计算脉冲在非线性耦合器中演化的Matlab 程序 O)R 7t3t GOYn\ N;V2 % This Matlab script file solves the coupled nonlinear Schrodinger equations of
(
}]37 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
r@*=|0(OrK % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
).0V%}> % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
tC2 )j7@ v Q-i xh %fid=fopen('e21.dat','w');
%_B:EMPd N = 128; % Number of Fourier modes (Time domain sampling points)
'2|1%NSW9 M1 =3000; % Total number of space steps
*[d~Nk%Y$ J =100; % Steps between output of space
n!0${QVnS T =10; % length of time windows:T*T0
~vW)1Xn K T0=0.1; % input pulse width
\LIy:$`8
MN1=0; % initial value for the space output location
@9OeC
O dt = T/N; % time step
= cf{f]N n = [-N/2:1:N/2-1]'; % Index
M&uzOK+ t = n.*dt;
*.kj]B oO u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
P$p@5 hl u20=u10.*0.0; % input to waveguide 2
sg3h i"Im u1=u10; u2=u20;
KI E k/]<H U1 = u1;
o"'iX UJ U2 = u2; % Compute initial condition; save it in U
PHQ{-b?4t ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
`t{D 7 I7 w=2*pi*n./T;
'R^i KN Ps g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
wzD\8_;6N L=4; % length of evoluation to compare with S. Trillo's paper
O24Jj\" dz=L/M1; % space step, make sure nonlinear<0.05
-M"IVyy@ for m1 = 1:1:M1 % Start space evolution
wl7 M fyU u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
qTyg~]e9( u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
N=>- Q) ca1 = fftshift(fft(u1)); % Take Fourier transform
e Q $N:] ca2 = fftshift(fft(u2));
x S c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
>$2 E1HW. c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
0Vf)Rw1%I
u2 = ifft(fftshift(c2)); % Return to physical space
0-*Z<cu%l u1 = ifft(fftshift(c1));
!+m@AQ:, if rem(m1,J) == 0 % Save output every J steps.
.D+RLO z U1 = [U1 u1]; % put solutions in U array
]}BB/KQy^ U2=[U2 u2];
FQ+8J 7 MN1=[MN1 m1];
Z*9L'd"D| z1=dz*MN1'; % output location
.
=&Jo9 end
e{5,'(1] end
KL
"Y!PN: hg=abs(U1').*abs(U1'); % for data write to excel
])C>\@c6Gm ha=[z1 hg]; % for data write to excel
moCK- : t1=[0 t'];
Po> e kz_E hh=[t1' ha']; % for data write to excel file
LaDY`u0G% %dlmwrite('aa',hh,'\t'); % save data in the excel format
\ [cH/{nt figure(1)
RYt6=R+f waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
sD2
^_w6j figure(2)
9X3yp:>V waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
q'.;W@m N*f^Z#B] 非线性超快脉冲耦合的数值方法的Matlab程序 TaOO q}8c# WJAYM2
6\ 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。
3g;T?E 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
^+M><jE9 +I&J7ICV0 L%f;J/ b7!UZu]IEv % This Matlab script file solves the nonlinear Schrodinger equations
m*gj|1k % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
C,.-Q"juH % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
@m?{80;uQ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
R3?:\d{ +lKrj\Xj C=1;
i *B:El1 M1=120, % integer for amplitude
l]$40 j M3=5000; % integer for length of coupler
Ih() /( N = 512; % Number of Fourier modes (Time domain sampling points)
QhCY}Q?X dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
v{.\iIg N T =40; % length of time:T*T0.
o_O+u%y dt = T/N; % time step
)
o xIzF n = [-N/2:1:N/2-1]'; % Index
E3f9<hm t = n.*dt;
P% Q@9kO> ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
-?5$ PH w=2*pi*n./T;
l~['[Ub0) g1=-i*ww./2;
?ql2wWsQO g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
n26>>N g3=-i*ww./2;
kxh 5}eB P1=0;
v
J-LPTB P2=0;
SF^x=[ir P3=1;
* 0~M P=0;
g#qNHR for m1=1:M1
H*rx{ F? p=0.032*m1; %input amplitude
lBmm(<~Z s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
sQtf,e|p s1=s10;
LE K/mCL s20=0.*s10; %input in waveguide 2
Af9+HI
O s30=0.*s10; %input in waveguide 3
H}
6CKP} s2=s20;
]~ 8v^A7u s3=s30;
&n|*uLn
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
J\{ $ot %energy in waveguide 1
;E#\ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
Q&PB]D{ %energy in waveguide 2
&bLC(e ] p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
sB6dp D %energy in waveguide 3
Gqt-_gga for m3 = 1:1:M3 % Start space evolution
FsY(02 s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
D %U:!|G s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
&6/%k kv s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
x'qWM/ sca1 = fftshift(fft(s1)); % Take Fourier transform
Sdx Y>; sca2 = fftshift(fft(s2));
hiwIWd:H sca3 = fftshift(fft(s3));
@KA1"Wb_ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
> :Ze4}( sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
!| xZ6KV sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
wb i3lH:; s3 = ifft(fftshift(sc3));
Qn.[{ rw s2 = ifft(fftshift(sc2)); % Return to physical space
QrC/ssf} s1 = ifft(fftshift(sc1));
VNj @5s end
8;#AO8+U7) p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
-72j:nk p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
9tk" :ld p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
9P.(^SD][z P1=[P1 p1/p10];
J>%t<xYf4 P2=[P2 p2/p10];
LeHiT>aX! P3=[P3 p3/p10];
FVgMmYU
P=[P p*p];
V7C1FV2 end
#*2Rp8n figure(1)
FZXyfZw!| plot(P,P1, P,P2, P,P3);
qVBL>9O*. p 7C!G1+z 转自：
http://blog.163.com/opto_wang/
