计算脉冲在非线性耦合器中演化的Matlab 程序 &~e$:8 + N#C1-*[C % This Matlab script file solves the coupled nonlinear Schrodinger equations of
]bi)$j.9s % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
S8, Z;y % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
o*g|m.SjL % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
L,,*gK l8h&|RY[ %fid=fopen('e21.dat','w');
D]s]"QQ8 N = 128; % Number of Fourier modes (Time domain sampling points)
hsKm nH@# M1 =3000; % Total number of space steps
`Y=WMNy J =100; % Steps between output of space
qT :zEt5 T =10; % length of time windows:T*T0
JRMM? y T0=0.1; % input pulse width
'R<&d}@P*# MN1=0; % initial value for the space output location
z*$q8Z&7rg dt = T/N; % time step
Q7X3X, n = [-N/2:1:N/2-1]'; % Index
SLfFqc+n0 t = n.*dt;
E\nv~Y?SG u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
6$fYt&1 u20=u10.*0.0; % input to waveguide 2
wd(Hv u1=u10; u2=u20;
VdSv U1 = u1;
y! .J U2 = u2; % Compute initial condition; save it in U
'_k+ WH& ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
`1OgYs w=2*pi*n./T;
wCf~O'XLw g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
xM[Vc
L=4; % length of evoluation to compare with S. Trillo's paper
P + " Y dz=L/M1; % space step, make sure nonlinear<0.05
b1XRC`Gy for m1 = 1:1:M1 % Start space evolution
7!y5
SX8C u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
jOpcV |2 u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
qn1255fB ca1 = fftshift(fft(u1)); % Take Fourier transform
2Qp Hvsl_ ca2 = fftshift(fft(u2));
%?^6).aEK c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
z@Q@^
&0Mr c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
[%B f<
J< u2 = ifft(fftshift(c2)); % Return to physical space
!o=U19) u1 = ifft(fftshift(c1));
[[d(jV=* if rem(m1,J) == 0 % Save output every J steps.
l!}:|N Yh! U1 = [U1 u1]; % put solutions in U array
p
Dx-2:} U2=[U2 u2];
Ch$*Gm19Z MN1=[MN1 m1];
+YLejjQ z1=dz*MN1'; % output location
ae"]\a\&1o end
hQ6a~?f end
N,2s?Y_! hg=abs(U1').*abs(U1'); % for data write to excel
Hn>B!B m* ha=[z1 hg]; % for data write to excel
kF;D BN t1=[0 t'];
m-^ 8W[r+_ hh=[t1' ha']; % for data write to excel file
K{b(J
Nd %dlmwrite('aa',hh,'\t'); % save data in the excel format
fFj grK8 figure(1)
dVB~Smsr waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
bl _ H4 figure(2)
x8\A<(G_M= waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
D`J6h,=2l/ M?b6'd9f 非线性超快脉冲耦合的数值方法的Matlab程序 Le<w R A;\ 7|'4 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
o?1 ;<gs Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
M?&h~V1OI~ 2C{H$
A,pW B+^(ktZp@ 1+-_s % This Matlab script file solves the nonlinear Schrodinger equations
l]~n3IK" % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
K=!Bh* % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
qd"_Wu6aF= % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
dq[Mj5eC =@k%&* Y? C=1;
h/B>S M1=120, % integer for amplitude
2z\ zh[(w M3=5000; % integer for length of coupler
[m Eql ,x3 N = 512; % Number of Fourier modes (Time domain sampling points)
kJW N. dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
z1^gDjkZ T =40; % length of time:T*T0.
s"Pf+aTW dt = T/N; % time step
meN2ZB ?Y n = [-N/2:1:N/2-1]'; % Index
s
w39\urf t = n.*dt;
J|'7_0OAx ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
G8Nt
8 U~ w=2*pi*n./T;
+w=AJdc g1=-i*ww./2;
asY[ 8r?U g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
(JM4R8fR& g3=-i*ww./2;
JaB<EL-9r2 P1=0;
P!"&%d P2=0;
\:'%9 x P3=1;
z<B8mB P=0;
\P1S|ufv for m1=1:M1
6N)!aT9eo p=0.032*m1; %input amplitude
?c0xRO% y s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
JyR/1 W s1=s10;
p~*UpU8u s20=0.*s10; %input in waveguide 2
WVY\&|)$ s30=0.*s10; %input in waveguide 3
R(n^)^? s2=s20;
Bz5-ITX
s3=s30;
i1S>yV^l p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
2h[ 85\4 %energy in waveguide 1
[HCAmnb p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
keB&Bjd& %energy in waveguide 2
{uGP&cS~( p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
KiJT!moB %energy in waveguide 3
< yC for m3 = 1:1:M3 % Start space evolution
&3yD_P_3 s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
wm+/e#'& s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
ID#I`} h.k s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
Ug&,Y/tFw2 sca1 = fftshift(fft(s1)); % Take Fourier transform
eds26( sca2 = fftshift(fft(s2));
)T k1 QHU sca3 = fftshift(fft(s3));
B" 3dQwQ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
-eX5z sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
da (km+ sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
!qX_I db\ s3 = ifft(fftshift(sc3));
}# X 8@ s2 = ifft(fftshift(sc2)); % Return to physical space
:O(^w}sle s1 = ifft(fftshift(sc1));
=zyC-;r! end
}d< }FJ-, p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
!"eIV@7 p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
H@ t'~ZO p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
W"Gkq!3u{ P1=[P1 p1/p10];
`X3^ fg P2=[P2 p2/p10];
gdkwWoN . P3=[P3 p3/p10];
-&<Whhs.@ P=[P p*p];
Vb9',a?#n end
-YsLd 9^4 figure(1)
\?je Wyo plot(P,P1, P,P2, P,P3);
+wkjS r`e IEU^#= n 转自：
http://blog.163.com/opto_wang/
