计算脉冲在非线性耦合器中演化的Matlab 程序 }f'1x %RS^ sYP@> tHC % This Matlab script file solves the coupled nonlinear Schrodinger equations of
OIT;fKl9 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
sYI':UQe % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
W+S; Do % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
-{%''(G .4(f0RG %fid=fopen('e21.dat','w');
)eMh,r
N = 128; % Number of Fourier modes (Time domain sampling points)
\ \}/2#1=c M1 =3000; % Total number of space steps
<BA&S
_=4 J =100; % Steps between output of space
,LO-! \L T =10; % length of time windows:T*T0
D.!7jA# T0=0.1; % input pulse width
y ]%,Y=%X MN1=0; % initial value for the space output location
r, KK% B dt = T/N; % time step
{3Wc<&D
C1 n = [-N/2:1:N/2-1]'; % Index
_=x_"rz x t = n.*dt;
9D w&b u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
0.0!5D[ u20=u10.*0.0; % input to waveguide 2
Q0_W<+` u1=u10; u2=u20;
-Lb^O/ U1 = u1;
+N@F,3yNa U2 = u2; % Compute initial condition; save it in U
VrxH6 Y ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
0 Wm-` ZA w=2*pi*n./T;
mIo7 K5z{ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
l Hqx}n@e L=4; % length of evoluation to compare with S. Trillo's paper
A$6b=2hc> dz=L/M1; % space step, make sure nonlinear<0.05
LTc t0Gh for m1 = 1:1:M1 % Start space evolution
W10fjMC}^ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
1z:N$O _v u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
N|S xAg ca1 = fftshift(fft(u1)); % Take Fourier transform
- S-1<xR ca2 = fftshift(fft(u2));
Th^ #H c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
dhkpkt<G8 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
nWu4HFi u2 = ifft(fftshift(c2)); % Return to physical space
L{pg?#\yC u1 = ifft(fftshift(c1));
R!G7;m'N1 if rem(m1,J) == 0 % Save output every J steps.
EPRs %(w` U1 = [U1 u1]; % put solutions in U array
18`%WUPnT U2=[U2 u2];
N2e<Y_T MN1=[MN1 m1];
V+z)B+ z1=dz*MN1'; % output location
w'XgW0j{ end
i@L2W>{P end
3fTI&2: hg=abs(U1').*abs(U1'); % for data write to excel
s\!vko'M ha=[z1 hg]; % for data write to excel
Bdepvc}[# t1=[0 t'];
#+k[[; 0 hh=[t1' ha']; % for data write to excel file
![^h<Om %dlmwrite('aa',hh,'\t'); % save data in the excel format
{Z.@-Tl_ figure(1)
tvRy8u; waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
1bkUT_ figure(2)
hh&y2#Io waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
pa-4|)q Y 1+($"$ZC&B 非线性超快脉冲耦合的数值方法的Matlab程序 edx'p`%d5 [^~9wFNtd 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。
y@_?3m7B= 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
RiG!TTa
b w-Fk&dC69 A!yLwkc:5 lJ# >Y5Qg % This Matlab script file solves the nonlinear Schrodinger equations
8$Yf#;m[ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
'O9=*L) X % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
d
4R+gIA % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
G|_aU8b|t 3~rc= e C=1;
1A-EP@# J M1=120, % integer for amplitude
&y\2:IyA M3=5000; % integer for length of coupler
DU8LU*q' N = 512; % Number of Fourier modes (Time domain sampling points)
%WR"85 dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
+to9].O7y T =40; % length of time:T*T0.
!3# }ZC2 dt = T/N; % time step
]M;! ])b$ n = [-N/2:1:N/2-1]'; % Index
\-w s[ t = n.*dt;
<t{AY^:r ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
H%aLkV!J w=2*pi*n./T;
vW3Z u B g1=-i*ww./2;
%$| k3[4V g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
0EXNq*=EE g3=-i*ww./2;
Qpf]3 P1=0;
zAJUL P2=0;
@8yFM % P3=1;
y: [] + P=0;
7g+ ] for m1=1:M1
Ct+% p=0.032*m1; %input amplitude
Qe.kN dT+_ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
IQ ~7vk() s1=s10;
l}c2l' s20=0.*s10; %input in waveguide 2
a@ }r[0O s30=0.*s10; %input in waveguide 3
;NeEgqW " s2=s20;
/j@ `aG(a s3=s30;
rxeXz< p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
ZY$@_D OB} %energy in waveguide 1
; @~*z4U p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
rd4'y~#S %energy in waveguide 2
)m;qv'=! p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
l?_!eA %energy in waveguide 3
q.km>XRk~ for m3 = 1:1:M3 % Start space evolution
q|l|mO s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
-GVG1#5 s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
Ik Nt!
2s_ s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
$IZZ`Z]B sca1 = fftshift(fft(s1)); % Take Fourier transform
% ul{nL: sca2 = fftshift(fft(s2));
R9G)X] sca3 = fftshift(fft(s3));
vaJX X sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
)0MshgM sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
chzR4"WZFt sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
Vp"Ug,1 s3 = ifft(fftshift(sc3));
Go7hDmu s2 = ifft(fftshift(sc2)); % Return to physical space
+J8/,d s1 = ifft(fftshift(sc1));
$!C+i"q$ end
_k.bGYldk p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
r ;8z"* p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
h!CX`pBM p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
i9k]Q(o P1=[P1 p1/p10];
y$V)^-U>fw P2=[P2 p2/p10];
~<OjXuYu P3=[P3 p3/p10];
|hQ|'VCN P=[P p*p];
C-^%g [# end
(H %d] figure(1)
3N0X?* (x| plot(P,P1, P,P2, P,P3);
ruA+1-<f r tmt 3 转自：
http://blog.163.com/opto_wang/
