计算脉冲在非线性耦合器中演化的Matlab 程序 ^s_BY+# Sas &P:# r % This Matlab script file solves the coupled nonlinear Schrodinger equations of
ZT \=:X*e % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
aOj (=s % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
dZ1/w0<M2 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Vlk] -f+U:/'.>v %fid=fopen('e21.dat','w');
BO3# *J5S\ N = 128; % Number of Fourier modes (Time domain sampling points)
2,nVo^13} M1 =3000; % Total number of space steps
l20fA-T
_I J =100; % Steps between output of space
_qZ?|;o^ T =10; % length of time windows:T*T0
U=<d;2N# T0=0.1; % input pulse width
*Z+8L*k97 MN1=0; % initial value for the space output location
Z uh!{_x; dt = T/N; % time step
a2{ nrGD n = [-N/2:1:N/2-1]'; % Index
P2q'P& t = n.*dt;
? ^E B"{ u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
&K 1\" u20=u10.*0.0; % input to waveguide 2
.fQ/a`AsU u1=u10; u2=u20;
&g{b5x{iD U1 = u1;
u;[*Z U2 = u2; % Compute initial condition; save it in U
OJkiTs{ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
ranLH m.nB w=2*pi*n./T;
Guc~]
B g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
r M
sd) L=4; % length of evoluation to compare with S. Trillo's paper
5iG+O4n% dz=L/M1; % space step, make sure nonlinear<0.05
xS4B" / for m1 = 1:1:M1 % Start space evolution
Jj~c&LxrO u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
+, SUJ| u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
:|GC~JElo5 ca1 = fftshift(fft(u1)); % Take Fourier transform
@dy<=bh~ ca2 = fftshift(fft(u2));
zjzW;bo( d c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
` q NhB\ c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
(#dwIBBFt u2 = ifft(fftshift(c2)); % Return to physical space
\Kx@?, u1 = ifft(fftshift(c1));
?f\;z<e| if rem(m1,J) == 0 % Save output every J steps.
*@XJ7G[ U1 = [U1 u1]; % put solutions in U array
Aj TkQ )
U2=[U2 u2];
-R~! N#y MN1=[MN1 m1];
Au q) z1=dz*MN1'; % output location
"|2| Vju% end
hU:M]O0 uw end
3Ishe" hg=abs(U1').*abs(U1'); % for data write to excel
Tn$/9<Q ha=[z1 hg]; % for data write to excel
y5td o'Ex t1=[0 t'];
q,ry3Nr4n hh=[t1' ha']; % for data write to excel file
3 6NENzK %dlmwrite('aa',hh,'\t'); % save data in the excel format
rQ^X3J*` figure(1)
Hcp)Q7 6X waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
"Y9PS_u(~ figure(2)
0 > waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
x >u \ k *a?E y$ 非线性超快脉冲耦合的数值方法的Matlab程序 Px!M^
T!Pi O#}'QZd' 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。
z L1 *w@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
[hLSK-K 9 .,)C^hs@ Ur`jmB F __(iX xC % This Matlab script file solves the nonlinear Schrodinger equations
Fq]ht* % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
'nK(cKDIG % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
ICJ p- % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
X3z$f(lF%) y>:-6)pv C=1;
d"E@e21 M1=120, % integer for amplitude
i2a"" zac M3=5000; % integer for length of coupler
#cN0ciCT' N = 512; % Number of Fourier modes (Time domain sampling points)
F,t
,Ja dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
)1P Z# T =40; % length of time:T*T0.
sH//*y dt = T/N; % time step
l!U_ 7)s/ n = [-N/2:1:N/2-1]'; % Index
2wHvHH! t = n.*dt;
#].n0[ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
^ -s'Ad3 w=2*pi*n./T;
Im
NTk g1=-i*ww./2;
*, /ADtL g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
FME&v Uh/ g3=-i*ww./2;
{uurM` f}: P1=0;
(*.t~6c?5 P2=0;
TRQ@= . P3=1;
3DNw=Ic0k P=0;
uQ^r 1 $# for m1=1:M1
wVI 1sR p=0.032*m1; %input amplitude
YbMeSU/sX s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
q/
x(:yol s1=s10;
"bO\Wt#Mf s20=0.*s10; %input in waveguide 2
%i7bkdcwk s30=0.*s10; %input in waveguide 3
yPgDb[V+ s2=s20;
%J*z!Fe8s s3=s30;
D1 &%N{ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
iKy_DV;J %energy in waveguide 1
0K\Xxo.= p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
B{\cV-X$0 %energy in waveguide 2
K~j&Q{yws@ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
9uV'# sR %energy in waveguide 3
'#~$Od4&= for m3 = 1:1:M3 % Start space evolution
1 _D|;/aI s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
_JlbVe[< s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
zp "Lp>i s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
RUJkfi=$ sca1 = fftshift(fft(s1)); % Take Fourier transform
Dc,h( 2 sca2 = fftshift(fft(s2));
0 mJvoz\j8 sca3 = fftshift(fft(s3));
X!} t` ` sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
( x} >tm sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
JArSJ:} sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
(!-gX" <b s3 = ifft(fftshift(sc3));
[dG&"%5vD s2 = ifft(fftshift(sc2)); % Return to physical space
,o $F~KPu s1 = ifft(fftshift(sc1));
8MHYk>O~{G end
j2V"w&>b} p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
`[hc{ynO| p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
}T@^wY_Ow p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
oCE=!75 P1=[P1 p1/p10];
)E--E+j P2=[P2 p2/p10];
/az}<r8 P3=[P3 p3/p10];
X?,ly3, P=[P p*p];
hE|Z~5\Y,> end
?2hS<qXX figure(1)
axJuJ`+Y plot(P,P1, P,P2, P,P3);
fj2pD Cic k)Y}X)\36 转自：
http://blog.163.com/opto_wang/
