计算脉冲在非线性耦合器中演化的Matlab 程序 `$3P@SO" OT)`)PZ" % This Matlab script file solves the coupled nonlinear Schrodinger equations of
F%{z E ANm % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
ZC ^?ng % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
E sg: % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
q zo)\, -ucR@P] %fid=fopen('e21.dat','w');
#}Ays#wA>? N = 128; % Number of Fourier modes (Time domain sampling points)
a{?>F&vnU M1 =3000; % Total number of space steps
6jl{^dI J =100; % Steps between output of space
(m.jC}J T =10; % length of time windows:T*T0
8@T0]vH& T0=0.1; % input pulse width
F1`mq2^@ MN1=0; % initial value for the space output location
=ae hhs> dt = T/N; % time step
~ r$I&8 n = [-N/2:1:N/2-1]'; % Index
MU N: }S t = n.*dt;
> 4#\ U! u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
_,- \; u20=u10.*0.0; % input to waveguide 2
(hv} K*c{ u1=u10; u2=u20;
:4COPUBpPV U1 = u1;
Ja@ ?.gW U2 = u2; % Compute initial condition; save it in U
DFGgyF ay ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
icK U) w=2*pi*n./T;
rj5)b:c} g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
[Kbna>` L=4; % length of evoluation to compare with S. Trillo's paper
Me; Nn$'% dz=L/M1; % space step, make sure nonlinear<0.05
ab 6D & for m1 = 1:1:M1 % Start space evolution
2b :I . u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
mj y+_ u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
*I9G" R8 ca1 = fftshift(fft(u1)); % Take Fourier transform
0E&XD&D ca2 = fftshift(fft(u2));
!}xRwkN c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
CR|>?9V c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
fK=vLcH u2 = ifft(fftshift(c2)); % Return to physical space
gti=GmL(L u1 = ifft(fftshift(c1));
`k08M) if rem(m1,J) == 0 % Save output every J steps.
rO1.8KKJ U1 = [U1 u1]; % put solutions in U array
x/92],.Mz U2=[U2 u2];
B_.>Q8tK; MN1=[MN1 m1];
mOYXd,xd z1=dz*MN1'; % output location
G&7 } m end
^}GR!990 end
jg3['hTJT hg=abs(U1').*abs(U1'); % for data write to excel
1+ Y;
"tT ha=[z1 hg]; % for data write to excel
@jD19= t1=[0 t'];
9893{}\cB hh=[t1' ha']; % for data write to excel file
v/wR) 9 %dlmwrite('aa',hh,'\t'); % save data in the excel format
,k/<Nv; figure(1)
] m^ECA$ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
NW Pd~l+ figure(2)
*P [N.5{ waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
/3~}= b KhbbGdmfS$ 非线性超快脉冲耦合的数值方法的Matlab程序 zPb "6%1B I~c}&'V 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。
9,
792b 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
vYG$>* 7jF2m'( Al]z = UgLJV2M6 % This Matlab script file solves the nonlinear Schrodinger equations
>Q^*h}IdW % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
HM\gOz % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
)i>T\B % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
dtq]_HvTJ 8m) E~6 C=1;
;4]l P M1=120, % integer for amplitude
cGjkx3l* M3=5000; % integer for length of coupler
{pB9T3ry] N = 512; % Number of Fourier modes (Time domain sampling points)
i{ /nHrN dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
.'N#qs_ T =40; % length of time:T*T0.
v_@&#!u` dt = T/N; % time step
y|Zj
M n = [-N/2:1:N/2-1]'; % Index
:~9F/Jx t = n.*dt;
& |o V\L ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
$d7{ q3K&1 w=2*pi*n./T;
<3Hu(Jx<O g1=-i*ww./2;
k$ } 6Qd g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
\t@|-` g3=-i*ww./2;
JTB5#S4W P1=0;
(*Y ENT} P2=0;
Cqk6I gw P3=1;
y< 5xlN(+v P=0;
Dn PV
Tp(> for m1=1:M1
^zaN?0%S33 p=0.032*m1; %input amplitude
bDPT1A`F s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
1Y Mu\( s1=s10;
RpY#_\^hI s20=0.*s10; %input in waveguide 2
Yt;.Z$i , s30=0.*s10; %input in waveguide 3
-n~VMLd?@ s2=s20;
yf6&'Y{ s3=s30;
7e&%R4{b p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
Zx]"2U# %energy in waveguide 1
K<+h/Ok p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
3^zO G2 %energy in waveguide 2
) 4'@=q p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
JEes'H}Y %energy in waveguide 3
Gwkp(9d for m3 = 1:1:M3 % Start space evolution
FeFH_ s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
?wx|n_3<: s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
07+Qai-] s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
Wc$1Re{z sca1 = fftshift(fft(s1)); % Take Fourier transform
hw&R .F sca2 = fftshift(fft(s2));
4m6E~_:F sca3 = fftshift(fft(s3));
< tg>1,C sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
3J}bI {3 sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
j7 D\O sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
oa |nQ`[ s3 = ifft(fftshift(sc3));
bmO[9
)G s2 = ifft(fftshift(sc2)); % Return to physical space
DP9hvu /85 s1 = ifft(fftshift(sc1));
FiqcM-Af4 end
6]^}GyM! p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
6^.< 5SJ} p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
PZ "=t! p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
/^\6 q"' P1=[P1 p1/p10];
L% JmdY; P2=[P2 p2/p10];
ZW SYh>" P3=[P3 p3/p10];
x*[\ $E`v P=[P p*p];
g+k0Fw]! end
7 0:a2m figure(1)
mPxph>o plot(P,P1, P,P2, P,P3);
; ,]T|> M
sD* 8:Hl 转自：
http://blog.163.com/opto_wang/
