计算脉冲在非线性耦合器中演化的Matlab 程序 PH4bM I EsD = % This Matlab script file solves the coupled nonlinear Schrodinger equations of
=/'*(\C2 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
^d $e^cU % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
8}`8lOE7 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
K[;,/:Y VKf HN_m* %fid=fopen('e21.dat','w');
Hf]}OvT>Z N = 128; % Number of Fourier modes (Time domain sampling points)
/Ta0}Y(y M1 =3000; % Total number of space steps
Ecl 7=-y J =100; % Steps between output of space
Jz8#88cY T =10; % length of time windows:T*T0
ZC-evy T0=0.1; % input pulse width
o>rlrqr?_ MN1=0; % initial value for the space output location
8uD%]k= #! dt = T/N; % time step
oW1olmpp= n = [-N/2:1:N/2-1]'; % Index
eS%6 h U b t = n.*dt;
(>lqp%G~ u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
ZTz(NS
EK u20=u10.*0.0; % input to waveguide 2
^p%+r B.j[ u1=u10; u2=u20;
v&,VC~RN-J U1 = u1;
mb6? $1j U2 = u2; % Compute initial condition; save it in U
K>JU/( ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
,ui'^8{gK w=2*pi*n./T;
MZMv.OeYt, g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
en6AAr:U} L=4; % length of evoluation to compare with S. Trillo's paper
NbMH@6%E dz=L/M1; % space step, make sure nonlinear<0.05
8 r| for m1 = 1:1:M1 % Start space evolution
Pw{{+PBu R u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
t4W0~7 u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
| 2` $g ca1 = fftshift(fft(u1)); % Take Fourier transform
YZu# 0) ca2 = fftshift(fft(u2));
UHszOl c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
Uy'ZL(2 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
XzFqQ- H u2 = ifft(fftshift(c2)); % Return to physical space
d#,V^ u1 = ifft(fftshift(c1));
r<H^%##,w if rem(m1,J) == 0 % Save output every J steps.
dOgM9P U1 = [U1 u1]; % put solutions in U array
j`M<M[C*4N U2=[U2 u2];
#yOY&W: N MN1=[MN1 m1];
fBh|:2u z1=dz*MN1'; % output location
3/<^R}w\
end
j~>
#{" C end
WZ-{K"56 hg=abs(U1').*abs(U1'); % for data write to excel
A+ *(Pds ha=[z1 hg]; % for data write to excel
*Z(C' )7r t1=[0 t'];
!Bbwl-e` hh=[t1' ha']; % for data write to excel file
f3|=T8"t %dlmwrite('aa',hh,'\t'); % save data in the excel format
jl29~^@}1i figure(1)
itMc!bUQ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
} +Z;zm@/6 figure(2)
QZP;k!"w waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
\:28z UZ0O
j5B. 非线性超快脉冲耦合的数值方法的Matlab程序 ,fL e%RP G?(:Z= 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。
{D.0_=y~2 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
nrhpI d Cagq0-:(p Y0'^S<ox A |nU
_* % This Matlab script file solves the nonlinear Schrodinger equations
k( ^ b % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
}('QIvq2 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
GUZi }a|= % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
g-uFs s +T;qvx6 C=1;
c67!OHu mP M1=120, % integer for amplitude
>u[ln@ l M3=5000; % integer for length of coupler
JYU Ks~Qt N = 512; % Number of Fourier modes (Time domain sampling points)
~kFRy { z dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
0 ']M,iC/ T =40; % length of time:T*T0.
%"B$I>h dt = T/N; % time step
.6( i5K n = [-N/2:1:N/2-1]'; % Index
g}h0J%s t = n.*dt;
NE nP3A ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
AIo;\35 w=2*pi*n./T;
3P>@ : g1=-i*ww./2;
{$.{VE+v5 g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
m8` A~ g3=-i*ww./2;
0$
EJ4 P1=0;
94/}@<d-= P2=0;
?!vW&KJZx P3=1;
XRin~wz|S P=0;
HX[#tT |m~ for m1=1:M1
?RyvM_(N6 p=0.032*m1; %input amplitude
Q5ao2-\ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
{)xrg sB s1=s10;
_en 8hi@Z s20=0.*s10; %input in waveguide 2
\NRRN eu| s30=0.*s10; %input in waveguide 3
o!&*4>tF s2=s20;
?whp _ s3=s30;
rk p0ej2- p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
N~YeAe~+ %energy in waveguide 1
@n3PCH6:Ao p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
O%{>Zo_< %energy in waveguide 2
} z i6 F. p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
(~4AG \ %energy in waveguide 3
Ja2.1v|r . for m3 = 1:1:M3 % Start space evolution
B dUyI_Ks: s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
q3t@)+l>* s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
b87d'# . s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
`^x^=
og' sca1 = fftshift(fft(s1)); % Take Fourier transform
Pd?YS!+S sca2 = fftshift(fft(s2));
4|UIyDt8 sca3 = fftshift(fft(s3));
)L Ul? sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
&aU+6'+QXB sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
v%w]Q B sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
,'}ZcN2) s3 = ifft(fftshift(sc3));
9EW 7,m{A s2 = ifft(fftshift(sc2)); % Return to physical space
TY}?>t+ s1 = ifft(fftshift(sc1));
CJ >=odK[ end
%8/ $CR p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
9:WKG'E8a p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
zjS<e
XLs[ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
5irOK9hK P1=[P1 p1/p10];
aY~IS?! ; P2=[P2 p2/p10];
+iR ;D$w P3=[P3 p3/p10];
]0O$2 j_ 7 P=[P p*p];
X5=7DE ] end
BN67o]*]< figure(1)
I&9B^fF6 plot(P,P1, P,P2, P,P3);
g}7B0 yo *9PQJeyR 转自：
http://blog.163.com/opto_wang/
