计算脉冲在非线性耦合器中演化的Matlab 程序 jiLJiYMg . _`rh % This Matlab script file solves the coupled nonlinear Schrodinger equations of
WjM7s]ZRv % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
.q[}e);) % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
ylQj2B,CB % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
]yZ% wU9!
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" %fid=fopen('e21.dat','w');
P +OS N = 128; % Number of Fourier modes (Time domain sampling points)
:Q@/ F;Z? M1 =3000; % Total number of space steps
{P_ 7AM J =100; % Steps between output of space
yTZ o4c " T =10; % length of time windows:T*T0
n^O!93a T0=0.1; % input pulse width
% %>nM'4< MN1=0; % initial value for the space output location
|\G^: V[. dt = T/N; % time step
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o(Qm n = [-N/2:1:N/2-1]'; % Index
M6N p!0G t = n.*dt;
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$;1a u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
RwOOe7mv u20=u10.*0.0; % input to waveguide 2
\x]\W#C u1=u10; u2=u20;
5s`r&2 w U1 = u1;
u#Jr_ ze U2 = u2; % Compute initial condition; save it in U
x SSEDf q ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
;e/F( J w=2*pi*n./T;
ctjQBWE g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
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M L=4; % length of evoluation to compare with S. Trillo's paper
NMf#0Nz- dz=L/M1; % space step, make sure nonlinear<0.05
N)R5#JX for m1 = 1:1:M1 % Start space evolution
}f? [m&< u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
QKlsBq u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
NX.5 u8Pf ca1 = fftshift(fft(u1)); % Take Fourier transform
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X)1R ca2 = fftshift(fft(u2));
q^Oj/w s c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
0Bh cXH t c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
%DXBl:!Y` u2 = ifft(fftshift(c2)); % Return to physical space
q#8yU\J|, u1 = ifft(fftshift(c1));
jnT Tj l if rem(m1,J) == 0 % Save output every J steps.
BI %XF
9{ U1 = [U1 u1]; % put solutions in U array
vB{i w}Hi! U2=[U2 u2];
~?HK,` 0h> MN1=[MN1 m1];
dr: x0>
z1=dz*MN1'; % output location
Sp:w _;{# end
3Ke6lV)uq end
1PUZB`"3 hg=abs(U1').*abs(U1'); % for data write to excel
F@f4-NR> ha=[z1 hg]; % for data write to excel
:/$ WeAg t1=[0 t'];
{tY1$} R hh=[t1' ha']; % for data write to excel file
Dm5 Uy^F} %dlmwrite('aa',hh,'\t'); % save data in the excel format
8(L2w|+B< figure(1)
8B?U\cfa^ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
>Bf3X&uS figure(2)
-n"w XOx3 waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
1Kk6n UIN vszm9Qf 非线性超快脉冲耦合的数值方法的Matlab程序 .'<K$:8@| Q!V:=d 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。
m:[I$b6AY Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
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/[\g8U{5B} 'g ,h % This Matlab script file solves the nonlinear Schrodinger equations
;<m`mb4x[ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
d!0rq4v7 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
%
_ E?3 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
pr z CO w -8Mb~Hfl0 C=1;
3c3;8h$k M1=120, % integer for amplitude
n{sk M3=5000; % integer for length of coupler
nM2<u[{gF N = 512; % Number of Fourier modes (Time domain sampling points)
NGl
8*Af dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
k)S1Z s~G T =40; % length of time:T*T0.
~ a`[p\ dt = T/N; % time step
0r1GGEW`s n = [-N/2:1:N/2-1]'; % Index
__.M S6"N t = n.*dt;
C:5- h(# ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
qfE0J;e w=2*pi*n./T;
u*)/e9C g1=-i*ww./2;
}" vxYB!h3 g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
K8X7I E g3=-i*ww./2;
J~]@#=,v P1=0;
=N\; ?eF( P2=0;
L4m Vk P3=1;
ZxwrlaA P=0;
s~A-qG> for m1=1:M1
D~ Y6%9 p=0.032*m1; %input amplitude
HC6U_d1-6 s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
b ^ h_` s1=s10;
o&E8<e s20=0.*s10; %input in waveguide 2
>U{iof< s30=0.*s10; %input in waveguide 3
cE
'LE1DK s2=s20;
b3E1S+\=~ s3=s30;
. F 6US<] p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
| du%c`wl %energy in waveguide 1
3u/JcU-< p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
CE`]X;#y %energy in waveguide 2
:&vX0
Ce: p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
V RQ`-# %energy in waveguide 3
/x ?@M n> for m3 = 1:1:M3 % Start space evolution
6 -_g1vq s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
I$t8Ko._" s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
h{^v756L s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
4@{c K| sca1 = fftshift(fft(s1)); % Take Fourier transform
EyA
ny\" sca2 = fftshift(fft(s2));
H@ 1'El\9 sca3 = fftshift(fft(s3));
3&^hf^yg sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
8Re[]bE sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
\+R %KA/F sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
Q /4-7 s3 = ifft(fftshift(sc3));
>S7t s2 = ifft(fftshift(sc2)); % Return to physical space
cj>UxU][eS s1 = ifft(fftshift(sc1));
m1pA]}Y/5o end
A[+ )PkR p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
Qy" J t ]O p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
y2 _rm p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
w{*kbGB8s7 P1=[P1 p1/p10];
FE!jN-# P2=[P2 p2/p10];
MrHJ)x"hy P3=[P3 p3/p10];
:6nD "5( P=[P p*p];
gv uv>A}vJ end
LVB wWlJ figure(1)
q8d](MaX plot(P,P1, P,P2, P,P3);
kJ5z['4 ? .8|wc 转自：
http://blog.163.com/opto_wang/
