{ng\d*KE} ca2 = fftshift(fft(u2));
it,%T)2H c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
(F)zj< {f c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
nxt1Y04,H u2 = ifft(fftshift(c2)); % Return to physical space
LP ~$7a u1 = ifft(fftshift(c1));
[Y*UCFhI0 if rem(m1,J) == 0 % Save output every J steps.
qfu;X-$4 U1 = [U1 u1]; % put solutions in U array
=mZw71, U2=[U2 u2];
k"Is.[I?^ MN1=[MN1 m1];
0 kkiS 3T z1=dz*MN1'; % output location
rT#QA=YB end
iT%UfN/q=I end
}fhVn;~}8 hg=abs(U1').*abs(U1'); % for data write to excel
5s>9 v ha=[z1 hg]; % for data write to excel
+a|4XyN t1=[0 t'];
YS ]RG/' hh=[t1' ha']; % for data write to excel file
T:ck/:ZH %dlmwrite('aa',hh,'\t'); % save data in the excel format
W% P&o}' figure(1)
j% nd waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
f,1rmX1 figure(2)
ji2#O. waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
YJ9 _cA'A @s Dd:> t 非线性超快脉冲耦合的数值方法的Matlab程序 W+#?3s[ FV GgtL./m 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
`{/=i| 6 Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
DW-LkgfA >#ou8}0 N
8OPeY Y /+ D4^ L % This Matlab script file solves the nonlinear Schrodinger equations
~t}:vGD j % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
X;1q1X)K % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
xv2;h4{< % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
_EY :vv HCu1vjU(] C=1;
a'\`Mi@rb M1=120, % integer for amplitude
1>2397 M3=5000; % integer for length of coupler
=nsY[ s< N = 512; % Number of Fourier modes (Time domain sampling points)
7Ct m({I- dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
0Zq" - T =40; % length of time:T*T0.
rf~Ss< dt = T/N; % time step
h {m]n! n = [-N/2:1:N/2-1]'; % Index
O<K r6+
- t = n.*dt;
;?&;I! ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
rYLNV!_ w=2*pi*n./T;
OYKV* g1=-i*ww./2;
HGKm?'[' g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
-or9!:8 g3=-i*ww./2;
1a' JN e$ P1=0;
}QI*Ns P2=0;
Q.fBuF P3=1;
s:_5p`w> P=0;
&M2x` for m1=1:M1
&a0%7ea`.S p=0.032*m1; %input amplitude
''6"Xi|5 s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
?G{fF
H s1=s10;
6!'yU=Z ` s20=0.*s10; %input in waveguide 2
Tx xc-$z s30=0.*s10; %input in waveguide 3
U` U/|@6 s2=s20;
FYj3 !
H s3=s30;
)SQ g p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
52 ~k:"c %energy in waveguide 1
ux }DWrR p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
vQ h'C. %energy in waveguide 2
hImCy9i} p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
6nDx;x&Q %energy in waveguide 3
]gEfm~Y V for m3 = 1:1:M3 % Start space evolution
' ZJ6p0 s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
N >z8\y s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
OJK/> s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
Vg3&:g5 / sca1 = fftshift(fft(s1)); % Take Fourier transform
!6KE W, sca2 = fftshift(fft(s2));
kju:/kY A sca3 = fftshift(fft(s3));
2H /a&uo@n sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
itvwmI,m\ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
k.0C*3 ' sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
|N g[^ s3 = ifft(fftshift(sc3));
D^u{zZy@e s2 = ifft(fftshift(sc2)); % Return to physical space
$ D89|sy s1 = ifft(fftshift(sc1));
t EeMl =u end
DXiD>1( q p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
8}0
D? p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
&a:aW;^A7 p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
gV7o
eZ5 P1=[P1 p1/p10];
:Y'nye3: P2=[P2 p2/p10];
D9Z5g3s7R P3=[P3 p3/p10];
xq{4i|d) P=[P p*p];
f]lDJ?+
M end
u>E+HxUJ figure(1)
cnsGP*w plot(P,P1, P,P2, P,P3);
(UM+?]Qwy F&P)mbz1 转自：
http://blog.163.com/opto_wang/
