计算脉冲在非线性耦合器中演化的Matlab 程序 & =Y%4 vq =zp{ ^mC % This Matlab script file solves the coupled nonlinear Schrodinger equations of
m+pK,D~{" % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
u!Vr MH % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
?^8.Sa{ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
n:<Xp[;R S!R (ae^} %fid=fopen('e21.dat','w');
8y?q)y9h N = 128; % Number of Fourier modes (Time domain sampling points)
OMjx,@9 M1 =3000; % Total number of space steps
g'-hSV/@}@ J =100; % Steps between output of space
^@'zQa T =10; % length of time windows:T*T0
_|{pO7x]oG T0=0.1; % input pulse width
v,3 }YDu MN1=0; % initial value for the space output location
M|.ykA<D dt = T/N; % time step
NfCo)C -t n = [-N/2:1:N/2-1]'; % Index
[H`5mY @ t = n.*dt;
6 iH]N*]S^ u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
h9. Yux u20=u10.*0.0; % input to waveguide 2
nu16L$ ] u1=u10; u2=u20;
bGj<Dojl U1 = u1;
tKi ^0vE8 U2 = u2; % Compute initial condition; save it in U
#g
Rns ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
i Nn?G C> w=2*pi*n./T;
s"wz !{G4 g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
$M4C4_oPy L=4; % length of evoluation to compare with S. Trillo's paper
xaIe7.Z"xo dz=L/M1; % space step, make sure nonlinear<0.05
b h5 C for m1 = 1:1:M1 % Start space evolution
4`"Q!T_' u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
7: C2xC u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
iA"H*0 ca1 = fftshift(fft(u1)); % Take Fourier transform
`| [UF^9 ca2 = fftshift(fft(u2));
'GZ, c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
8 vvNn>Q c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
$fW8S8 u2 = ifft(fftshift(c2)); % Return to physical space
ugW.nf*O u1 = ifft(fftshift(c1));
s*kSl:T @O if rem(m1,J) == 0 % Save output every J steps.
H"V)dEm U1 = [U1 u1]; % put solutions in U array
dpcv'cRfw U2=[U2 u2];
#W L>ha
v MN1=[MN1 m1];
'&y+,2?;Y[ z1=dz*MN1'; % output location
| e&hm
~R1 end
8{Wh4~|+ end
M[=sQnnSFW hg=abs(U1').*abs(U1'); % for data write to excel
<QK2Wc_}-" ha=[z1 hg]; % for data write to excel
# 9ZO1\ t1=[0 t'];
jpfFJon)w hh=[t1' ha']; % for data write to excel file
zhACNz4tJ %dlmwrite('aa',hh,'\t'); % save data in the excel format
`?(9Bl figure(1)
[sG!|@ r waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
~u O9>(?D figure(2)
{y>Kcfc/?E waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
OFw93UJ Y $K~ t'wr 非线性超快脉冲耦合的数值方法的Matlab程序 }RkD7 "Ze<dB#,Y 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。
Ktf lbI! 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
G^w :c] `S/;S<' ; gG46hO-M%x R<8! lQ4s % This Matlab script file solves the nonlinear Schrodinger equations
0hju@& Aa % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
qH*Fv:qnM % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
WcE /,<^* % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
=MMSmu5! (fnp\j3w C=1;
C5'#0 }6i M1=120, % integer for amplitude
_O>8jH!# M3=5000; % integer for length of coupler
kT{d pGU9 N = 512; % Number of Fourier modes (Time domain sampling points)
;kF+V* dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
!W45X}/o T =40; % length of time:T*T0.
C %kI xa) dt = T/N; % time step
1"} u51 n = [-N/2:1:N/2-1]'; % Index
4VfZw\^ t = n.*dt;
| <l=i( ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
lhx]r}@'MC w=2*pi*n./T;
\MFjb IL g1=-i*ww./2;
;*8,PV0b_< g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
+,ojlTVlt g3=-i*ww./2;
EEO)b_( P1=0;
/%T d( P2=0;
c o%-d P3=1;
$ #F7C[2N P=0;
CN<EgNt1kN for m1=1:M1
=G%L:m* p=0.032*m1; %input amplitude
XSz)$9~hk s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
SW_jTn#x s1=s10;
S -KHot ? s20=0.*s10; %input in waveguide 2
$n@B:kv5p s30=0.*s10; %input in waveguide 3
Lkl ^
` s2=s20;
:B] yreg s3=s30;
K-dr N) o p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
R3%&\<a)9 %energy in waveguide 1
H)l7:a p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
;*XH[>I %energy in waveguide 2
B1Cu?k);. p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
l^%W/b> ?b %energy in waveguide 3
E(G&mf hb for m3 = 1:1:M3 % Start space evolution
ptEChoZ6 s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
"Z*u2_ H s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
ORP-@-dap s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
L4-v' Z; sca1 = fftshift(fft(s1)); % Take Fourier transform
t bEJyA sca2 = fftshift(fft(s2));
|(\T;~ 7' sca3 = fftshift(fft(s3));
ae|j#!~oi sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
Z1Z jQt#~+ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
i- *ZW: sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
2 VyJ s3 = ifft(fftshift(sc3));
_Kf8,|+ s2 = ifft(fftshift(sc2)); % Return to physical space
g<$q#l~4xH s1 = ifft(fftshift(sc1));
B (h%>mT[ end
2Bg0
M p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
xb~8uD5 p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
k]9v${Ke p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
q,v)X P1=[P1 p1/p10];
Kk9W =vd P2=[P2 p2/p10];
2\J-7o=P P3=[P3 p3/p10];
XdxSi"+ P=[P p*p];
W 2.Ap end
)7s(]~z figure(1)
8%Hc%T[RnT plot(P,P1, P,P2, P,P3);
o{?R z3z Ne9S90HsB6 转自：
http://blog.163.com/opto_wang/
