计算脉冲在非线性耦合器中演化的Matlab 程序 &vFq e,Z ] /o12p I % This Matlab script file solves the coupled nonlinear Schrodinger equations of
X<Th{kM2 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
ckf<N9 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
KZrMf77= % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
$W/+nmb)@K p]h*6nH>~ %fid=fopen('e21.dat','w');
o=-Vt,2{ N = 128; % Number of Fourier modes (Time domain sampling points)
$h 08Z M1 =3000; % Total number of space steps
xBL$]> J =100; % Steps between output of space
8Q^6ibE T =10; % length of time windows:T*T0
~&DB!6* T0=0.1; % input pulse width
XVrm3aj(m MN1=0; % initial value for the space output location
R81{<q'%X dt = T/N; % time step
+HOCVqx n = [-N/2:1:N/2-1]'; % Index
C(V [wvL t = n.*dt;
zNV!@ Yr u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
$!|8 g`Tm u20=u10.*0.0; % input to waveguide 2
ceb s.sF: u1=u10; u2=u20;
b W=. K>| U1 = u1;
X -)RU? U2 = u2; % Compute initial condition; save it in U
wC(vr.,F ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
&c!j`86y* w=2*pi*n./T;
%NT`C9][ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
M&qh]v g C L=4; % length of evoluation to compare with S. Trillo's paper
yV:E K{E dz=L/M1; % space step, make sure nonlinear<0.05
axK 6sIxx for m1 = 1:1:M1 % Start space evolution
sK`~Csb
iB u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
~K~b`|1 u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
'yPCZ`5H( ca1 = fftshift(fft(u1)); % Take Fourier transform
eVw\v#gd ca2 = fftshift(fft(u2));
9Z,*h-o c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
E0"10Qbi c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
lAdDu u2 = ifft(fftshift(c2)); % Return to physical space
bA@
/B' u1 = ifft(fftshift(c1));
9VoDhsKk if rem(m1,J) == 0 % Save output every J steps.
~L %Pz0Gg U1 = [U1 u1]; % put solutions in U array
&W=V%t>Z U2=[U2 u2];
;wij}y-6 MN1=[MN1 m1];
E?3 0J3 S z1=dz*MN1'; % output location
m:)Z6 end
0U82f1ei end
lLu ID hg=abs(U1').*abs(U1'); % for data write to excel
uY^v"cw/F ha=[z1 hg]; % for data write to excel
xS6(K t1=[0 t'];
#ZG3|#Q=L hh=[t1' ha']; % for data write to excel file
x9 &-(kBU %dlmwrite('aa',hh,'\t'); % save data in the excel format
9=t#5J#O figure(1)
<^lJr82 waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
([:]T$0 # figure(2)
qbS'|--wH waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
v5(q) h ;i<$7MR.e 非线性超快脉冲耦合的数值方法的Matlab程序 g%`i=s&N% ecr88 6 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
XB0 a dp Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
u~s
Sk ;~ W8v.EW Ho 3dsh ) 0B=[80K;8 % This Matlab script file solves the nonlinear Schrodinger equations
\Sg<='/{L; % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
;wJ~ha C % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
eP f+[pV3 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
exfm q W7H&R, C=1;
V,V*30K5 M1=120, % integer for amplitude
q`XW5VV{K M3=5000; % integer for length of coupler
< &4nOt N = 512; % Number of Fourier modes (Time domain sampling points)
<0CzB"Ap dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
!Citzor T =40; % length of time:T*T0.
# @ 9)h dt = T/N; % time step
]b 3/E s+ n = [-N/2:1:N/2-1]'; % Index
>A-<ZS*N t = n.*dt;
6gXIt9B.h$ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
$ tI]rU w=2*pi*n./T;
Y 4d 3n g1=-i*ww./2;
>D 97c|?c g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
g3Z:{@m g3=-i*ww./2;
wZ#Rlv,3Wa P1=0;
).LTts7c P2=0;
KkEv#2n P3=1;
:z]}ZZ P=0;
7_-w_"X for m1=1:M1
VZ$=6CavH p=0.032*m1; %input amplitude
7W"/ N #G s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
[r(Qs| s1=s10;
#O" s20=0.*s10; %input in waveguide 2
BT]ua]T+ s30=0.*s10; %input in waveguide 3
/RGNAHtI i s2=s20;
g?B 3!,!9 s3=s30;
jk$86ma! p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
['z!{Ez %energy in waveguide 1
$(ewk): p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
U[R@x` %energy in waveguide 2
Wt^|BjbB4 p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
QdQ d(4/1 %energy in waveguide 3
6SVqRD<` for m3 = 1:1:M3 % Start space evolution
f/,tgA s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
Ur^j$B} s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
2#3^skj s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
2jl)mL sca1 = fftshift(fft(s1)); % Take Fourier transform
<\" .L sca2 = fftshift(fft(s2));
A3HF,EG sca3 = fftshift(fft(s3));
i(*I@ku sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
' _dzcN,z sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
w1r$='*I sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
Rs*v m s3 = ifft(fftshift(sc3));
Po(]rQbE s2 = ifft(fftshift(sc2)); % Return to physical space
nBN&.+3t s1 = ifft(fftshift(sc1));
[$\z'} end
z% 1{ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
*:_P8G; p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
B<7/,d' p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
EATu KLP\ P1=[P1 p1/p10];
y: d{jG^ P2=[P2 p2/p10];
@m~RtC-Q P3=[P3 p3/p10];
;Wc4qJ.@ P=[P p*p];
/4$4h;_8 end
fj>C@p figure(1)
>`'O7 .R plot(P,P1, P,P2, P,P3);
g%xGOA xY\ 0 z Q 转自：
http://blog.163.com/opto_wang/
