计算脉冲在非线性耦合器中演化的Matlab 程序 g/3t@7*< fX:=_ c % This Matlab script file solves the coupled nonlinear Schrodinger equations of
qnO>F^itF % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
T~D2rt\ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
WR :I2-1 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
bX*>Zm ,M?K3lG\g[ %fid=fopen('e21.dat','w');
n?a?U : N = 128; % Number of Fourier modes (Time domain sampling points)
;*+wg5| M1 =3000; % Total number of space steps
%p; 'l J =100; % Steps between output of space
H;D C kVL T =10; % length of time windows:T*T0
yq6Gyoi< T0=0.1; % input pulse width
sa?Ul)L2 MN1=0; % initial value for the space output location
QZZt9rA; dt = T/N; % time step
",, W1]"% n = [-N/2:1:N/2-1]'; % Index
9_Ws8nE t = n.*dt;
B!j 7vXM2 u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
1#Q~aY u20=u10.*0.0; % input to waveguide 2
j 3t,Cx u1=u10; u2=u20;
k`(Cwp{Oc U1 = u1;
ORDVyb_x U2 = u2; % Compute initial condition; save it in U
%mF Z!( ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
xq@_'
3X w=2*pi*n./T;
Od]B;&F g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
Bb C aIt L=4; % length of evoluation to compare with S. Trillo's paper
H$M{thW dz=L/M1; % space step, make sure nonlinear<0.05
4Pv Pp{Y for m1 = 1:1:M1 % Start space evolution
d_] sV 4[ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
SoJ=[ 5W u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
goje4; ca1 = fftshift(fft(u1)); % Take Fourier transform
0wE)1w<C~ ca2 = fftshift(fft(u2));
YQ$Wif:@(n c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
p|0ZP6!| c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
7;rf$\-& u2 = ifft(fftshift(c2)); % Return to physical space
) RCva3Ul u1 = ifft(fftshift(c1));
@3v[L<S{ if rem(m1,J) == 0 % Save output every J steps.
h an S8 U1 = [U1 u1]; % put solutions in U array
{ b,#l]v U2=[U2 u2];
}trQ<*D MN1=[MN1 m1];
crlC N z1=dz*MN1'; % output location
/D~MHO{ end
W*WSjuFr2 end
8#h~J>u . hg=abs(U1').*abs(U1'); % for data write to excel
BenUyv1d ha=[z1 hg]; % for data write to excel
8{B]_:
-: t1=[0 t'];
W6&mXJ^3L hh=[t1' ha']; % for data write to excel file
T`W37fz0 %dlmwrite('aa',hh,'\t'); % save data in the excel format
qA>C<NL figure(1)
@.8FVF waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
c[zGWF#1 > figure(2)
o?`^
UG- waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
Aa!#=V1d L43]0k 非线性超快脉冲耦合的数值方法的Matlab程序 M
$\!SXL 1zG hX]z 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
S%IhpTSe6 Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
I4Rd2G_ ;y]BXW&l& S]g`Ds< VK[`e[.C % This Matlab script file solves the nonlinear Schrodinger equations
Aq,&p,m03 % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
:TRhk. % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
i~ITRi@ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
f l+dL#] E5Zxp3 N C=1;
_)a! g-Do7 M1=120, % integer for amplitude
N?l M3=5000; % integer for length of coupler
&pFP =|Pq N = 512; % Number of Fourier modes (Time domain sampling points)
&'"dYZj{ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
,tl(\4n T =40; % length of time:T*T0.
(Y~gItej dt = T/N; % time step
jpt-5@5O n = [-N/2:1:N/2-1]'; % Index
~v V+)KI t = n.*dt;
xz*MFoE ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
8c<OX! w=2*pi*n./T;
q vGP$g g1=-i*ww./2;
A &UGr971 g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
Q7(I' g3=-i*ww./2;
0NMmN_Lr P1=0;
r68d\N`. P2=0;
L8~zQV $h P3=1;
8],tGMu P=0;
#<8 1`% for m1=1:M1
fK10{>E1 p=0.032*m1; %input amplitude
LNOz.2fr> s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
V]6CHE:BS s1=s10;
Jk_ }y s20=0.*s10; %input in waveguide 2
v {O(}@ s30=0.*s10; %input in waveguide 3
fYiof]v@_m s2=s20;
{O5(O oDa s3=s30;
c3!YA"5 p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
qrkJ: %energy in waveguide 1
@2/ xu p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
^-g-]?q %energy in waveguide 2
|*JMCI@Mz p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
{(_> A\zi %energy in waveguide 3
dw3H9(-lp for m3 = 1:1:M3 % Start space evolution
_KA g1Ww s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
8Uoqj=5F s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
P$Fq62;}r4 s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
gh<2i\})' sca1 = fftshift(fft(s1)); % Take Fourier transform
A k+MR EG sca2 = fftshift(fft(s2));
q4]Qvf > sca3 = fftshift(fft(s3));
9PWqoz2c sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
j!/=w q sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
}HxC ~J" sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
!b?`TUt s3 = ifft(fftshift(sc3));
SxW.dT8{ s2 = ifft(fftshift(sc2)); % Return to physical space
E=RX^ 3+} s1 = ifft(fftshift(sc1));
Ct9dV7SH end
QP< vjj% p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
P*3PDa@ p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
9N;y^
Y\ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
2}kJN8\F P1=[P1 p1/p10];
8~:s$~&r P2=[P2 p2/p10];
m?`?T
P3=[P3 p3/p10];
hZ UnNQ P=[P p*p];
4C`p`AQqpQ end
>36>{b<'$* figure(1)
gF~#M1!! plot(P,P1, P,P2, P,P3);
"q3W& @ ^9
Pae) 转自：
http://blog.163.com/opto_wang/
