计算脉冲在非线性耦合器中演化的Matlab 程序 5 CnNp?.t^ @ws&W=NQ % This Matlab script file solves the coupled nonlinear Schrodinger equations of
W,8Uu 1X = % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
N-N]BS6 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
KyIUz9$ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
mBIksts5 h USART}Us4 %fid=fopen('e21.dat','w');
~xzr8 P N = 128; % Number of Fourier modes (Time domain sampling points)
&SIf |IX. M1 =3000; % Total number of space steps
7 @\ i5 J =100; % Steps between output of space
/ 8O=3 T =10; % length of time windows:T*T0
8XV RRk T0=0.1; % input pulse width
NvzPZ9=@- MN1=0; % initial value for the space output location
)E9c 6'd dt = T/N; % time step
'xd8rN %T n = [-N/2:1:N/2-1]'; % Index
h_-4Q"fb( t = n.*dt;
)fo0YpE^| u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
h5P ]`r u20=u10.*0.0; % input to waveguide 2
"E<+id oz u1=u10; u2=u20;
;/NC[:'$D U1 = u1;
nK< v U2 = u2; % Compute initial condition; save it in U
]@ y%j'e ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
0f j C>AS w=2*pi*n./T;
y?cN g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
ftmP dha%+ L=4; % length of evoluation to compare with S. Trillo's paper
1N65 M=) dz=L/M1; % space step, make sure nonlinear<0.05
,g'>Ib% for m1 = 1:1:M1 % Start space evolution
,J 2qLH1 u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
[PXq<ST u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
x A^E+f:W_ ca1 = fftshift(fft(u1)); % Take Fourier transform
8@ f!,!Wn ca2 = fftshift(fft(u2));
7"Nda3 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
C - ORI}o c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
d@^%fVhG u2 = ifft(fftshift(c2)); % Return to physical space
El TB{C>u u1 = ifft(fftshift(c1));
3AE NY @* if rem(m1,J) == 0 % Save output every J steps.
;HYEJ3 U1 = [U1 u1]; % put solutions in U array
[$K 8y&\L U2=[U2 u2];
(z;lNl(*C MN1=[MN1 m1];
1mHS -oI9J z1=dz*MN1'; % output location
iN[6}V6Sm end
Zs|Ga, T end
Rkg)yme!N hg=abs(U1').*abs(U1'); % for data write to excel
@}PXBU ha=[z1 hg]; % for data write to excel
Fa `%MR1 t1=[0 t'];
\{Q_\ s&) hh=[t1' ha']; % for data write to excel file
Y8%l)g %dlmwrite('aa',hh,'\t'); % save data in the excel format
`uLr^G=; figure(1)
c ?<)!9: waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
iM7 ^ figure(2)
t+ d7{&B waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
Q%~BD@Io L9^ M?.a 非线性超快脉冲耦合的数值方法的Matlab程序 #c' B2Jn A *:| d~ 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。
@ x*xgf 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
L1+s0g> tz?3R#rM n>,GmC o o R8'^G0< % This Matlab script file solves the nonlinear Schrodinger equations
TH y?Y % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
]7TOA$Q % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
z.(DDj % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
`e;r$Vpd_ t%e<]2 -8 C=1;
*MlEfmB( M1=120, % integer for amplitude
LRWM}'.s M3=5000; % integer for length of coupler
. * `]x N = 512; % Number of Fourier modes (Time domain sampling points)
'Qg!ww 7O dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
-B/'ArOo] T =40; % length of time:T*T0.
IDf\! QG x dt = T/N; % time step
) RT Wt` n = [-N/2:1:N/2-1]'; % Index
_ U LzA
t = n.*dt;
`<~=6H ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
9fs-|E[ 5 w=2*pi*n./T;
2[ =3-1c g1=-i*ww./2;
!#%>,X#+ g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
7.
$wK. g3=-i*ww./2;
Wj!+
E{y<r P1=0;
B#IUSH C P2=0;
ckV\f({ P3=1;
)l!
/7WKY P=0;
{U>N*&_ ` for m1=1:M1
nC[aEZ7 p=0.032*m1; %input amplitude
m rsmul{ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
I0H]s/*C%9 s1=s10;
b{aB^a:f=L s20=0.*s10; %input in waveguide 2
y]P uY \+ s30=0.*s10; %input in waveguide 3
?Bq^#i |m s2=s20;
< @GO]vY s3=s30;
L 58#ri= p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
/;}% E %energy in waveguide 1
|.m)UFV p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
\6MM7x(U3 %energy in waveguide 2
tw.GBR p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
SWhz cqp %energy in waveguide 3
M :oM(K+ for m3 = 1:1:M3 % Start space evolution
~Gh7i>n* s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
e
T ;@pc s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
uh.;Jj; s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
= #pYd~ sca1 = fftshift(fft(s1)); % Take Fourier transform
f@Jrbg sca2 = fftshift(fft(s2));
sG_/E-%5' sca3 = fftshift(fft(s3));
G!B:>P|\l sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
^$%
Sg// sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
^ Lc\{,m sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
KiI+ V;o s3 = ifft(fftshift(sc3));
]&P\|b1*g s2 = ifft(fftshift(sc2)); % Return to physical space
P%Vq#5 s1 = ifft(fftshift(sc1));
z k}AGw end
uY>M3h#qx p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
w1-P6cf p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
N >*+Wg$Ne p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
XKws_ P1=[P1 p1/p10];
Pf,@U'f| P2=[P2 p2/p10];
b+:J ?MR;} P3=[P3 p3/p10];
/RqWrpzx@ P=[P p*p];
H
I_uR$m end
ZQf PDH= figure(1)
-L]-u6kC[ plot(P,P1, P,P2, P,P3);
Mh~}RA"H &V~l(1 转自：
http://blog.163.com/opto_wang/
