计算脉冲在非线性耦合器中演化的Matlab 程序 lFTF ,G [HCAmnb % This Matlab script file solves the coupled nonlinear Schrodinger equations of
J>u
7, % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
B<C* % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
Du c#$YfGm % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
*
S=\l@EW D@!=d@V. %fid=fopen('e21.dat','w');
?_I[,N?@41 N = 128; % Number of Fourier modes (Time domain sampling points)
me OMq1 M1 =3000; % Total number of space steps
4.IU !.Uo J =100; % Steps between output of space
#> j.$2G> T =10; % length of time windows:T*T0
6;|n]m\Vd T0=0.1; % input pulse width
MNSbtT*^ MN1=0; % initial value for the space output location
2(/g} dt = T/N; % time step
Yv:55+ e!| n = [-N/2:1:N/2-1]'; % Index
bf9a 1<\ t = n.*dt;
$V1;l a! u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
QR1{ w'c u20=u10.*0.0; % input to waveguide 2
ar:+;.n u1=u10; u2=u20;
4C FB"?n0 U1 = u1;
8P=o4lO+ U2 = u2; % Compute initial condition; save it in U
o tk} y8 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
EY \H=@A w=2*pi*n./T;
b, :QT~g= g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
<n(*Xak{a L=4; % length of evoluation to compare with S. Trillo's paper
_1U1(^) dz=L/M1; % space step, make sure nonlinear<0.05
?wO-cnl for m1 = 1:1:M1 % Start space evolution
6P';DB u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
;pnD0bH u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
8>7& E- ca1 = fftshift(fft(u1)); % Take Fourier transform
4q<=K= F ca2 = fftshift(fft(u2));
R9B&dvG c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
L:9F:/G c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
H/Llj. -jg u2 = ifft(fftshift(c2)); % Return to physical space
23h%
< , u1 = ifft(fftshift(c1));
8jyG" %WO if rem(m1,J) == 0 % Save output every J steps.
L(U"U#QZ U1 = [U1 u1]; % put solutions in U array
Fy.\7CL> U2=[U2 u2];
5< ja3 MN1=[MN1 m1];
@'|)~,"bx z1=dz*MN1'; % output location
KCWc` Oz end
Ntbg`LGf'! end
uJ6DO#d`P hg=abs(U1').*abs(U1'); % for data write to excel
aXL{TD:] ha=[z1 hg]; % for data write to excel
U4cY_p? t1=[0 t'];
2 aL ) hh=[t1' ha']; % for data write to excel file
$]8h $ %dlmwrite('aa',hh,'\t'); % save data in the excel format
*W
kIq> figure(1)
i F+v l] waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
$#]]K figure(2)
7PkJ-JBA waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
Mb]rY>B4 qM.bF&&Go 非线性超快脉冲耦合的数值方法的Matlab程序 lv]hTH 4T <A#
l
35 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
0C>%LJ8r Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
&-m X , !tp1:'KG 8KRba4[ g>J<%z, }2 % This Matlab script file solves the nonlinear Schrodinger equations
AhNq/?Q Q~ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
Hbpqyl%O> % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
v.]Q$q^ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
4)("v-p &SrO) C=1;
*f?4
M1=120, % integer for amplitude
ZfB "
E M3=5000; % integer for length of coupler
z SFDUZ]A3 N = 512; % Number of Fourier modes (Time domain sampling points)
Kh MSL dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
qs QNjt T =40; % length of time:T*T0.
OD5 m9XS dt = T/N; % time step
L>YU,I\o n = [-N/2:1:N/2-1]'; % Index
3Oi
nK[' t = n.*dt;
qv@$ZL R ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
m o:D9 w=2*pi*n./T;
lg b?)= g1=-i*ww./2;
o9H^?Rut g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
tuhA
9}E g3=-i*ww./2;
GxKqD;;u?= P1=0;
_~ T !9 P2=0;
>>5NX"{ P3=1;
k bMYMx.[ P=0;
QPfc(Z for m1=1:M1
~SnSEhE p=0.032*m1; %input amplitude
IqD_GL)Ms s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
L\#<JxY$p s1=s10;
1[yq0^\]M[ s20=0.*s10; %input in waveguide 2
X3V'Cy/sy s30=0.*s10; %input in waveguide 3
6 C+"`(u%V s2=s20;
8f3vjK' s3=s30;
J52
o
g4l p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
:at$ HCaK %energy in waveguide 1
Ba/Yl p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
]~E0gsq %energy in waveguide 2
4A2?Uhp y p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
l@ap]R %energy in waveguide 3
d{E}6)1= for m3 = 1:1:M3 % Start space evolution
7__Q1 > o s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
7IjQi=#: s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
9s_,crq5 s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
yfC^x%d7G sca1 = fftshift(fft(s1)); % Take Fourier transform
k+DR]icv sca2 = fftshift(fft(s2));
I:d[Q
s sca3 = fftshift(fft(s3));
:.4 5u}[ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
PgRDKygE sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
INyk3 `FT sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
7 %{ | s3 = ifft(fftshift(sc3));
T9879[ZU\ s2 = ifft(fftshift(sc2)); % Return to physical space
[mPjP%{=@ s1 = ifft(fftshift(sc1));
14"J d\M8 end
?|ZTaX6A p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
as>L[jyG/ p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
#2EI\E&$ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
`8Lo { P P1=[P1 p1/p10];
]Ty isaT P2=[P2 p2/p10];
.({smN,B P3=[P3 p3/p10];
Ey4z.s'-l P=[P p*p];
P'O#I}Dmw< end
8{Fsm;UsY figure(1)
HO' '&hz plot(P,P1, P,P2, P,P3);
/ 0eYMG+K= J:kmqk! 转自：
http://blog.163.com/opto_wang/
