计算脉冲在非线性耦合器中演化的Matlab 程序 b,C aWg o
LvZ % This Matlab script file solves the coupled nonlinear Schrodinger equations of
'_V2!?+RU+ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
{~F4WjHJp % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
;UxP
Kpl % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
utIX %0 l,kUhZ@W %fid=fopen('e21.dat','w');
0( S"{Ov N = 128; % Number of Fourier modes (Time domain sampling points)
1PpyV f M1 =3000; % Total number of space steps
Y./2Ely J =100; % Steps between output of space
~J P=T T =10; % length of time windows:T*T0
m@^ 1 JlH T0=0.1; % input pulse width
>(;{C<6|^ MN1=0; % initial value for the space output location
/Z$&pqs! dt = T/N; % time step
({q?d[q[ n = [-N/2:1:N/2-1]'; % Index
%HL*c = t = n.*dt;
Y*UA, <- u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
Z:*76PP, u20=u10.*0.0; % input to waveguide 2
(2=Zm@Zp f u1=u10; u2=u20;
1&-
</G# U1 = u1;
( vca&wI! U2 = u2; % Compute initial condition; save it in U
8|" XSN ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
v61[ .oS w=2*pi*n./T;
7Zh~lM
g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
1~PV[2a L=4; % length of evoluation to compare with S. Trillo's paper
THS.GvT9[ dz=L/M1; % space step, make sure nonlinear<0.05
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for m1 = 1:1:M1 % Start space evolution
^pYxKU_O u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
& 9<+;*/ u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
,]d,-)KX8 ca1 = fftshift(fft(u1)); % Take Fourier transform
Wr( y)D<y} ca2 = fftshift(fft(u2));
8@tPm$ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
bdc&1I$ c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
WS`qVL]^& u2 = ifft(fftshift(c2)); % Return to physical space
q,+yqrt u1 = ifft(fftshift(c1));
3J5!oF{H if rem(m1,J) == 0 % Save output every J steps.
fP.
6HF_p_ U1 = [U1 u1]; % put solutions in U array
HbxL:~:}J U2=[U2 u2];
hK_LEwd; MN1=[MN1 m1];
K|Di1)7=/ z1=dz*MN1'; % output location
sPR1?:0: end
sn)3Z A end
{o>j6RS\ hg=abs(U1').*abs(U1'); % for data write to excel
f e9LEM8j ha=[z1 hg]; % for data write to excel
c|#8T*`C t1=[0 t'];
fy Byz=pl hh=[t1' ha']; % for data write to excel file
o/+13C %dlmwrite('aa',hh,'\t'); % save data in the excel format
r_-_a(1R: figure(1)
o<|P9#(U" waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
ekWePL;rR2 figure(2)
b4QI)z waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
y $_eCmq *exS6@N] 非线性超快脉冲耦合的数值方法的Matlab程序 o*o/q],C9- HxIIO[h 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
E6pMT^{K Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
JW3B'_0 rv|)n>m s;6 CExH Qx+%"YO % This Matlab script file solves the nonlinear Schrodinger equations
x;8A!8w % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
H{=21\a\ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
!lj| cT9 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
<c2'0I > Z7= `VNHc C=1;
#~< 0t(3Q M1=120, % integer for amplitude
_t Yx~J2.Q M3=5000; % integer for length of coupler
1*@'-mj N = 512; % Number of Fourier modes (Time domain sampling points)
n:{qC{D-qS dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
U
15H2-` T =40; % length of time:T*T0.
;n&t>pBM dt = T/N; % time step
@
<
Q|5 n = [-N/2:1:N/2-1]'; % Index
5nKj
)RH7M t = n.*dt;
!Rhl f.x ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
XBp? w w=2*pi*n./T;
]% IT|/;9Y g1=-i*ww./2;
U
G~b a g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
v%iof1 T'
g3=-i*ww./2;
p_${Nj P1=0;
[<
&oF P2=0;
Ljp%CI[i P3=1;
C<m{*C-`a P=0;
V{:A3C41 for m1=1:M1
pUV/ Ul] p=0.032*m1; %input amplitude
4*Hgv:0?kI s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
4\4FolsK s1=s10;
- UOj>{- s20=0.*s10; %input in waveguide 2
p(/dBt[3k s30=0.*s10; %input in waveguide 3
\cUC9/
b s2=s20;
)|DM~%$QM s3=s30;
E: $P=%b p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
mj KS{ %energy in waveguide 1
r} mb Xvn p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
J
/f
%energy in waveguide 2
.Z JRO>S p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
"saUai4z %energy in waveguide 3
UH TvCc for m3 = 1:1:M3 % Start space evolution
&GB:|I'%7 s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
L 8dc(Z%v s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
Wb?8j M s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
>o7n+Rb: sca1 = fftshift(fft(s1)); % Take Fourier transform
<c qbUL sca2 = fftshift(fft(s2));
P8*=Ls+-F sca3 = fftshift(fft(s3));
2gCX}4^3b sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
{ZI)nQ{ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
*rIk:FehLB sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
S|]X'f s3 = ifft(fftshift(sc3));
Zw ^kmSL" s2 = ifft(fftshift(sc2)); % Return to physical space
#]ypHVE s1 = ifft(fftshift(sc1));
cM$ P`{QrM end
_YLf L p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
to=y#$_ p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
( ?(zH3 p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
:"xzj< ( P1=[P1 p1/p10];
"3)4vuX@;c P2=[P2 p2/p10];
eFL=G% P3=[P3 p3/p10];
/p+>NZ"b P=[P p*p];
&iA?+kV end
2IKnhBSV3 figure(1)
,z-}t&
_t plot(P,P1, P,P2, P,P3);
s0k`p<q " 6u s#T 转自：
http://blog.163.com/opto_wang/
