计算脉冲在非线性耦合器中演化的Matlab 程序 ZH;VE X pZUckQ % This Matlab script file solves the coupled nonlinear Schrodinger equations of
:{bvCos<) % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
Xd@ - % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
c+,F)i^` % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
b^_#f:_j AX,V*
s %fid=fopen('e21.dat','w');
Q^>"AhOiU N = 128; % Number of Fourier modes (Time domain sampling points)
X|fl_4NC > M1 =3000; % Total number of space steps
?j9 J6=2 J =100; % Steps between output of space
yaza T =10; % length of time windows:T*T0
^ 0p y T0=0.1; % input pulse width
jU.z{(s MN1=0; % initial value for the space output location
`w';}sQA7 dt = T/N; % time step
?-%Q[W n = [-N/2:1:N/2-1]'; % Index
jI %v[]V t = n.*dt;
#pO=\lJ, u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
k/o"E u20=u10.*0.0; % input to waveguide 2
Ndq/n21j u1=u10; u2=u20;
L"{qF<@V7& U1 = u1;
|fqYMhA U U2 = u2; % Compute initial condition; save it in U
kKL'rT6z ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
BC*62m w=2*pi*n./T;
9"hH2jc
g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
Q46^i7= L=4; % length of evoluation to compare with S. Trillo's paper
CAg~K[ dz=L/M1; % space step, make sure nonlinear<0.05
Ey96XJV for m1 = 1:1:M1 % Start space evolution
G(gJt l u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
E#}OIZ\S u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
qg1s]c~0u ca1 = fftshift(fft(u1)); % Take Fourier transform
EZnX S"z ca2 = fftshift(fft(u2));
=f0qih5.4 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
z,dh ?%H>X c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
M|8vP53=q u2 = ifft(fftshift(c2)); % Return to physical space
)N$T& u1 = ifft(fftshift(c1));
E| eEAa
if rem(m1,J) == 0 % Save output every J steps.
AB(WK9o U1 = [U1 u1]; % put solutions in U array
~ +DPq|-O U2=[U2 u2];
X)7_@,7 MN1=[MN1 m1];
EM y>X z1=dz*MN1'; % output location
#C^)W/dP end
1%Hc/ N- end
3{c6)vR2 hg=abs(U1').*abs(U1'); % for data write to excel
;B*im
S10 ha=[z1 hg]; % for data write to excel
r+ v?~m! t1=[0 t'];
D 2}N6 i hh=[t1' ha']; % for data write to excel file
wr);+.T9R %dlmwrite('aa',hh,'\t'); % save data in the excel format
}@6Tcn1 figure(1)
]q^6az(Ud waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
!UHWCJ<
<w figure(2)
((0nJJjz waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
PY81MTv0; EPeKg{w 非线性超快脉冲耦合的数值方法的Matlab程序 9r2l~zE $[f-{B{>* 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。
{:=sCY! 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
ri.}G T. d1? [vv $"$z LH}]& >F % This Matlab script file solves the nonlinear Schrodinger equations
} ejZk
bP % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
M'gGoH}B+q % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
a+mrsyM % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
6LRvl6ik P;8nC:z L C=1;
'u g:ic M1=120, % integer for amplitude
c'|](vOd] M3=5000; % integer for length of coupler
WwDd62g N = 512; % Number of Fourier modes (Time domain sampling points)
q4MR9ig1E_ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
JjMa T =40; % length of time:T*T0.
[L m dt = T/N; % time step
[&(~{#}M: n = [-N/2:1:N/2-1]'; % Index
bW-sTGjRD t = n.*dt;
i0}f@pCB?X ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
~a$h\F'6
w=2*pi*n./T;
}G/!9Zq g1=-i*ww./2;
WuuF &0?8C g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
Q{[l 1: g3=-i*ww./2;
S( ^HIJK P1=0;
5Z@0XI P2=0;
y 5{Vx{V"Q P3=1;
AZ.$g?3w P=0;
2A=q{7 s for m1=1:M1
3N[Rrxe2 p=0.032*m1; %input amplitude
*fCmZ$U:{ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
Gf=3h4 s1=s10;
O!G!Gq& s20=0.*s10; %input in waveguide 2
(b;Kl1Ql] s30=0.*s10; %input in waveguide 3
@}\i`H1s s2=s20;
xyD2<?dGUb s3=s30;
5>6:#.f%!e p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
E1j3c
:2 %energy in waveguide 1
[H[L};%=j p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
[XE\2Qa8e %energy in waveguide 2
4mHk,Dd9, p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
r;^%D( %energy in waveguide 3
,njlKkFw^Z for m3 = 1:1:M3 % Start space evolution
>[ 2; s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
A?b q Dy s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
%Q]3`k xp s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
eDsB. ^|l sca1 = fftshift(fft(s1)); % Take Fourier transform
ZkJL q[:cM sca2 = fftshift(fft(s2));
n$ rgJ sca3 = fftshift(fft(s3));
@<.ei)cqb sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
xa'^:H $X sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
&\=Tm~ sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
#;[0:jU0 s3 = ifft(fftshift(sc3));
.?vHoNvo s2 = ifft(fftshift(sc2)); % Return to physical space
O DEFs?%' s1 = ifft(fftshift(sc1));
",xTgB3?V end
..kFn!5(g p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
5sANF9o! p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
7B<, nKd p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
dS8ydG2 P1=[P1 p1/p10];
d#OAM;0}5 P2=[P2 p2/p10];
R<
L =&I P3=[P3 p3/p10];
]$u C~b P=[P p*p];
f^-ot@w end
mW$ Oi++'d figure(1)
7},oY"" 8 plot(P,P1, P,P2, P,P3);
DcNp-X40I ^RJ @9`P&t 转自：
http://blog.163.com/opto_wang/
