计算脉冲在非线性耦合器中演化的Matlab 程序 kso*} uh0 C2/}d? bki % This Matlab script file solves the coupled nonlinear Schrodinger equations of
%Q4i%: Qi % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
{THqz$KN % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
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VadOBQ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
G]*|H0j 6 bO; & %fid=fopen('e21.dat','w');
U5+vN[ K N = 128; % Number of Fourier modes (Time domain sampling points)
4JO@BV >t M1 =3000; % Total number of space steps
|_zO_F rtp J =100; % Steps between output of space
$YM_G=k T =10; % length of time windows:T*T0
^^}Hs-{ T T0=0.1; % input pulse width
b{&FuvQg 2 MN1=0; % initial value for the space output location
=r6qX dt = T/N; % time step
n?QZFeI` n = [-N/2:1:N/2-1]'; % Index
Yx%bn?%;& t = n.*dt;
[m2+9MMl u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
!O)qYmK]| u20=u10.*0.0; % input to waveguide 2
PRr*]$\&Mj u1=u10; u2=u20;
5w< A;f U1 = u1;
+AI`R`Tm U2 = u2; % Compute initial condition; save it in U
DTY<0Q. ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
c`kQvXx w=2*pi*n./T;
h-XY4gq/ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
tXq)nfGe{ L=4; % length of evoluation to compare with S. Trillo's paper
nS S=%,? dz=L/M1; % space step, make sure nonlinear<0.05
BD *G1k_q for m1 = 1:1:M1 % Start space evolution
)=_ycf^MC u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
LmL Gki$w u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
]gP5f @` ca1 = fftshift(fft(u1)); % Take Fourier transform
JN[0L : ca2 = fftshift(fft(u2));
PT]GJ<K/ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
w^;DG c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
a j8Rb& u2 = ifft(fftshift(c2)); % Return to physical space
0k[2j h u1 = ifft(fftshift(c1));
EHI 'xt if rem(m1,J) == 0 % Save output every J steps.
o 8S"&O
? U1 = [U1 u1]; % put solutions in U array
# c Fr U2=[U2 u2];
o"q+,"QL MN1=[MN1 m1];
p'Bm8=AwD z1=dz*MN1'; % output location
q7Es$zjX end
xJhU<q~? end
3W&S.$l hg=abs(U1').*abs(U1'); % for data write to excel
=G${[V \ ha=[z1 hg]; % for data write to excel
hIU(P Dl4 t1=[0 t'];
H3O @ 9YU hh=[t1' ha']; % for data write to excel file
ht6244: %dlmwrite('aa',hh,'\t'); % save data in the excel format
aC^$*qN-) figure(1)
9- )qZ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
U A-7nb figure(2)
..qd,9H waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
u, kU$ J;QUPpH Z 非线性超快脉冲耦合的数值方法的Matlab程序 K+d2m9C = l-O$ m 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。
Vxdp| 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
}iww:H-1 bB 6[Xj{ Qn+:/ zA; EX
"|H. ( % This Matlab script file solves the nonlinear Schrodinger equations
M$S]}
% for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
D"l+iVbBP % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
7@;">`zvm % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
: 1 aL
? 7"2b H C=1;
Z i
ESlf$ M1=120, % integer for amplitude
? Rr2/W#F M3=5000; % integer for length of coupler
X?Pl<l& N = 512; % Number of Fourier modes (Time domain sampling points)
LN^f1/ b* dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
]r/^9XaqtA T =40; % length of time:T*T0.
Fo|xzLm9*| dt = T/N; % time step
m $dV< n = [-N/2:1:N/2-1]'; % Index
_D;@v?n6!O t = n.*dt;
fZN><3MO> ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
M\2"gT-LV w=2*pi*n./T;
5ukp^O xE g1=-i*ww./2;
p 2O~>97t1 g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
+c$I&JO g3=-i*ww./2;
ocQWQ P1=0;
1~yZ T P2=0;
B6M+mx"G P3=1;
H3KTir"on P=0;
lj[, |[X7` for m1=1:M1
c:hK$C)T p=0.032*m1; %input amplitude
]k%PG-9 s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
M]rO;^ ;6? s1=s10;
M {a
# s20=0.*s10; %input in waveguide 2
_GA$6#] s30=0.*s10; %input in waveguide 3
j,-C{ K s2=s20;
tw K^I6@ s3=s30;
`DW2spd p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
3YL
l;TP_ %energy in waveguide 1
-4 Ux,9& p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
:%4imgY` %energy in waveguide 2
c:4P%({ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
9Sg<K)Mc %energy in waveguide 3
Jfhk@2 7T for m3 = 1:1:M3 % Start space evolution
3MBN:dbQ s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
=
[@)R!3H s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
WlwY <) s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
x_<qzlQt sca1 = fftshift(fft(s1)); % Take Fourier transform
-"TR\/ sca2 = fftshift(fft(s2));
4{na+M sca3 = fftshift(fft(s3));
1,t)3;o$ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
b]fzRdhl sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
WNX5i wm sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
/@oLe[Mz$ s3 = ifft(fftshift(sc3));
K 1#ji*Tp s2 = ifft(fftshift(sc2)); % Return to physical space
1y"3 s1 = ifft(fftshift(sc1));
pmc=NTr&< end
FY'dJY3O p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
<z)m%*l vU p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
D ]03eu p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
.2:\:H~3 P1=[P1 p1/p10];
)P
Jw+5 P2=[P2 p2/p10];
1%~ZRmd e P3=[P3 p3/p10];
CXaWgxlK:a P=[P p*p];
X` r* ob end
zc+@lJy figure(1)
!PU ZWO plot(P,P1, P,P2, P,P3);
c0- ;VZ' l|`^*%W@u6 转自：
http://blog.163.com/opto_wang/
