计算脉冲在非线性耦合器中演化的Matlab 程序 F*\4l;NJ OG}KqG!n % This Matlab script file solves the coupled nonlinear Schrodinger equations of
]]y[t|6 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
[q"NU&SX % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
~`[8"YUL % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
.vaJ Avg T#r=<YH[C %fid=fopen('e21.dat','w');
[gn[nP9 N = 128; % Number of Fourier modes (Time domain sampling points)
)_Iz>) M1 =3000; % Total number of space steps
]}~4J.Yn J =100; % Steps between output of space
"XB4yExy T =10; % length of time windows:T*T0
FfSI n3 T0=0.1; % input pulse width
acae=c|X MN1=0; % initial value for the space output location
;@4sd%L8V dt = T/N; % time step
;qb Dbg n = [-N/2:1:N/2-1]'; % Index
5M.Red.L t = n.*dt;
6sy,A~e u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
>~wu3q u20=u10.*0.0; % input to waveguide 2
'M -)Os " u1=u10; u2=u20;
c(&AnIlS U1 = u1;
|*1xrM:v~ U2 = u2; % Compute initial condition; save it in U
R8ZD#,; ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
%mL5+d-oP w=2*pi*n./T;
D 2$ ^ " g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
_.-#E$6s#q L=4; % length of evoluation to compare with S. Trillo's paper
?RJdn]`4j dz=L/M1; % space step, make sure nonlinear<0.05
oX {@'B for m1 = 1:1:M1 % Start space evolution
^XNw$@&', u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
Z9f/-|r5 u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
Y{j7Q4{ ca1 = fftshift(fft(u1)); % Take Fourier transform
e# <4/FR ca2 = fftshift(fft(u2));
g/B\ObY c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
Rdj8 *f c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
`GS cRhbh u2 = ifft(fftshift(c2)); % Return to physical space
c dDY]"k u1 = ifft(fftshift(c1));
l.uN$B if rem(m1,J) == 0 % Save output every J steps.
->3uOF!q U1 = [U1 u1]; % put solutions in U array
&t_A0z U2=[U2 u2];
yWmrdvL MN1=[MN1 m1];
lJ lhl7 z1=dz*MN1'; % output location
$$\V 2%v end
W[fT
R?n end
H7}g!n? hg=abs(U1').*abs(U1'); % for data write to excel
GI?PGAT ha=[z1 hg]; % for data write to excel
IqXBz.p t1=[0 t'];
\#2
s4RCji hh=[t1' ha']; % for data write to excel file
%rw}u"3T %dlmwrite('aa',hh,'\t'); % save data in the excel format
"R 8.P/ 3 figure(1)
y]7 %$*
< waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
@ "0uM?_)- figure(2)
`ReGnT[ waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
HS(U4 J ZA*{n2 非线性超快脉冲耦合的数值方法的Matlab程序 'H!V54
\j 3Qk/ Ll 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
[0wP\{% Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
<c(&T<$ 7MoR9,( 6-ti Rk~ hcQSB00D^ % This Matlab script file solves the nonlinear Schrodinger equations
el}hcAY/RP % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
PP],HB+*[ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
:Jm!=U%'Z % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
*!i,?vn ~};]k } C=1;
+;YE)~R? M1=120, % integer for amplitude
r1+c/;TpZ M3=5000; % integer for length of coupler
gt~9"I N = 512; % Number of Fourier modes (Time domain sampling points)
#jOOsfH|k dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
ftxTX3X T =40; % length of time:T*T0.
y 2GQN:X dt = T/N; % time step
gU~
L@R_D n = [-N/2:1:N/2-1]'; % Index
(x}A _ i t = n.*dt;
>B`Cch/ 'U ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
g
,`F<CF9 w=2*pi*n./T;
6={IMkmA g1=-i*ww./2;
1]Gf)| g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
5[nmP95YK g3=-i*ww./2;
JaA&e T| P1=0;
tc"T}huypU P2=0;
' J2ewW5 P3=1;
Y$>+U P=0;
E1#H{ )G for m1=1:M1
WUzS l Zq p=0.032*m1; %input amplitude
cW=Qh-`jU; s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
MST:.x ; s1=s10;
0 4P.p6 s20=0.*s10; %input in waveguide 2
Fs?( UM s30=0.*s10; %input in waveguide 3
L^6"' # s2=s20;
NS
h%t+XU] s3=s30;
P`7ojXy p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
uFz/PDOZ@ %energy in waveguide 1
3(MoXA* p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
6euR'd^Qi %energy in waveguide 2
d:A\<F p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
Yd[U %energy in waveguide 3
pi|\0lH6W for m3 = 1:1:M3 % Start space evolution
52da]BW< s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
bh{E& 1sLh s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
:b.3CL\.6 s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
,;9ak-$8p sca1 = fftshift(fft(s1)); % Take Fourier transform
5BrU' NF sca2 = fftshift(fft(s2));
)>ug{ M%g sca3 = fftshift(fft(s3));
>Dk1axZ!>/ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
EV:_Kx8f P sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
:x8Jy4L sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
2r
%>]y s3 = ifft(fftshift(sc3));
@P*ylB}?Q s2 = ifft(fftshift(sc2)); % Return to physical space
H~~7~1"x s1 = ifft(fftshift(sc1));
^!q 08`0 end
8w03{H
0 p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
7 ESN! p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
n>u .3w L p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
s4x'f$r P1=[P1 p1/p10];
976E3u"Vt P2=[P2 p2/p10];
s.|!Ti!] P3=[P3 p3/p10];
d^ 2u}^kG P=[P p*p];
vEu
Ka<5 end
<l* agH-.3 figure(1)
jn.R.}TT plot(P,P1, P,P2, P,P3);
7h(HG ?2Y x*NqA( r 转自：
http://blog.163.com/opto_wang/
