计算脉冲在非线性耦合器中演化的Matlab 程序 +1otn~(E |av*!i5Q % This Matlab script file solves the coupled nonlinear Schrodinger equations of
e >L5.~i % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
yGb a % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
zKIGWH=qqm % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
iYk' :iv}S Uc_jQ4e_ %fid=fopen('e21.dat','w');
[J a)<!]< N = 128; % Number of Fourier modes (Time domain sampling points)
/xl4ohL$a M1 =3000; % Total number of space steps
\hs/D+MCk J =100; % Steps between output of space
r_b8,I6{] T =10; % length of time windows:T*T0
}1QI"M* T0=0.1; % input pulse width
z-n>9 MN1=0; % initial value for the space output location
Z5((1J9 dt = T/N; % time step
Yo >`h2C4 n = [-N/2:1:N/2-1]'; % Index
Ct4LkmD t = n.*dt;
Oo FgQEr@ u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
an3~'g? u20=u10.*0.0; % input to waveguide 2
fv|]= e u1=u10; u2=u20;
aXMv(e+ U1 = u1;
%b=Y
<v U2 = u2; % Compute initial condition; save it in U
o^HNF+sm ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
:1:3Svb<Y w=2*pi*n./T;
d; 9*l!CF g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
7=} 6H3|& L=4; % length of evoluation to compare with S. Trillo's paper
+ c`AE dz=L/M1; % space step, make sure nonlinear<0.05
z)}3**3'y for m1 = 1:1:M1 % Start space evolution
,mB Z`X@N
u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
{}V$` L8 u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
4w 'lu"U ca1 = fftshift(fft(u1)); % Take Fourier transform
F "!agc2! ca2 = fftshift(fft(u2));
YPu9Q c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
ful#Px6m c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
2b5 #PcKa u2 = ifft(fftshift(c2)); % Return to physical space
+}P%HH]E/p u1 = ifft(fftshift(c1));
J0=7'@(p if rem(m1,J) == 0 % Save output every J steps.
q(,cYu U1 = [U1 u1]; % put solutions in U array
djW cbC=g_ U2=[U2 u2];
1j11|~ MN1=[MN1 m1];
^V[/ (Lq z1=dz*MN1'; % output location
.Y;b)]@f end
1@xP(XS end
2d-{Q 8Pi hg=abs(U1').*abs(U1'); % for data write to excel
m+?N7 ha=[z1 hg]; % for data write to excel
R,%_deV\( t1=[0 t'];
C\7u<2c hh=[t1' ha']; % for data write to excel file
yf!,4SUkU %dlmwrite('aa',hh,'\t'); % save data in the excel format
98GlhogWt figure(1)
u#1%P5r&X waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
wzd`l?o, figure(2)
{;*}WPYb waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
^K+:C;Q| wq UQ "d 非线性超快脉冲耦合的数值方法的Matlab程序 6O pa{] TXjloGv^ 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。
E !zX)|Z< 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
C}q>YRubZ BWh }^3?l D|l,08n"? pE2QnNr' % This Matlab script file solves the nonlinear Schrodinger equations
% #u.J
% for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
P^pFqUL7# % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
/t*YDW Lg % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Z0$] tS %]!adro~ C=1;
Ql8bt77eI- M1=120, % integer for amplitude
~O{W;Cyh M3=5000; % integer for length of coupler
%t*[T N = 512; % Number of Fourier modes (Time domain sampling points)
LEZ&W ;bCo dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
/ ;Yy@oc T =40; % length of time:T*T0.
vg)Z]F=t( dt = T/N; % time step
oaK.kO o n = [-N/2:1:N/2-1]'; % Index
FbAW_Am( t = n.*dt;
v8m`jxII64 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
e`iEy=W w=2*pi*n./T;
9 #qeFBI g1=-i*ww./2;
&+01+-1hW g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
]!O ue_-; g3=-i*ww./2;
,(N[*)G P1=0;
z\T Lsx P2=0;
[k $efwJ P3=1;
Ja|{ 1&J . P=0;
0}]SUe^ for m1=1:M1
RF?DtNuq p=0.032*m1; %input amplitude
NLyXBV[hV s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
wC`;f5- > s1=s10;
^2 S# Uk s20=0.*s10; %input in waveguide 2
KxIyc7. s30=0.*s10; %input in waveguide 3
AOb]q c s2=s20;
GS;%zdH~ s3=s30;
| kXm}K p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
)&, {?$ . %energy in waveguide 1
_Zc4=c,K p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
6ZOy&fd,Ty %energy in waveguide 2
xq[Yg15d% p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
D."=k{r. %energy in waveguide 3
~Y7dH
Dn for m3 = 1:1:M3 % Start space evolution
})Yv9],6 s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
@0NJ{ s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
fDh] tua s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
X(*!2u S sca1 = fftshift(fft(s1)); % Take Fourier transform
Y3Oz'%B sca2 = fftshift(fft(s2));
`s"d]/85VW sca3 = fftshift(fft(s3));
pf&ag#nr sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
p? # pT}1 sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
hH>``gK sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
D-&a n@ s3 = ifft(fftshift(sc3));
94/BG0 s2 = ifft(fftshift(sc2)); % Return to physical space
taWqS q! s1 = ifft(fftshift(sc1));
!<<AzLVL end
)C~9E 5E p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
!wE}(0B Tx p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
V
'.a)6 p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
[XR$F@o P1=[P1 p1/p10];
{ci.V*:" P2=[P2 p2/p10];
/M=3X|| P3=[P3 p3/p10];
56}X/ u P=[P p*p];
rD
&D) w end
ezm&]F` figure(1)
7DD&~ZcD plot(P,P1, P,P2, P,P3);
f&KdlpxKv = QO g 6 转自：
http://blog.163.com/opto_wang/
