计算脉冲在非线性耦合器中演化的Matlab 程序 IA(+}V nep-?7 x % This Matlab script file solves the coupled nonlinear Schrodinger equations of
];7/DM#Np % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
48W-Tf6v| % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
(cpaMn@)g % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
!<AY0fpY ffibS0aM %fid=fopen('e21.dat','w');
?]Z EK8c N = 128; % Number of Fourier modes (Time domain sampling points)
1}DUe. a M1 =3000; % Total number of space steps
'boAv%1_sa J =100; % Steps between output of space
]>" q>XgnI T =10; % length of time windows:T*T0
o P`y BX T0=0.1; % input pulse width
YA'_Ba(v) MN1=0; % initial value for the space output location
wJb"X=i* dt = T/N; % time step
1Zi(5S) n = [-N/2:1:N/2-1]'; % Index
h_?#.z0ih; t = n.*dt;
d\ {a&\v u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
+f]\>{o4 u20=u10.*0.0; % input to waveguide 2
FK!UUy; u1=u10; u2=u20;
i#1 ~<U U1 = u1;
3!<} -sW4 U2 = u2; % Compute initial condition; save it in U
=F>nqklc ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
:eR[lR^4*
w=2*pi*n./T;
@"$rR+r' g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
W*D].| L=4; % length of evoluation to compare with S. Trillo's paper
uL[% R2 dz=L/M1; % space step, make sure nonlinear<0.05
$ix*xm. 4m for m1 = 1:1:M1 % Start space evolution
`ek On@T0 u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
;x~[om21; u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
$KGp cl ca1 = fftshift(fft(u1)); % Take Fourier transform
A Q e~F ca2 = fftshift(fft(u2));
H,5 ##@X c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
EHC^ [5 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
cQ<* (KU u2 = ifft(fftshift(c2)); % Return to physical space
GP._C=] ?c u1 = ifft(fftshift(c1));
Vo-]&u&cr
if rem(m1,J) == 0 % Save output every J steps.
*iW$>Yjb U1 = [U1 u1]; % put solutions in U array
WKB@9Vfju U2=[U2 u2];
Qx% ]u8s MN1=[MN1 m1];
r" )zR, z1=dz*MN1'; % output location
sxBRg= end
0-{l4;o end
^FZ7) T hg=abs(U1').*abs(U1'); % for data write to excel
A1u|L^ ha=[z1 hg]; % for data write to excel
D_MNF =7 t1=[0 t'];
OJH:k~]0! hh=[t1' ha']; % for data write to excel file
<(<19t5 . %dlmwrite('aa',hh,'\t'); % save data in the excel format
}bxx]rDl figure(1)
x w%'R- waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
uY5Gn . Y figure(2)
;zl/ waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
^"?b!=n! J@I-tS 非线性超快脉冲耦合的数值方法的Matlab程序 >RMp`HxDf Fo1|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。
I$7TnM ug 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
l .wf= / {=K u9\ 0Q_@2 1q[vNP=g& % This Matlab script file solves the nonlinear Schrodinger equations
$CY B&|d % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
) 5M9Ro7 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
rLm:qu(F1 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
}M I9?\"q ?8LRd5LH C=1;
yv!,iK9 M1=120, % integer for amplitude
U.@j !UrZ M3=5000; % integer for length of coupler
fDa$TbhjI N = 512; % Number of Fourier modes (Time domain sampling points)
@$( /6]4p dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
xedbr T =40; % length of time:T*T0.
7v~\c%1V dt = T/N; % time step
=k(~PB^> n = [-N/2:1:N/2-1]'; % Index
1jhGshhp t = n.*dt;
#VwA?$4g` ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
2Rp'ju~O)/ w=2*pi*n./T;
|5}~n"R5 g1=-i*ww./2;
y&.[Nt '+ g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
v$`AN4)} g3=-i*ww./2;
vkXdKL(q P1=0;
B !hrr P2=0;
t7%!~s=,M P3=1;
T Z7{ cekQ P=0;
Yz?1]<X for m1=1:M1
~!,Q<? p=0.032*m1; %input amplitude
#6tb{ws3 s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
~la=rh 3 s1=s10;
E&/D%} Wl s20=0.*s10; %input in waveguide 2
3d{v5. C#X s30=0.*s10; %input in waveguide 3
gJy Ft8Z< s2=s20;
w:z@!< s3=s30;
!S/hH% C p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
=9
TAs? = %energy in waveguide 1
#@m*yJg< p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
at/v.U |F %energy in waveguide 2
%rQ5 <U p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
PUUB n"U- %energy in waveguide 3
;n*N9-|. for m3 = 1:1:M3 % Start space evolution
bT @7& s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
#pxc6W / s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
=#i#IF42? s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
GRC=G&G sca1 = fftshift(fft(s1)); % Take Fourier transform
3:rH1vG.m sca2 = fftshift(fft(s2));
2&W(@w T$ sca3 = fftshift(fft(s3));
<%JRZYZ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
,~Y5vnaOQ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
#EpDIL sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
F6T@YS P s3 = ifft(fftshift(sc3));
JlF0 L%Rc s2 = ifft(fftshift(sc2)); % Return to physical space
=*q :R9V s1 = ifft(fftshift(sc1));
*|x2"?d-F: end
Z; @F.r p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
Q^v8 n1 p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
j\nnx8`7 p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
rb nu:+! P1=[P1 p1/p10];
<?P UF, P2=[P2 p2/p10];
i&^?p|eKa P3=[P3 p3/p10];
R0fZ9_d7} P=[P p*p];
E jB<`yT end
lX`)Avqa figure(1)
unmuY^+< plot(P,P1, P,P2, P,P3);
&b}!KD1 b9(d@2MtK 转自：
http://blog.163.com/opto_wang/
