计算脉冲在非线性耦合器中演化的Matlab 程序 ],Y+|uX-> ~`VD}{[,B % This Matlab script file solves the coupled nonlinear Schrodinger equations of
)}T0 SGY % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
<{A |Xs % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
1.q
a//'RW % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
~H`(z zk I#](mRJ6 %fid=fopen('e21.dat','w');
+q)B4A'J! N = 128; % Number of Fourier modes (Time domain sampling points)
_,E ! < M1 =3000; % Total number of space steps
yA-UXKT J =100; % Steps between output of space
O`='8'6zW\ T =10; % length of time windows:T*T0
m# t T0=0.1; % input pulse width
yyu f MN1=0; % initial value for the space output location
*D uxabo? dt = T/N; % time step
PH]ui= n = [-N/2:1:N/2-1]'; % Index
nV?e(}D t = n.*dt;
" ?Xb$V7 u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
+L<x0-& u20=u10.*0.0; % input to waveguide 2
"p kn u1=u10; u2=u20;
>[TJ-%V>oR U1 = u1;
~b SjZ1` U2 = u2; % Compute initial condition; save it in U
gX *i" Y# ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
ewzZb*\ w=2*pi*n./T;
\d"M& -O g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
p +|(lrYC L=4; % length of evoluation to compare with S. Trillo's paper
G bbD) dz=L/M1; % space step, make sure nonlinear<0.05
UNd+MHE74I for m1 = 1:1:M1 % Start space evolution
/*)
=o+ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
^1w*$5YI u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
D*o [a #2_ ca1 = fftshift(fft(u1)); % Take Fourier transform
)w!*6< ca2 = fftshift(fft(u2));
zu|=1C#5h c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
~:lN("9OI c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
BX6]d:S u2 = ifft(fftshift(c2)); % Return to physical space
"ku ?A ^f u1 = ifft(fftshift(c1));
P*sb@ y>}O if rem(m1,J) == 0 % Save output every J steps.
B3i U# U1 = [U1 u1]; % put solutions in U array
L# NW<T U2=[U2 u2];
1r;. r| MN1=[MN1 m1];
#u6ZCv7u z1=dz*MN1'; % output location
.#$D\cwV end
9<S};I; end
Y'%k
G5nF hg=abs(U1').*abs(U1'); % for data write to excel
G9i?yd4n=B ha=[z1 hg]; % for data write to excel
^J$? [@qD t1=[0 t'];
&nEQ `3~F hh=[t1' ha']; % for data write to excel file
+idp1SJ4 %dlmwrite('aa',hh,'\t'); % save data in the excel format
G u P1 figure(1)
+~]LvZt I_ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
^zVBS7`J figure(2)
dJwE/s waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
{QRrAi l\{{iAC]I 非线性超快脉冲耦合的数值方法的Matlab程序 a)G T\1q gXI8$W> 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。
BSib/)p 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
>,. x'{ "vG ~2J R-2 V C >X!A/; $ % This Matlab script file solves the nonlinear Schrodinger equations
-%#F5br% % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
IHlTp0? % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
=ADdfuKN % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
JHZ`LWq P_f^gB7 C=1;
Ue22,Pp6 M1=120, % integer for amplitude
El)WjcmH M3=5000; % integer for length of coupler
h16 i]V N = 512; % Number of Fourier modes (Time domain sampling points)
($ l
t@j dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
)0 W-S9e< T =40; % length of time:T*T0.
#b?)fqRJL dt = T/N; % time step
dNMz(~A[Y n = [-N/2:1:N/2-1]'; % Index
K9(Su`zr t = n.*dt;
9:tn! <^=I ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
}yW*vy6` w=2*pi*n./T;
2XN];,{ g1=-i*ww./2;
HQO z g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
?H2{R: g3=-i*ww./2;
&=d0'3k> P1=0;
j\S}TaH0e P2=0;
PRE\ 2lLY P3=1;
>^fkHbgNQ P=0;
\h }a?T6 for m1=1:M1
>X" V p=0.032*m1; %input amplitude
Q7-d ]xJ^ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
t$W~X~// s1=s10;
^cy.iolt s20=0.*s10; %input in waveguide 2
0=^A{V!m s30=0.*s10; %input in waveguide 3
yx t ` s2=s20;
}.j09[< s3=s30;
4pfv?!Oj p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
OAhCW*B %energy in waveguide 1
h7h[! > p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
MSw:Ay [9 %energy in waveguide 2
If*t$f>y4N p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
~20O&2 %energy in waveguide 3
z sZP\ for m3 = 1:1:M3 % Start space evolution
*&VqAc%qD s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
oMj;9,WK' s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
L,B# % t s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
v)a$;P% sca1 = fftshift(fft(s1)); % Take Fourier transform
s28r j6q sca2 = fftshift(fft(s2));
>pV|c\ sca3 = fftshift(fft(s3));
U%~L){<V[ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
6fOh * sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
s$s]D\N sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
xxN=,p s3 = ifft(fftshift(sc3));
rfdT0xfcU s2 = ifft(fftshift(sc2)); % Return to physical space
pg %'_+$~m s1 = ifft(fftshift(sc1));
Xt!%W end
Ew|VDD(. p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
\!["U `\.K p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
7Q>*] p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
?u`TX_OsB P1=[P1 p1/p10];
Y^Olcz P2=[P2 p2/p10];
N<\U$\i P3=[P3 p3/p10];
3 oG5E"G P=[P p*p];
l$_Yl&!q$ end
Y GZX} - figure(1)
W\tSXM-Hg plot(P,P1, P,P2, P,P3);
_FET$$>z N JY|f zL 转自：
http://blog.163.com/opto_wang/
