计算脉冲在非线性耦合器中演化的Matlab 程序 ,
'pYR]3 DsdM:u*s % This Matlab script file solves the coupled nonlinear Schrodinger equations of
EavBUX$O % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
;As~T GiT % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
v `S5[{6 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
.}dLqw 7Jb&~{DVk %fid=fopen('e21.dat','w');
[+[ W\6 N = 128; % Number of Fourier modes (Time domain sampling points)
yX&#
rI M1 =3000; % Total number of space steps
: w^:Z$-hf J =100; % Steps between output of space
\] x`f3F T =10; % length of time windows:T*T0
q`e0%^U T0=0.1; % input pulse width
$xu2ZBK MN1=0; % initial value for the space output location
: /5+p>Ep} dt = T/N; % time step
t #(NfzN n = [-N/2:1:N/2-1]'; % Index
2"6L\8hd2 t = n.*dt;
@fd< u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
Z!v,;MW u20=u10.*0.0; % input to waveguide 2
#]Vw$X_S u1=u10; u2=u20;
WA n@8!9 U1 = u1;
!{ &r|6 U2 = u2; % Compute initial condition; save it in U
"@x( 2(Y& ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
!WyJ@pFU^ w=2*pi*n./T;
D4$b-?y g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
48p3m) 5
L=4; % length of evoluation to compare with S. Trillo's paper
>\JP X dz=L/M1; % space step, make sure nonlinear<0.05
]D6<6OB for m1 = 1:1:M1 % Start space evolution
H VM %B{( u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
,88B@a u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
~D5
-G?%$" ca1 = fftshift(fft(u1)); % Take Fourier transform
*RY}e ca2 = fftshift(fft(u2));
RY5e%/bg~U c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
k7Nx#%xx c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
M.g2y &8 u2 = ifft(fftshift(c2)); % Return to physical space
4f j}d.? u1 = ifft(fftshift(c1));
H [+'>Id: if rem(m1,J) == 0 % Save output every J steps.
8i6i ynR U1 = [U1 u1]; % put solutions in U array
3n2^;b/ ] U2=[U2 u2];
caEIE0H~ MN1=[MN1 m1];
wo9R :kQ z1=dz*MN1'; % output location
frbd{o end
&wNr2PHd# end
zZ}. 2He8 hg=abs(U1').*abs(U1'); % for data write to excel
m#h`i W ha=[z1 hg]; % for data write to excel
6UI S4 _
t1=[0 t'];
j Hq+/\ hh=[t1' ha']; % for data write to excel file
2K~v`c*4 %dlmwrite('aa',hh,'\t'); % save data in the excel format
CQ!D{o= figure(1)
PCCE+wC6 waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
y95
#t figure(2)
Z@q1&}D! waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
xEG:KSH H 8HH) ^ 非线性超快脉冲耦合的数值方法的Matlab程序 @ !$xSH *r>Y]VG;S 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。
ZZi 9<g1 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
d Np %=gIj "4XjABJ4' 5!Er ;e pTA m } % This Matlab script file solves the nonlinear Schrodinger equations
2 zo>`;l % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
\1R*M % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
8?~>FLWTXZ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
''2:ZX X i% 0 qN C=1;
ca
&zYXy M1=120, % integer for amplitude
C4E* q3[Y M3=5000; % integer for length of coupler
QP%AJ[3ea% N = 512; % Number of Fourier modes (Time domain sampling points)
.yDR2 sW dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
h<IAH Cz;( T =40; % length of time:T*T0.
u}'m7|)8 dt = T/N; % time step
dnANlNMk? n = [-N/2:1:N/2-1]'; % Index
>>=zkPy t = n.*dt;
,9OER! $y ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
T&dc)t `o w=2*pi*n./T;
6\h*SBI?( g1=-i*ww./2;
*"|f!t g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
;&b=>kPlZ g3=-i*ww./2;
Y}vV.q P1=0;
=)#XZ[#F P2=0;
k H06Cb P3=1;
Kj"n
Id) P=0;
%i&am= for m1=1:M1
f`}u9!jVR p=0.032*m1; %input amplitude
?zo7.R-Vac s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
|r*y63\T s1=s10;
GWx?RIKF s20=0.*s10; %input in waveguide 2
LWo )x s30=0.*s10; %input in waveguide 3
45+kwo0 s2=s20;
Mt4 `~`6 s3=s30;
& Ai +t2 p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
j%!xb>< %energy in waveguide 1
s_u!
RrC p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
*eAt ' %energy in waveguide 2
TIV|7nKL p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
%z1hXh#+ %energy in waveguide 3
~N2 [j for m3 = 1:1:M3 % Start space evolution
AWZ4h,as{ s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
'p Aq;2AA s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
* @
\LS!N s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
m7,"M~\pX sca1 = fftshift(fft(s1)); % Take Fourier transform
?AQR\) P sca2 = fftshift(fft(s2));
++kVq$9@y sca3 = fftshift(fft(s3));
\a:-xwUu< sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
uN&49 o sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
7r3EMX\#Qm sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
P+p:Ed 80 s3 = ifft(fftshift(sc3));
N[=R$1\Z s2 = ifft(fftshift(sc2)); % Return to physical space
X)Rh&ui s1 = ifft(fftshift(sc1));
cMU mJH end
R*"zLJP p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
E-rGOm" m p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
?cr^.LV|h^ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
$+
\JT/eG9 P1=[P1 p1/p10];
c}7Rt|`c P2=[P2 p2/p10];
Nrp1` qY P3=[P3 p3/p10];
]gb?3a}A P=[P p*p];
B ?XqH_=0L end
-1F+,+m figure(1)
j&?@:Zg v plot(P,P1, P,P2, P,P3);
w##$SaTI ~<_P jV 转自：
http://blog.163.com/opto_wang/
