计算脉冲在非线性耦合器中演化的Matlab 程序 ]5QXiF8` ]!sCWR % This Matlab script file solves the coupled nonlinear Schrodinger equations of
E"p _!! 1 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
HLqN=vE6 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
1 +-Go}I % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
~ L%,9 kZG; \ %fid=fopen('e21.dat','w');
n=JV*h0 N = 128; % Number of Fourier modes (Time domain sampling points)
ga\ s5
M1 =3000; % Total number of space steps
$rk=#;6]v; J =100; % Steps between output of space
Q.eD:@%iE T =10; % length of time windows:T*T0
3]9wfT%d T0=0.1; % input pulse width
qzO Rv MN1=0; % initial value for the space output location
qvo!nr7 dt = T/N; % time step
w<THPFFF" n = [-N/2:1:N/2-1]'; % Index
9 #1?Pt^{< t = n.*dt;
'[8w8,v( u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
/*fx`0mY) u20=u10.*0.0; % input to waveguide 2
{a V,h@> u1=u10; u2=u20;
LNR1 YC1c U1 = u1;
( z)#}TC U2 = u2; % Compute initial condition; save it in U
> O?<? ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
zQ,M795@EA w=2*pi*n./T;
"{E%Y* g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
q] pHD})O L=4; % length of evoluation to compare with S. Trillo's paper
Z]{=Jy !F dz=L/M1; % space step, make sure nonlinear<0.05
Ws2?sn#x for m1 = 1:1:M1 % Start space evolution
PB"=\>]`N u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
|ITCw$T u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
V\L%*6O ca1 = fftshift(fft(u1)); % Take Fourier transform
H)Me!^@[D ca2 = fftshift(fft(u2));
@N<h`vDa c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
A9]& w c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
KwaxNb5 u2 = ifft(fftshift(c2)); % Return to physical space
'J0I$-QYk u1 = ifft(fftshift(c1));
ws QuJrG if rem(m1,J) == 0 % Save output every J steps.
sl@>GbnS U1 = [U1 u1]; % put solutions in U array
o/ a2n<4 U2=[U2 u2];
7D>_<)%d= MN1=[MN1 m1];
HbPn<x^7 z1=dz*MN1'; % output location
ADOA&r[ end
u' kG(<0Y end
%zY5'$v ` hg=abs(U1').*abs(U1'); % for data write to excel
\v=@' ha=[z1 hg]; % for data write to excel
Crj7n/mp]s t1=[0 t'];
bFL2NH 5 hh=[t1' ha']; % for data write to excel file
vN_ 8qzWk %dlmwrite('aa',hh,'\t'); % save data in the excel format
; }T+ImjA figure(1)
m}D;=>2$ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
=~W=} figure(2)
JJg;X :p waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
Ylu\]pr9|C nTtEv~a_n 非线性超快脉冲耦合的数值方法的Matlab程序 OJA_OqVp$K !fe_w5S ^ 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
#1*7eANfr Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
0:I<TJ~P P'}B5 I~ EBL-+%J8 3'i(wI~<[ % This Matlab script file solves the nonlinear Schrodinger equations
k$f2i,7' % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
E8nj_ ^Z % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
O/#uQn} % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
d)Z&_v<| B1U!*yzG6 C=1;
`x >6Wk1 M1=120, % integer for amplitude
ue+{djz[4 M3=5000; % integer for length of coupler
rx9y^E5T`; N = 512; % Number of Fourier modes (Time domain sampling points)
{SXSQ '= dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
nnT#S T =40; % length of time:T*T0.
c1a$J` dt = T/N; % time step
Tjv'S
< n = [-N/2:1:N/2-1]'; % Index
]=i('|YG t = n.*dt;
:O&jm.2m ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
BAvz @H w=2*pi*n./T;
Prf G g1=-i*ww./2;
i0+e3!QU g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
[kxO v7a g3=-i*ww./2;
R6;#+ 1D P1=0;
z'1%%.r;FM P2=0;
0m> 8 P3=1;
}hg2}g99 P=0;
%-K 5sIz for m1=1:M1
0&Ftx%6% p=0.032*m1; %input amplitude
#6D>e~>n s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
KDP4 7A s1=s10;
,:'JJZg@ s20=0.*s10; %input in waveguide 2
b$*2bSdv0< s30=0.*s10; %input in waveguide 3
] &D= *:c s2=s20;
3}mg7KV& s3=s30;
Rmn{Vui9\ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
H7Z`a QC %energy in waveguide 1
qbS6#7D p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
Rcw[`q3/ %energy in waveguide 2
4 <E < sD p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
2.MUQ;OX %energy in waveguide 3
-}!mi V for m3 = 1:1:M3 % Start space evolution
52#6uBe s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
~&MDfpl s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
#l:
1R&F s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
6P>}7R} sca1 = fftshift(fft(s1)); % Take Fourier transform
&) ||~ sca2 = fftshift(fft(s2));
ohe[rV>EX sca3 = fftshift(fft(s3));
NR8`nc1~ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
6~W@$SP,F sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
!plu;w sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
9xzow,mi s3 = ifft(fftshift(sc3));
z9OpxW@Ou s2 = ifft(fftshift(sc2)); % Return to physical space
`\;Z&jlpT s1 = ifft(fftshift(sc1));
VE I ct{ end
>D~8iuy]8. p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
F$'u` p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
$>yfu=]? p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
X9FO"(J P1=[P1 p1/p10];
sb8bCEm- \ P2=[P2 p2/p10];
> 3(,s^ P3=[P3 p3/p10];
5%fW X'mS P=[P p*p];
GU @#\3 end
yx4pQL7 figure(1)
N#e9w3Rli plot(P,P1, P,P2, P,P3);
2@z .ory. G
