计算脉冲在非线性耦合器中演化的Matlab 程序 ;>?h/tS6 nQc#AFg
% This Matlab script file solves the coupled nonlinear Schrodinger equations of
Era GG"+ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
dDPQDIx % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
G>V6{g2 Q % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
{.:$F 3T p
u(m HB %fid=fopen('e21.dat','w');
jn2=)KBa_ N = 128; % Number of Fourier modes (Time domain sampling points)
*1d Ds^D#| M1 =3000; % Total number of space steps
KG'i#(u[ J =100; % Steps between output of space
! K>iSF< T =10; % length of time windows:T*T0
=j,WQ6 6r3 T0=0.1; % input pulse width
B ?VTIq> MN1=0; % initial value for the space output location
LCHMh6 dt = T/N; % time step
j<<d A[X n = [-N/2:1:N/2-1]'; % Index
;/K2h_=3z t = n.*dt;
cszvt2BI g u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
-* ,CMw u20=u10.*0.0; % input to waveguide 2
<sH}X$/ u1=u10; u2=u20;
\Rny*px U1 = u1;
L80(9Y^xn U2 = u2; % Compute initial condition; save it in U
?"d$SK"6Z ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
VPUVPq~& w=2*pi*n./T;
. ;?!I_` g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
jo`ZuN{ L=4; % length of evoluation to compare with S. Trillo's paper
p-[WpY3 dz=L/M1; % space step, make sure nonlinear<0.05
75^6?#GS for m1 = 1:1:M1 % Start space evolution
":Dm/g u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
,>
zEG u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
|9I)YD ca1 = fftshift(fft(u1)); % Take Fourier transform
E#k{<L YI ca2 = fftshift(fft(u2));
ywa*?3?c c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
/'/I^ ab c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
'.mepxf< f u2 = ifft(fftshift(c2)); % Return to physical space
`S
{&gl u1 = ifft(fftshift(c1));
` R[Hxi if rem(m1,J) == 0 % Save output every J steps.
5'lPXKn+L U1 = [U1 u1]; % put solutions in U array
Ww7Ya]b.k U2=[U2 u2];
A l U^ ,X MN1=[MN1 m1];
A]z*#+Sl z1=dz*MN1'; % output location
9njl,Q: end
cr1x
CPJj end
!/zRw-q3B hg=abs(U1').*abs(U1'); % for data write to excel
v 4ot08 C ha=[z1 hg]; % for data write to excel
6\4-I^=B t1=[0 t'];
!U^{`V jp[ hh=[t1' ha']; % for data write to excel file
0t <nH%N}^ %dlmwrite('aa',hh,'\t'); % save data in the excel format
qkb'@f= figure(1)
X]0>0=^ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
)[Y B & figure(2)
g52a
vG waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
D|;O9iks# r"7n2 非线性超快脉冲耦合的数值方法的Matlab程序 #.Rn6|V/4 sXIYl% d 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。
pCIzpEsRs 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
isQ(O .JhQxXj ht3.e[%'b ~4~`bT 9 % This Matlab script file solves the nonlinear Schrodinger equations
]?Ef0?4 4 % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
}Z!D?( % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
tq3Wga!5 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
*r7v Dc Yd^@Ei9 C=1;
.|UQ) J?s M1=120, % integer for amplitude
u^80NR M3=5000; % integer for length of coupler
G-aR%]7$g N = 512; % Number of Fourier modes (Time domain sampling points)
$<} c[Nm dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
Zi!Ta"}8 T =40; % length of time:T*T0.
$NXP)Lic) dt = T/N; % time step
F@w; .e! n = [-N/2:1:N/2-1]'; % Index
xs$$fPAQ t = n.*dt;
3*b5V<}'| ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
[ERZ".? w=2*pi*n./T;
cnv >&6a) g1=-i*ww./2;
w0pMH p'Y g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
YG p+[|' g3=-i*ww./2;
zw0w. "V
P1=0;
%b W_,b P2=0;
xP;r3u
s P3=1;
C8N)!5(A P=0;
!rvEo =^ for m1=1:M1
)Fw/C u p=0.032*m1; %input amplitude
+.G"oo l s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
qWt}8_ " s1=s10;
t}EM X9SQ s20=0.*s10; %input in waveguide 2
N ##` s30=0.*s10; %input in waveguide 3
' W/M>!X s2=s20;
"q@m6 fs s3=s30;
MK$u }G p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
Tb/TP3 N %energy in waveguide 1
\ mqx ' p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
N.F5)04 %energy in waveguide 2
}pc9uvmIJ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
P]E-Wp'p %energy in waveguide 3
QrZ#<{,J5 for m3 = 1:1:M3 % Start space evolution
C0rf s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
ny={OhP- s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
~Bd=]a$mj s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
H}@:Bri sca1 = fftshift(fft(s1)); % Take Fourier transform
2G8pDvBr sca2 = fftshift(fft(s2));
eim +oms sca3 = fftshift(fft(s3));
C@rGa7 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
.R9Z$Kbq sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
U,
6iT sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
2_o#Gx' s3 = ifft(fftshift(sc3));
:| 7#D,2 s2 = ifft(fftshift(sc2)); % Return to physical space
5= dL` s1 = ifft(fftshift(sc1));
@ [$_cGR7 end
[,% =\%5 p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
Z 6jEj9?O p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
OMGggg p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
1I +9?fa P1=[P1 p1/p10];
)8Va%{j P2=[P2 p2/p10];
NE995; P3=[P3 p3/p10];
<N<Q9}`V P=[P p*p];
"L~(%Nx 3 end
md!6@)S-p figure(1)
_GOSqu!3Y plot(P,P1, P,P2, P,P3);
dWqn7+: |s| }u`(@9 转自：
http://blog.163.com/opto_wang/
