计算脉冲在非线性耦合器中演化的Matlab 程序 jdV E/5 U/&!F % This Matlab script file solves the coupled nonlinear Schrodinger equations of
p= jD "lq % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
N ~L3
9 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
2MmqGB}YcW % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
FQ>KbZh )s1W)J ?8 %fid=fopen('e21.dat','w');
V*SKWP N = 128; % Number of Fourier modes (Time domain sampling points)
ext`%$ U7 M1 =3000; % Total number of space steps
qsn6i%VH J =100; % Steps between output of space
}|MGYS ) T =10; % length of time windows:T*T0
Epsc2TuH7 T0=0.1; % input pulse width
a c6Lv}w_ MN1=0; % initial value for the space output location
B<(v \=xZ dt = T/N; % time step
D %kY n = [-N/2:1:N/2-1]'; % Index
vK)^;T ; t = n.*dt;
.]g >. u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
U) a}XRS u20=u10.*0.0; % input to waveguide 2
F`- |@k u1=u10; u2=u20;
vttmSdY U1 = u1;
|,L_d2lb U2 = u2; % Compute initial condition; save it in U
wQJY,|. ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
#>C.61Fx w=2*pi*n./T;
2 /O/h
g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
H2` aw3 L=4; % length of evoluation to compare with S. Trillo's paper
>t')ZSjRs dz=L/M1; % space step, make sure nonlinear<0.05
k !Nl#.j for m1 = 1:1:M1 % Start space evolution
Bh?K_{e u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
msOk~ZPE6\ u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
vBAds ca1 = fftshift(fft(u1)); % Take Fourier transform
Q9=vgOW+ ca2 = fftshift(fft(u2));
/PF X1hSu c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
!Vl>?U? AN c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
H Yt& MK u2 = ifft(fftshift(c2)); % Return to physical space
x0B|CO u1 = ifft(fftshift(c1));
= 7pLU+ u if rem(m1,J) == 0 % Save output every J steps.
SbU=L kx# U1 = [U1 u1]; % put solutions in U array
o^%4w>| U2=[U2 u2];
k/hE68<6i MN1=[MN1 m1];
JPW+(n|g z1=dz*MN1'; % output location
Y,z15i3j? end
/H& : end
0@z=0}0Z hg=abs(U1').*abs(U1'); % for data write to excel
LM }0QL
m? ha=[z1 hg]; % for data write to excel
n Av@^G2 t1=[0 t'];
*#{[9d hh=[t1' ha']; % for data write to excel file
.q#2 op %dlmwrite('aa',hh,'\t'); % save data in the excel format
YFgQ!\&59 figure(1)
VXlTA>a } waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
e8O[xM figure(2)
V E1 B"s</ waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
fvccut;K o\u31, 非线性超快脉冲耦合的数值方法的Matlab程序 m~ :W$x1+ LyR t o 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
Ub(zwR; Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Ex^| [iV 9v&{;
%U l@7X gsey W zYy< % This Matlab script file solves the nonlinear Schrodinger equations
,y@` = % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
10x o<@l % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
(NrH)+)J!a % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
ciO^2X SOQm>\U' i C=1;
C* Avu M1=120, % integer for amplitude
r!+-"hS! M3=5000; % integer for length of coupler
. OA_)J7 N = 512; % Number of Fourier modes (Time domain sampling points)
!/O c )Yk dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
}<`Mn34@ T =40; % length of time:T*T0.
L/9f"%kZ dt = T/N; % time step
LQ
pUyqR n = [-N/2:1:N/2-1]'; % Index
|r_S2)zH9m t = n.*dt;
E8# r<=(m ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
f.,ozL3* w=2*pi*n./T;
"P;_-i9O g1=-i*ww./2;
"pTyQT9P g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
2}:scag g3=-i*ww./2;
L>Bf}^ P1=0;
XmN3[j P2=0;
8$}1| "F P3=1;
/Y|oDfv P=0;
CI$pPY<u1 for m1=1:M1
JK0L&t< p=0.032*m1; %input amplitude
* fVs| s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
J@'}lG s1=s10;
13(JW
s20=0.*s10; %input in waveguide 2
h7mJXS)t| s30=0.*s10; %input in waveguide 3
f;M7y:A8q, s2=s20;
1!<k-vt s3=s30;
U{n< n8 p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
v
WKUV| %energy in waveguide 1
<EKDP>,~ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
]v96Q /a %energy in waveguide 2
D(6d#c p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
:=x-b3U %energy in waveguide 3
JJ l wzH for m3 = 1:1:M3 % Start space evolution
Ftu~ nh} s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
KZ^W@*`D s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
WF#eqU*& s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
8;>vgD sca1 = fftshift(fft(s1)); % Take Fourier transform
2lPj%i 5 sca2 = fftshift(fft(s2));
`h+ia/ sca3 = fftshift(fft(s3));
Z!o&};_j sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
Xi3:Ok6FZ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
-Gjz;/s%XH sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
++ !BSQ e s3 = ifft(fftshift(sc3));
((L=1]w s2 = ifft(fftshift(sc2)); % Return to physical space
;Kq H]h) s1 = ifft(fftshift(sc1));
7kapa59 end
EJ&[I%jU p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
jeM % XI p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
J5 PXmL p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
3 D>s y f P1=[P1 p1/p10];
O}\$E {- P2=[P2 p2/p10];
iW\cLp " P3=[P3 p3/p10];
C8i6ESmU P=[P p*p];
bp Q/#\Z end
;~Y0H9 ` figure(1)
9fR`un)f} plot(P,P1, P,P2, P,P3);
D4WvRxki ;A)w:"m 转自：
http://blog.163.com/opto_wang/
