计算脉冲在非线性耦合器中演化的Matlab 程序 w]{NaNIeq1 ?=]*r >a3 % This Matlab script file solves the coupled nonlinear Schrodinger equations of
h|!F'F{ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
R":nG7o % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
cXJtN W@ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Q1Jk t "5-S:+ %fid=fopen('e21.dat','w');
Y.Er!(pz N = 128; % Number of Fourier modes (Time domain sampling points)
='7n M1 =3000; % Total number of space steps
U?6YY` A8 J =100; % Steps between output of space
hr<E%J1k% T =10; % length of time windows:T*T0
#@m*yJg< T0=0.1; % input pulse width
S"iQQV{)Z MN1=0; % initial value for the space output location
NAj1ORy4pX dt = T/N; % time step
X^#.4:>. n = [-N/2:1:N/2-1]'; % Index
)y7SkH| t = n.*dt;
TXi$Q%0W u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
{V!Jj6n u20=u10.*0.0; % input to waveguide 2
eXa a'bTx u1=u10; u2=u20;
/
4K *iq U1 = u1;
nFl=D=50- U2 = u2; % Compute initial condition; save it in U
6 /9h=-w& ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
g#V3u=I8 ~ w=2*pi*n./T;
W?"Z>tgp g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
n
?%3=~9 L=4; % length of evoluation to compare with S. Trillo's paper
(WK $
)f dz=L/M1; % space step, make sure nonlinear<0.05
lHpo/ R : for m1 = 1:1:M1 % Start space evolution
HRx%m1H u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
-K`0`n} u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
-> - ca1 = fftshift(fft(u1)); % Take Fourier transform
Y 962rZ ca2 = fftshift(fft(u2));
=L$};ko c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
] t|KFk!) c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
)S$!36Ni[ u2 = ifft(fftshift(c2)); % Return to physical space
xXK7i\ny u1 = ifft(fftshift(c1));
kRgyvA,*; if rem(m1,J) == 0 % Save output every J steps.
.ukP)r Ge U1 = [U1 u1]; % put solutions in U array
=VlO53Hy{ U2=[U2 u2];
{MKq
Yl{ MN1=[MN1 m1];
YtN oYOB z1=dz*MN1'; % output location
{=7W;uL end
L_jwM ^8 end
(J):
>\a] hg=abs(U1').*abs(U1'); % for data write to excel
=M G ha=[z1 hg]; % for data write to excel
dCcV$BX,K
t1=[0 t'];
WjGv% ^? hh=[t1' ha']; % for data write to excel file
b K % go %dlmwrite('aa',hh,'\t'); % save data in the excel format
UJoWTx figure(1)
gtz!T2% waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
O#7 fkL figure(2)
)^)V yI`O waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
%|Vo Zx ^ 0i$jtCCL( 非线性超快脉冲耦合的数值方法的Matlab程序 U;KHF{Vm 2s
EdN$O 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
@l&5 |Cia Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
-nO('(t o C U8;z ]k{cPK 3OFv_<6 % This Matlab script file solves the nonlinear Schrodinger equations
E[LXZh % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
2Z,;#t % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
AY0o0\6cw % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
X8 b o?0 YFLWkdqAY C=1;
{Y'DUt5j M1=120, % integer for amplitude
itD1r?O{pV M3=5000; % integer for length of coupler
8&ZUkDGkJ N = 512; % Number of Fourier modes (Time domain sampling points)
|82V` CV dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
v{=-#9-4
& T =40; % length of time:T*T0.
>Z|4/PF dt = T/N; % time step
I_#)>%H n = [-N/2:1:N/2-1]'; % Index
#>~$`Sg t = n.*dt;
7z= Ss'O] ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
yN~=3b> w=2*pi*n./T;
c.&vWmLSGE g1=-i*ww./2;
Y!o@"Ct g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
V* fDvr0 g3=-i*ww./2;
;'ts dsu} P1=0;
I|9e4EX{ y P2=0;
C(iA G P3=1;
:":W(O P=0;
PpU : 4;en for m1=1:M1
\s<iM2]Kl p=0.032*m1; %input amplitude
X/i 8$yqv s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
o|alL- s1=s10;
? b8NEVjw s20=0.*s10; %input in waveguide 2
X^9_'T9 s30=0.*s10; %input in waveguide 3
i>,5b1x~ s2=s20;
)KB v[| s3=s30;
+#Ov9b p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
N4fuV?E` %energy in waveguide 1
ZQl[h7c/N p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
0<v~J9i %energy in waveguide 2
c !Pi) p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
7GK| A{r %energy in waveguide 3
{%S1x{U}W- for m3 = 1:1:M3 % Start space evolution
[ (ty{ s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
g-}Vu1w0{6 s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
Q:-H U bB s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
.D4 D!! sca1 = fftshift(fft(s1)); % Take Fourier transform
0yAvA x sca2 = fftshift(fft(s2));
{,s:vPoiA sca3 = fftshift(fft(s3));
3O#7OL68v sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
2[M:WZ.1 sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
mL6/NSSz sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
=n id #<X s3 = ifft(fftshift(sc3));
eX _}KH-Q s2 = ifft(fftshift(sc2)); % Return to physical space
x:l`e:`y9 s1 = ifft(fftshift(sc1));
HNU[W8mg8 end
IUc!nxF# p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
5QS d$J p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
U}Xc@- \ ? p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
z+-k4 P1=[P1 p1/p10];
k,?Y`s P2=[P2 p2/p10];
&]vd7Q.t P3=[P3 p3/p10];
},i? 3dSvl P=[P p*p];
Z Q20IY |, end
5>A3;P figure(1)
79x^zqLb plot(P,P1, P,P2, P,P3);
' R=o ,= f4g(hjETbu 转自：
http://blog.163.com/opto_wang/
