计算脉冲在非线性耦合器中演化的Matlab 程序 x`dHJq`_g
GrAujc5| % This Matlab script file solves the coupled nonlinear Schrodinger equations of
45MLt5^| % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
\u>"s % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
AG?d G j^ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
3T}izG] :9_L6 %fid=fopen('e21.dat','w');
7e#? e+5+A N = 128; % Number of Fourier modes (Time domain sampling points)
?hWwj6i& M1 =3000; % Total number of space steps
\&i P`v`K J =100; % Steps between output of space
. %Ta]!0 T =10; % length of time windows:T*T0
[vHv0" T0=0.1; % input pulse width
}c}|
$h^Y MN1=0; % initial value for the space output location
ulkJR-""& dt = T/N; % time step
n>^Y$yy}! n = [-N/2:1:N/2-1]'; % Index
r.>].~}4 t = n.*dt;
r;Gi+Ca5 u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
(s7;^)}z x u20=u10.*0.0; % input to waveguide 2
R%qGPO5Z\c u1=u10; u2=u20;
[I$ BmGQ U1 = u1;
6u`)QUmItg U2 = u2; % Compute initial condition; save it in U
72Iy^Y[MX ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
|*'cF-lp6v w=2*pi*n./T;
!>e5z|1 g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
,>eMG=C; g L=4; % length of evoluation to compare with S. Trillo's paper
0 DmMG dz=L/M1; % space step, make sure nonlinear<0.05
weE/TW\e for m1 = 1:1:M1 % Start space evolution
wm$}Pc h u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
!2'jrJGc
u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
x-AZ %)N9 ca1 = fftshift(fft(u1)); % Take Fourier transform
8& 3V#sn' ca2 = fftshift(fft(u2));
3`B6w$z>( c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
*IY*yR6 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
4)"n
RjGg u2 = ifft(fftshift(c2)); % Return to physical space
"E8zh| m o u1 = ifft(fftshift(c1));
?F6pEt4 if rem(m1,J) == 0 % Save output every J steps.
C0
/g1;p( U1 = [U1 u1]; % put solutions in U array
`(f!*Ru@/z U2=[U2 u2];
A Q+]|XYo_ MN1=[MN1 m1];
M5*{ z1=dz*MN1'; % output location
5K<5kHpvJ{ end
q|v(Edt|_[ end
@1 U&UH hg=abs(U1').*abs(U1'); % for data write to excel
.Y3pS/VI ha=[z1 hg]; % for data write to excel
KA){''>8 t1=[0 t'];
P~G 1EK|4 hh=[t1' ha']; % for data write to excel file
-x'z
XvWZ %dlmwrite('aa',hh,'\t'); % save data in the excel format
=7 C%P%yt figure(1)
Tjl:|F8 waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
72X0Tq 4 figure(2)
HE'2"t[a waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
8 XICF Xy@7y[s] 非线性超快脉冲耦合的数值方法的Matlab程序 9$Xu,y cu% C" 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
o4%y >d) Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
F6K4#t+9 MH{GR)ng:9 \uXcLhXN e?Ho a$k % This Matlab script file solves the nonlinear Schrodinger equations
;w %*M}`5 % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
rc/nFl 6# % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
QR
Ei7@t % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
qOUqs'7/] e89Xb;;w C=1;
]6{*^4 kX M1=120, % integer for amplitude
,daKC M3=5000; % integer for length of coupler
&3$ z4df
N = 512; % Number of Fourier modes (Time domain sampling points)
KGWy J dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
FI<q@HF T =40; % length of time:T*T0.
wAz &"rS dt = T/N; % time step
Oer^ Rk n = [-N/2:1:N/2-1]'; % Index
RtCkV xaEx t = n.*dt;
>TP7 }u| ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
Ma\ Gb+> w=2*pi*n./T;
7yx$N n`( g1=-i*ww./2;
}Y*VAnY6; g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
i-'9AYyw g3=-i*ww./2;
]_8qn '7 P1=0;
L9@ &2 ?k P2=0;
hBFP 1u/E' P3=1;
]b= P= P=0;
GG0R}',0 for m1=1:M1
*0}3t <5 p=0.032*m1; %input amplitude
Cxcr/9 s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
KMV=%o s1=s10;
+Ag!?T s20=0.*s10; %input in waveguide 2
Xu>r~^w=S s30=0.*s10; %input in waveguide 3
q~5 9F@ s2=s20;
PmR~ c, s3=s30;
Rt{B(L.?< p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
qt3PXqR7 : %energy in waveguide 1
(lGaPMEU} p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
u@.>Z{h %energy in waveguide 2
k~/>b~ .c p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
E^rb cGJ %energy in waveguide 3
C:uz6i1 for m3 = 1:1:M3 % Start space evolution
#_|sgS?1 s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
0z[dl Hi s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
C-?%uF s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
9 Li%K OY sca1 = fftshift(fft(s1)); % Take Fourier transform
|8.(Xs N sca2 = fftshift(fft(s2));
DwV4o^J:l sca3 = fftshift(fft(s3));
<97d[/7 i sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
U|5nNiJM sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
)
gzR=9l sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
sT/c_^y s3 = ifft(fftshift(sc3));
X! j{o s2 = ifft(fftshift(sc2)); % Return to physical space
[ G
e=kFB s1 = ifft(fftshift(sc1));
ErT{(t7 end
! {82D [5 p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
s%!`kWVJ. p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
%&Fk4Z }M p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
'r@:Cz3e*I P1=[P1 p1/p10];
qA:#iJ8w P2=[P2 p2/p10];
Ic{F*nnM P3=[P3 p3/p10];
p)=~% 7DV P=[P p*p];
g!`3{
/4 end
c=;:R0_'t figure(1)
-wv6s#"u plot(P,P1, P,P2, P,P3);
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w 转自：
http://blog.163.com/opto_wang/
