计算脉冲在非线性耦合器中演化的Matlab 程序 $.``OxJk% IeH^Wm&^ % This Matlab script file solves the coupled nonlinear Schrodinger equations of
|^ ?`Q.|c$ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
Bpm,mp4g\# % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
k&yQ98H$K" % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
8>ESD}( '^e0Ud, %fid=fopen('e21.dat','w');
( VfwLo># N = 128; % Number of Fourier modes (Time domain sampling points)
- Sx0qi'% M1 =3000; % Total number of space steps
l},dQ4R J =100; % Steps between output of space
hH#lTye T =10; % length of time windows:T*T0
z/)$D T0=0.1; % input pulse width
:,jPNuOA MN1=0; % initial value for the space output location
EG%I1F% dt = T/N; % time step
DQ%`v = n = [-N/2:1:N/2-1]'; % Index
ix:2Z- t = n.*dt;
'^8g9E .4K u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
c$.UE u20=u10.*0.0; % input to waveguide 2
E2h(w_l u1=u10; u2=u20;
HJc<Gwm U1 = u1;
[+y &HNf U2 = u2; % Compute initial condition; save it in U
,|6Y \L ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
"pOqd 8>] w=2*pi*n./T;
?0 HR(N(z! g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
@ <|6{N< L=4; % length of evoluation to compare with S. Trillo's paper
:wF b5 " dz=L/M1; % space step, make sure nonlinear<0.05
>ze>Xr'm5= for m1 = 1:1:M1 % Start space evolution
R_t~UTfI; u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
)uANmThOz u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
Rk}\)r\ ca1 = fftshift(fft(u1)); % Take Fourier transform
2TE\4j ca2 = fftshift(fft(u2));
G!n l'5|y c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
[SK2 x4 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
ur?d6 a u2 = ifft(fftshift(c2)); % Return to physical space
XAw2 X;F% u1 = ifft(fftshift(c1));
~azF+}x90N if rem(m1,J) == 0 % Save output every J steps.
_2wAaJvA U1 = [U1 u1]; % put solutions in U array
^cB49s+{e U2=[U2 u2];
${wU+E* MN1=[MN1 m1];
=g/4{IL % z1=dz*MN1'; % output location
Ii|uGxEc end
W^^K0yn`@ end
bjuY A/w< hg=abs(U1').*abs(U1'); % for data write to excel
&,^mM'
C ha=[z1 hg]; % for data write to excel
CR%D\I$o t1=[0 t'];
MomLda
V9Q hh=[t1' ha']; % for data write to excel file
!>CE(;E>z %dlmwrite('aa',hh,'\t'); % save data in the excel format
2O?Vr "
A figure(1)
/7c2OI=\ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
>_rzT9gX& figure(2)
j kSc & waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
W/#KX}4 f+*J
ue 非线性超快脉冲耦合的数值方法的Matlab程序 `)0Rv|? !y.ei1diw 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。
` 2Wl 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
_Syre6k J@oEV=L 7xX;MB & "2*G$\ % This Matlab script file solves the nonlinear Schrodinger equations
t.3Ct @wK % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
9 yh9HE % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
6XQ*:N/4al % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
|Dl*w/n
!Sh^LYqn C=1;
6Hc H'nmeN M1=120, % integer for amplitude
MDMtOf e| M3=5000; % integer for length of coupler
k)?,xY\AV N = 512; % Number of Fourier modes (Time domain sampling points)
\;nD)<)J dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
s/r5,IFR T =40; % length of time:T*T0.
\pj Rv dt = T/N; % time step
Nr> c'TH n = [-N/2:1:N/2-1]'; % Index
*LY ~l t = n.*dt;
aO~s i= ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
8
m%>:}o w=2*pi*n./T;
*ah>-}- g1=-i*ww./2;
( rA\_FOJ g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
2#>$%[ g3=-i*ww./2;
* ge].E P1=0;
UN
cYu9[ P2=0;
\[Sm2/9v P3=1;
FQ ;4'B^k] P=0;
ZA *b9W for m1=1:M1
9oZ }
h& p=0.032*m1; %input amplitude
8QkWgd7y s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
)e4WAlg8c s1=s10;
J!21`M-Ue s20=0.*s10; %input in waveguide 2
N&6_8=3z s30=0.*s10; %input in waveguide 3
qZT 4+&y s2=s20;
`_NnQ% s3=s30;
/#S4espE p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
nz ,Mqol %energy in waveguide 1
ig2{lEkF p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
.V5q$5j %energy in waveguide 2
$nUd\B$.= p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
8m#}S\m %energy in waveguide 3
,pQ'w7 for m3 = 1:1:M3 % Start space evolution
?noE TH z) s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
\iFMU# s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
{] t\`fjrg s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
c8bca` sca1 = fftshift(fft(s1)); % Take Fourier transform
XM$5S+e sca2 = fftshift(fft(s2));
ltCwns sca3 = fftshift(fft(s3));
21[K[ % sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
!Z<mrr;T@ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
\Dvl%:8 sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
4 7)+'` s3 = ifft(fftshift(sc3));
Bo\a s2 = ifft(fftshift(sc2)); % Return to physical space
D..{|29,: s1 = ifft(fftshift(sc1));
AijPN end
jI*}y[o p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
9[epr+ f p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
R9b/?*%=9 p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
EIq{C-( P1=[P1 p1/p10];
l _kg3e4 P2=[P2 p2/p10];
otmIu` h P3=[P3 p3/p10];
y1,?ZWTayr P=[P p*p];
jRv;D#Hp end
_~X8/p/Qh figure(1)
^%K1R; plot(P,P1, P,P2, P,P3);
n9<roH A%NK0j$;} 转自：
http://blog.163.com/opto_wang/
