计算脉冲在非线性耦合器中演化的Matlab 程序 fc:87ZR{ K
L9h L@ % This Matlab script file solves the coupled nonlinear Schrodinger equations of
unYPvrd % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
x?6^EB|@ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
lKQ jG+YF % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
* >iJ=H :n <l0 %fid=fopen('e21.dat','w');
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K-7z N = 128; % Number of Fourier modes (Time domain sampling points)
:'t"kS M1 =3000; % Total number of space steps
~&0lWa J =100; % Steps between output of space
mFpj@=^_G T =10; % length of time windows:T*T0
!
, ] Fx T0=0.1; % input pulse width
U2_; MN1=0; % initial value for the space output location
T}p|_)&y dt = T/N; % time step
JKYtB XOl n = [-N/2:1:N/2-1]'; % Index
fm%4ab30T t = n.*dt;
` T2DGv u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
|a1zJ_t4 u20=u10.*0.0; % input to waveguide 2
'bji2#z[ u1=u10; u2=u20;
muK)Y w[#N U1 = u1;
UQ e1rf U2 = u2; % Compute initial condition; save it in U
R $/q=*k ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
M+=q"#& w=2*pi*n./T;
i+-=I+L3 g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
^s8JW" H L=4; % length of evoluation to compare with S. Trillo's paper
%AgCE"! dz=L/M1; % space step, make sure nonlinear<0.05
B aCzN;) for m1 = 1:1:M1 % Start space evolution
}/ xdHt u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
0 0W_XhJ u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
Mv%B#J ca1 = fftshift(fft(u1)); % Take Fourier transform
_=5\ $6 ca2 = fftshift(fft(u2));
}q/[\3 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
sQzr+ ]+#9 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
$iy( + } u2 = ifft(fftshift(c2)); % Return to physical space
\bSakh71 u1 = ifft(fftshift(c1));
R'1"`@f G if rem(m1,J) == 0 % Save output every J steps.
^3&-!<* U1 = [U1 u1]; % put solutions in U array
Df $Yn U2=[U2 u2];
dI,H:g MN1=[MN1 m1];
n 8| z1=dz*MN1'; % output location
k"`^vV[{F end
] %5gPfv[T end
Yj>\WH hg=abs(U1').*abs(U1'); % for data write to excel
w^ $$'5= ha=[z1 hg]; % for data write to excel
MIv,$ t1=[0 t'];
%+$!ct n hh=[t1' ha']; % for data write to excel file
#
WL5p. %dlmwrite('aa',hh,'\t'); % save data in the excel format
1 rmN) figure(1)
N jA\*M9 waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
GsWf$/iC: figure(2)
`? f sU waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
$)O\i^T DV bY 非线性超快脉冲耦合的数值方法的Matlab程序 wlX
K2D H:
; S1D 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
|SsmVW$B| 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
Of$gs- @v\jL+B+m #fe zUU h3-dJgb % This Matlab script file solves the nonlinear Schrodinger equations
(7P VfS>; % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
Bk4|ik} % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
<C7/b#4>\ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
p["20 ?^ gG6BEsGa, C=1;
3n T pL # M1=120, % integer for amplitude
^t)alN Gos M3=5000; % integer for length of coupler
I#t# %!InH N = 512; % Number of Fourier modes (Time domain sampling points)
cA
B^]j dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
^$\#aTyFK T =40; % length of time:T*T0.
x@"`KiEUs dt = T/N; % time step
ML_[Z_Q<z n = [-N/2:1:N/2-1]'; % Index
q/\Hh9` t = n.*dt;
Zv1/J}+ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
BO=j*.YKy w=2*pi*n./T;
"C%* 'k g1=-i*ww./2;
LfS]m>>e g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
:j!N7c{ g3=-i*ww./2;
/T/7O P1=0;
[]eZO_o6j P2=0;
q"^T}d d, P3=1;
N%+ C5e< P=0;
*6*/kV? F for m1=1:M1
*Ry
"`" p=0.032*m1; %input amplitude
Uv /?/;si s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
EY
9N{ s1=s10;
ID v|i .q3 s20=0.*s10; %input in waveguide 2
!F*CE cB s30=0.*s10; %input in waveguide 3
,!g%`@u s2=s20;
cY \"{o"C s3=s30;
wrt^0n'r)c p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
79(Px2H2 %energy in waveguide 1
be{t y V
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
;F'/[l{+ %energy in waveguide 2
5U&?P p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
ns1@=f cO %energy in waveguide 3
4wQ>HrS)( for m3 = 1:1:M3 % Start space evolution
ZnYoh/ s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
q'awV5 y s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
|G]M"3^ s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
[ 6t!}q sca1 = fftshift(fft(s1)); % Take Fourier transform
k%?A= h sca2 = fftshift(fft(s2));
rn8t<=ptH3 sca3 = fftshift(fft(s3));
r6eApKZ>f6 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
}7jg>3ng( sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
%7bZnK`C sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
t{)J#8:g s3 = ifft(fftshift(sc3));
BPz lt s2 = ifft(fftshift(sc2)); % Return to physical space
?rgk s1 = ifft(fftshift(sc1));
)D q/f W end
YV0K &d p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
Fps.F hm p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
?rn#S8nNx< p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
2 r=A' P1=[P1 p1/p10];
l6EDl0~r P2=[P2 p2/p10];
Hh1OD?N ) P3=[P3 p3/p10];
<+c6CM$#}V P=[P p*p];
:X6A9jmd end
e7.!=R{6 figure(1)
kdry a plot(P,P1, P,P2, P,P3);
[8QE}TFic jF BnP,WQ 转自：
http://blog.163.com/opto_wang/
