计算脉冲在非线性耦合器中演化的Matlab 程序 */n)_ /)xG%J7H % This Matlab script file solves the coupled nonlinear Schrodinger equations of
jl=<Q.Mm7 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
qDO4&NO % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
3Bz0B a % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
:xfD>K QH6Lb%]/ %fid=fopen('e21.dat','w');
0sRby! N = 128; % Number of Fourier modes (Time domain sampling points)
8ltHR]v M1 =3000; % Total number of space steps
*lg1iP{] J =100; % Steps between output of space
qbkvwL9 T =10; % length of time windows:T*T0
%,GY&hTw T0=0.1; % input pulse width
&2{h]V6 MN1=0; % initial value for the space output location
nv(Pwb3B dt = T/N; % time step
k=O2s'F` n = [-N/2:1:N/2-1]'; % Index
sD.bBz t = n.*dt;
Ay!=Yk^~ u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
vt[4"eU u20=u10.*0.0; % input to waveguide 2
_`L,}=um' u1=u10; u2=u20;
uYS?# g U1 = u1;
UHz*Tfjb U2 = u2; % Compute initial condition; save it in U
EW1L!3K ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
3KfZI&g w=2*pi*n./T;
abUn{X+f~ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
7Rj!vj/ L=4; % length of evoluation to compare with S. Trillo's paper
2s;/*<WM dz=L/M1; % space step, make sure nonlinear<0.05
BUv;BzyV
for m1 = 1:1:M1 % Start space evolution
L*9^-, u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
%L{ H_;z u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
dZRz'd ca1 = fftshift(fft(u1)); % Take Fourier transform
*J?QXsg ca2 = fftshift(fft(u2));
Lm9y!>1"O c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
*~M=2Fj;i c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
BN@*CG u2 = ifft(fftshift(c2)); % Return to physical space
>\8Bu#&s4 u1 = ifft(fftshift(c1));
i)\`"&.j>N if rem(m1,J) == 0 % Save output every J steps.
0^|)[2m! U1 = [U1 u1]; % put solutions in U array
-c%GlpZw U2=[U2 u2];
LS4c|Dv MN1=[MN1 m1];
bc5+}&W z1=dz*MN1'; % output location
,v$gQU2 end
\*!?\Ko`W end
yEtSyb~GK hg=abs(U1').*abs(U1'); % for data write to excel
JTpKF_Za< ha=[z1 hg]; % for data write to excel
KSuP'.l t1=[0 t'];
,m!j2H}8 hh=[t1' ha']; % for data write to excel file
&7T0nB/) %dlmwrite('aa',hh,'\t'); % save data in the excel format
;or(:Yoc- figure(1)
{LY$ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
?
8S0 figure(2)
N6$pOQ waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
6CLrP}
u d37l/I 非线性超快脉冲耦合的数值方法的Matlab程序 vAq`*]W+ 6t
TLyI$+ 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。
+XJj:%yt 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
Mvrc[s+o s9~W( Wi 4
Yc9Ij DL|,:2` % This Matlab script file solves the nonlinear Schrodinger equations
u1ggLH!U % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
[U]*OQH`e % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
wQ*vcbQX* % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Jj|HeZ1C f LS Na C=1;
9cWl/7;zXO M1=120, % integer for amplitude
z*YkD"]B M3=5000; % integer for length of coupler
p<'#f,o N = 512; % Number of Fourier modes (Time domain sampling points)
kG
&.| dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
PLKp<kg T =40; % length of time:T*T0.
wS <d8gw dt = T/N; % time step
'[~NRKQJ n = [-N/2:1:N/2-1]'; % Index
Bra>C t = n.*dt;
^u:7U4 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
782be-n w=2*pi*n./T;
-B9C2 g1=-i*ww./2;
/0d_{Y+9 g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
J8J~$DU\Gv g3=-i*ww./2;
V?
w;YTg P1=0;
5 1@V""m P2=0;
*&+e2itmp P3=1;
]=2Ba<)m P=0;
%8>s :YG for m1=1:M1
{%9)l, p=0.032*m1; %input amplitude
\^iJv~d s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
~+A?!f;-J s1=s10;
x
%L2eXL s20=0.*s10; %input in waveguide 2
xpx=t71Hq s30=0.*s10; %input in waveguide 3
Z2(z,pK s2=s20;
7UejK r s3=s30;
0_}OKn)J p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
$}jp=?,t %energy in waveguide 1
8t!(!<iF0 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
4v33{sp %energy in waveguide 2
>t)vQ&:;u p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
f/~"_O% %energy in waveguide 3
*j?tcxq for m3 = 1:1:M3 % Start space evolution
,u#uk7V s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
<MB]W`5 s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
m beM/ s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
2xhwi.u sca1 = fftshift(fft(s1)); % Take Fourier transform
BDNn~aU#m sca2 = fftshift(fft(s2));
z~L''X7g sca3 = fftshift(fft(s3));
sD7Qt sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
9
#TzW9 sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
MGfDxHg] sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
-GD_xk s3 = ifft(fftshift(sc3));
%2f``48# s2 = ifft(fftshift(sc2)); % Return to physical space
n`2d s1 = ifft(fftshift(sc1));
d=o|)kV end
jA$g0> p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
9 JBPE p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
;o8C(5xE| p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
2qo=ud P1=[P1 p1/p10];
K}tl,MMU P2=[P2 p2/p10];
&M,a+|yuY P3=[P3 p3/p10];
1 "?KQU P=[P p*p];
Y;8Y s&/t end
"=@b>d6U+ figure(1)
l~;H~h!h/ plot(P,P1, P,P2, P,P3);
PUV)w\!&is :'91qA%Wr 转自:
http://blog.163.com/opto_wang/