计算脉冲在非线性耦合器中演化的Matlab 程序 gg[WlRQK4A ?3%` bY+3; % This Matlab script file solves the coupled nonlinear Schrodinger equations of
>_o} % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
e<=cdze % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
S'A>2> % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
P/c&@_b A v"R[) %fid=fopen('e21.dat','w');
Jd %H2` N = 128; % Number of Fourier modes (Time domain sampling points)
}2( ,K[? M1 =3000; % Total number of space steps
(IC]?n} J =100; % Steps between output of space
&0NFb^8+ T =10; % length of time windows:T*T0
R#2 t)y T0=0.1; % input pulse width
qp/v^$EA MN1=0; % initial value for the space output location
T?
tG~ dt = T/N; % time step
.#1~Rz1r n = [-N/2:1:N/2-1]'; % Index
?0)&U t = n.*dt;
\=uKHNP?# u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
4"{ooy^Q u20=u10.*0.0; % input to waveguide 2
]<H&+ &! u1=u10; u2=u20;
q8^^H$<Db U1 = u1;
MP_'D+LS U2 = u2; % Compute initial condition; save it in U
X=hYB}}n u ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
&z>e5_. w=2*pi*n./T;
!OBEM1~
1 g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
>iD )eB L=4; % length of evoluation to compare with S. Trillo's paper
MKy[hT: dz=L/M1; % space step, make sure nonlinear<0.05
c.,2GwW for m1 = 1:1:M1 % Start space evolution
nx8a$vI-TY u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
{.QEc0- u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
T2SP
W@#Z3 ca1 = fftshift(fft(u1)); % Take Fourier transform
|_`E1Y}} ca2 = fftshift(fft(u2));
V#cqRE3XNi c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
%7"X(Ts7B c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
:@ %4 u2 = ifft(fftshift(c2)); % Return to physical space
"NgxkbDEbG u1 = ifft(fftshift(c1));
|
\'rP_I> if rem(m1,J) == 0 % Save output every J steps.
T{Sb^-H#X U1 = [U1 u1]; % put solutions in U array
VwOW=4`6 U2=[U2 u2];
GG@ md_ MN1=[MN1 m1];
oXxCXO,q z1=dz*MN1'; % output location
GFel(cx:K end
O)ME"@r@: end
I9:Cb)hbU] hg=abs(U1').*abs(U1'); % for data write to excel
-TM 0]{ ha=[z1 hg]; % for data write to excel
qW!]co t1=[0 t'];
|g
#K]v hh=[t1' ha']; % for data write to excel file
y($ %;l %dlmwrite('aa',hh,'\t'); % save data in the excel format
COW}o~3-4 figure(1)
e'0{?B waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
e XfZ5(na figure(2)
5dB'&8DX waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
ve%
xxn: *M$0J'-BQ 非线性超快脉冲耦合的数值方法的Matlab程序 Bx/L<J@ _i o+YzS 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
: {IO=^D=$ 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
1jc,
Y.mP du)~kU>l Dh5X/y 9(6I<]# % This Matlab script file solves the nonlinear Schrodinger equations
w:? oTuw % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
&|!7 Z4N % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
Kj<^zo% w % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
L{(QpgHZ ?r?jl;A& C=1;
" )V130< M1=120, % integer for amplitude
Q($Z%1S M3=5000; % integer for length of coupler
s VJ!FC N = 512; % Number of Fourier modes (Time domain sampling points)
B<~ NS)w dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
'UMXq~RMe T =40; % length of time:T*T0.
;_^fk&+ dt = T/N; % time step
| fSe>uVZ n = [-N/2:1:N/2-1]'; % Index
L2, 1Kt7 t = n.*dt;
|37
g ~ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
E;1Jh(58)b w=2*pi*n./T;
/)dF K~ g1=-i*ww./2;
f-5:wM& g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
mZx&Xez_G g3=-i*ww./2;
u$-U*r P1=0;
3bDQk
:L P2=0;
:PtF+{N> P3=1;
7{I h_.# P=0;
xia |+ for m1=1:M1
cIp
D~0\ p=0.032*m1; %input amplitude
'3<fsK= s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
~i2 1%$ s1=s10;
L3n_ 5| s20=0.*s10; %input in waveguide 2
=e8bNg s30=0.*s10; %input in waveguide 3
C&6IU8l \ s2=s20;
M?[h0{^K s3=s30;
'
4E R00 p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
qA!]E^0*Ke %energy in waveguide 1
jq+A-T}@ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
1!.(4gV %energy in waveguide 2
)=-0M9e.{ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
X+~ XJ
%energy in waveguide 3
_>v<(7 for m3 = 1:1:M3 % Start space evolution
Vo7dAHHL s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
vmLxkjUm# s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
C#H:-Q& s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
8,a tX+t c sca1 = fftshift(fft(s1)); % Take Fourier transform
2KQoy; sca2 = fftshift(fft(s2));
!YP @m~ sca3 = fftshift(fft(s3));
/__PSK sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
2hee./F` sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
IN,(y a C sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
*b xzCI7b s3 = ifft(fftshift(sc3));
XEdzpkB s2 = ifft(fftshift(sc2)); % Return to physical space
|gsE2vV s1 = ifft(fftshift(sc1));
=&},;VOh end
tqy@iEz+ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
{O+Kw<d p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
NHl|x4Zpw p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
^1wA:?uN} P1=[P1 p1/p10];
\'M3|w`f P2=[P2 p2/p10];
E"L2&. P3=[P3 p3/p10];
EaWS. eK P=[P p*p];
z.CywME<)t end
w=}uwvn NX figure(1)
e5OsI Vtjr plot(P,P1, P,P2, P,P3);
CT\;xt,S @o-B{ EH8 转自：
http://blog.163.com/opto_wang/
