计算脉冲在非线性耦合器中演化的Matlab 程序 0Da9,&D g9 .b6}w! % This Matlab script file solves the coupled nonlinear Schrodinger equations of
feOX] g#
% soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
Vf S&V* un % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
xij`Mr % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
2y/|/IW= 4L(/Z}( %fid=fopen('e21.dat','w');
1m$:Rn^ N = 128; % Number of Fourier modes (Time domain sampling points)
m22FOjk\ M1 =3000; % Total number of space steps
,Y|WSKY* J =100; % Steps between output of space
dTN[E6#R T =10; % length of time windows:T*T0
Gh3b*O_, T0=0.1; % input pulse width
s+{ )K MN1=0; % initial value for the space output location
`w@8i[2J dt = T/N; % time step
%3B0s?,I n = [-N/2:1:N/2-1]'; % Index
pSM\( kVKa t = n.*dt;
:77dl/d% u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
4-RzWSFbo` u20=u10.*0.0; % input to waveguide 2
&jJj6
+P\ u1=u10; u2=u20;
fU y:TCS U1 = u1;
9$)I=Rpk = U2 = u2; % Compute initial condition; save it in U
qx,>j4y w ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
eEvE 3=,hg w=2*pi*n./T;
k /MrNiC g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
F Xbf7G)H L=4; % length of evoluation to compare with S. Trillo's paper
XcfvmlBoD- dz=L/M1; % space step, make sure nonlinear<0.05
[
+w= for m1 = 1:1:M1 % Start space evolution
WCc7 MK u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
~\;s}Fv. u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
9?8Yf(MC%u ca1 = fftshift(fft(u1)); % Take Fourier transform
Gt >*y.] ca2 = fftshift(fft(u2));
cB,O"- c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
HE>6A|rgDr c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
Yy l(<,Yi u2 = ifft(fftshift(c2)); % Return to physical space
s Fh mp u1 = ifft(fftshift(c1));
1ztL._Td if rem(m1,J) == 0 % Save output every J steps.
QahM)Gb U1 = [U1 u1]; % put solutions in U array
rVo0H.+N)` U2=[U2 u2];
?)x"+[2 MN1=[MN1 m1];
~.-o * z1=dz*MN1'; % output location
"UUzLa_ end
7OF6;@< end
ces|HPBa&6 hg=abs(U1').*abs(U1'); % for data write to excel
-_<rmR[:] ha=[z1 hg]; % for data write to excel
g<ZB9;FX % t1=[0 t'];
:xd)]Ns hh=[t1' ha']; % for data write to excel file
{ek a xSR %dlmwrite('aa',hh,'\t'); % save data in the excel format
Y
6B7qp figure(1)
;3~+M:{2 waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
-M{.KqyW figure(2)
AXK6AZjX waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
uvbXsO"z]] /XfE6SBz 非线性超快脉冲耦合的数值方法的Matlab程序 Jat|n97$ 'J A<q-Gn 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。
M$@Do nx 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
t@hE}R >M `ryM2=D NT3Ti
?J, X:3W9`s )* % This Matlab script file solves the nonlinear Schrodinger equations
>ZX&2 { % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
nIWZo ~ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
J0%e6{C1 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
"9>.,nzt j>D[iHrH C=1;
Z4@%0mFll M1=120, % integer for amplitude
vz{Z
tE" M3=5000; % integer for length of coupler
-pb>=@Yq N = 512; % Number of Fourier modes (Time domain sampling points)
x(r>iy dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
[PR Qa[_ T =40; % length of time:T*T0.
8ux?K5_ dt = T/N; % time step
1/hk3m(C n = [-N/2:1:N/2-1]'; % Index
V~tZNR J- t = n.*dt;
d5 U?* ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
BRSOE U\= w=2*pi*n./T;
Aw7oyC! g1=-i*ww./2;
Hi V7 g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
i'6>_,\( g3=-i*ww./2;
k|kn#X3X P1=0;
Py}] {? P2=0;
Ug2^cgL P3=1;
LBCat=d< P=0;
5:" zs for m1=1:M1
-~PiPYX p=0.032*m1; %input amplitude
"q<}#] u s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
:h (r2?=7 s1=s10;
ggQB Q/ L s20=0.*s10; %input in waveguide 2
E:!qnc L: s30=0.*s10; %input in waveguide 3
n#\ t_/\ s2=s20;
7ThGF s3=s30;
liU/O :Ap p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
R=/^5DZ} %energy in waveguide 1
ZvSWIQ6 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
DrY5Q&S %energy in waveguide 2
Zo12F**{ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
q>n0'`q %energy in waveguide 3
s]lIDp} for m3 = 1:1:M3 % Start space evolution
K1*oYH B s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
\H6[6*JuB s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
ug?])nO.C s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
Lt< KRs sca1 = fftshift(fft(s1)); % Take Fourier transform
+ f+#W sca2 = fftshift(fft(s2));
I z^lED sca3 = fftshift(fft(s3));
H.H$5(?O sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
$t1XoL sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
U"0Ts!CABA sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
o(q][:,h s3 = ifft(fftshift(sc3));
a ,EApUWw s2 = ifft(fftshift(sc2)); % Return to physical space
Bkq3-rX\ s1 = ifft(fftshift(sc1));
"i5Rh^ end
cD!y d^QE p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
x kl XV p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
M8,_E\* p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
.5ItH^ P1=[P1 p1/p10];
reU*apZ/ P2=[P2 p2/p10];
p,cw- lN P3=[P3 p3/p10];
8B|qNf `Yi P=[P p*p];
Z'@a@Y+ end
Y)7LkZO(y figure(1)
Y,
?- [] plot(P,P1, P,P2, P,P3);
oph QdJM HHZGu8tzt 转自：
http://blog.163.com/opto_wang/
