计算脉冲在非线性耦合器中演化的Matlab 程序 ^1<i7u F I~=A/: % This Matlab script file solves the coupled nonlinear Schrodinger equations of
OzR<jCOS % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
Cx e(iwa. % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
E33WT{H&_' % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
#99 =wn 6PC ?*^v %fid=fopen('e21.dat','w');
d.
ZfK N = 128; % Number of Fourier modes (Time domain sampling points)
"p+JME( M1 =3000; % Total number of space steps
o_5[}d J =100; % Steps between output of space
= J]M#6N0 T =10; % length of time windows:T*T0
Z$%!H7w T0=0.1; % input pulse width
/%)(Uz MN1=0; % initial value for the space output location
1H -~+lf dt = T/N; % time step
Ggy?5N7P n = [-N/2:1:N/2-1]'; % Index
lXEn m-_ t = n.*dt;
mHa~c(x u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
_xBhMu2f u20=u10.*0.0; % input to waveguide 2
BB_(!omq[ u1=u10; u2=u20;
~Q5]?ZNX U1 = u1;
c= ?Tu U2 = u2; % Compute initial condition; save it in U
d=
?lPEzSA ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
r%NzKPW' w=2*pi*n./T;
F`,Hf Cb\ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
=#A/d `2
b L=4; % length of evoluation to compare with S. Trillo's paper
L\!Oj5 dz=L/M1; % space step, make sure nonlinear<0.05
4,?beA for m1 = 1:1:M1 % Start space evolution
lkC| g%f u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
o)$eIu}Wg u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
J|@D @\?7 ca1 = fftshift(fft(u1)); % Take Fourier transform
hegH^IN M ca2 = fftshift(fft(u2));
"xn,' `a c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
_;:_ !` c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
s,l*=< u2 = ifft(fftshift(c2)); % Return to physical space
m\E=I5*/ u1 = ifft(fftshift(c1));
NG2 3 if rem(m1,J) == 0 % Save output every J steps.
"z= ~7g U1 = [U1 u1]; % put solutions in U array
RD ;A U2=[U2 u2];
V #R; -C MN1=[MN1 m1];
4vND ~9d z1=dz*MN1'; % output location
.u`A4;;Gw end
Sz]1`%_H/ end
TtQd#mSI\ hg=abs(U1').*abs(U1'); % for data write to excel
rq\<zx]au ha=[z1 hg]; % for data write to excel
qT &zg @m t1=[0 t'];
`tcX[(` hh=[t1' ha']; % for data write to excel file
DZA '0- %dlmwrite('aa',hh,'\t'); % save data in the excel format
E>O@Bv figure(1)
7|"$YV'DM waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
c%&*yR figure(2)
* P&lAyt6 waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
52^ ,qP'6 8 i<]$ 非线性超快脉冲耦合的数值方法的Matlab程序 5@
Hg 4. G({VK 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。
|34w<0Pc, 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
JSaF7(a = ~:| V,1 $iA:3DM07 _1WA:7$C % This Matlab script file solves the nonlinear Schrodinger equations
Y{Lxo])e % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
@\>7
wt_' % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
Bgp%hK % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
I|;C} lfp ` .]oH1\ C=1;
c0w1
N]+Ne M1=120, % integer for amplitude
(E~6fb "c M3=5000; % integer for length of coupler
l)'*jZ N = 512; % Number of Fourier modes (Time domain sampling points)
gA3f@7}d dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
#&?}h)Jr' T =40; % length of time:T*T0.
D 5:'2i dt = T/N; % time step
H
]! P[? n = [-N/2:1:N/2-1]'; % Index
|CQ0{1R1 t = n.*dt;
KP $AT}D ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
-3 "<znv w=2*pi*n./T;
G]mD_J1$ g1=-i*ww./2;
}wI +e Mr g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
7s;;2<k;_ g3=-i*ww./2;
=E U;%f P1=0;
tCA0H\' ; P2=0;
4Y4zBD=< P3=1;
.' h^ P=0;
P :%b[7 for m1=1:M1
5fz
K*[B p=0.032*m1; %input amplitude
pRUQMPn ( s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
NJ;m&Tm,DF s1=s10;
e-1G\}E s20=0.*s10; %input in waveguide 2
uc|ej9N s30=0.*s10; %input in waveguide 3
O`aNNy s2=s20;
.C5JQO s3=s30;
TefPxvd p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
~dP\0x0AB %energy in waveguide 1
_j*I\ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
; E >#qYC6 %energy in waveguide 2
w@n}DC Ft p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
9E0x\%2K %energy in waveguide 3
iOL/u)
for m3 = 1:1:M3 % Start space evolution
'/A X 'U8Y s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
*O\lR-z!k s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
^&$86-PB/ s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
rp2g./2 sca1 = fftshift(fft(s1)); % Take Fourier transform
}z|9F(I sca2 = fftshift(fft(s2));
2^w{Hcf sca3 = fftshift(fft(s3));
mgM"u94-] sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
9`? M-U sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
<(V~eo
e sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
<=w!: s3 = ifft(fftshift(sc3));
.])X.7@x s2 = ifft(fftshift(sc2)); % Return to physical space
_N>#/v)Yi s1 = ifft(fftshift(sc1));
_}T )\o end
o|#F@L3i p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
wb h=v; p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
|2rOV&@l9 p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
LnsYtkb r P1=[P1 p1/p10];
obPG]*3 P2=[P2 p2/p10];
(hIo0 . P3=[P3 p3/p10];
6BM$u v4 P=[P p*p];
Z+[W@ 5q end
$H]NC-\+> figure(1)
|`V=hqe{ plot(P,P1, P,P2, P,P3);
%Y5F@=>& KG I <G 转自：
http://blog.163.com/opto_wang/
