计算脉冲在非线性耦合器中演化的Matlab 程序 M:3h e "xHg qgFyO % This Matlab script file solves the coupled nonlinear Schrodinger equations of
Y 2S J7 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
: b~6i%b % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
D'A/wG % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
TGe ;HZ , %Up0Rr, %fid=fopen('e21.dat','w');
B'EKM)dA N = 128; % Number of Fourier modes (Time domain sampling points)
C
#6dC0 M1 =3000; % Total number of space steps
\z7SkZt,GT J =100; % Steps between output of space
;R?I4}O#R8 T =10; % length of time windows:T*T0
+0q>fp_K(+ T0=0.1; % input pulse width
4^Q : MN1=0; % initial value for the space output location
fKeT~z{ ~ dt = T/N; % time step
pg% aI, n = [-N/2:1:N/2-1]'; % Index
K7Wk 6Aw t = n.*dt;
Z%Zd2
v u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
#x3ujJ u20=u10.*0.0; % input to waveguide 2
'-b*EZU8t u1=u10; u2=u20;
S"$m] U1 = u1;
I{ :(z3 U2 = u2; % Compute initial condition; save it in U
1u(.T0j7f ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
Ej>g.vp8I w=2*pi*n./T;
i21Gw41p: g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
GJp85B!PlO L=4; % length of evoluation to compare with S. Trillo's paper
_Bp1co85MQ dz=L/M1; % space step, make sure nonlinear<0.05
c#]q^L\x for m1 = 1:1:M1 % Start space evolution
hcbv;[bG u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
h!:~f-@j4 u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
Y> Wu ca1 = fftshift(fft(u1)); % Take Fourier transform
_({A\}Q| ca2 = fftshift(fft(u2));
S"k *6 U c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
iVT GF< c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
?Wt$6{) u2 = ifft(fftshift(c2)); % Return to physical space
`8>Py~ u1 = ifft(fftshift(c1));
d[^~'V if rem(m1,J) == 0 % Save output every J steps.
>P $;79< U1 = [U1 u1]; % put solutions in U array
X'% ;B U2=[U2 u2];
B 0!"A MN1=[MN1 m1];
O
Wj@< N z1=dz*MN1'; % output location
-7&Gi
+] end
+_xOLi u
end
0}xFD6{X hg=abs(U1').*abs(U1'); % for data write to excel
BQ2wn Gc ha=[z1 hg]; % for data write to excel
e^Ky<*Y t1=[0 t'];
*"r~- &IL hh=[t1' ha']; % for data write to excel file
B8%{ }[q %dlmwrite('aa',hh,'\t'); % save data in the excel format
Tk O[rAC figure(1)
h=_0+\% waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
0 Ir<y figure(2)
[mr9(m[F waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
9{8GP >ap1"n9k 非线性超快脉冲耦合的数值方法的Matlab程序 )){9&5,0: }sFm9j7yR 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
S#Sb ] Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
F0UVo f5= =";eP H'UR8 % l-$uHHyu* % This Matlab script file solves the nonlinear Schrodinger equations
Z@%HvB7 % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
i^!ez5z % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
<Ex Z:ip % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
ed_ FiQd %F*|;o7 s C=1;
1#4PG'H M1=120, % integer for amplitude
{Pu\?Cq M3=5000; % integer for length of coupler
T' aec]u N = 512; % Number of Fourier modes (Time domain sampling points)
k') E/n dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
2 ',w[I
T =40; % length of time:T*T0.
?kz+R' dt = T/N; % time step
yj(vkifEB n = [-N/2:1:N/2-1]'; % Index
b4""|P?L t = n.*dt;
fn/7wO$! ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
S"hTE7` w=2*pi*n./T;
tD Cw- g1=-i*ww./2;
d@3}U6, g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
EK$Kee}~ g3=-i*ww./2;
;u(Du-Os! P1=0;
?`Y\)'} P2=0;
}/,CbKi,+ P3=1;
02k4 N% P=0;
DF{ Qw@P! for m1=1:M1
l w (e3j p=0.032*m1; %input amplitude
F("#^$ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
@&hnL9D8lL s1=s10;
] k8/#@19 s20=0.*s10; %input in waveguide 2
|uH %6&\ s30=0.*s10; %input in waveguide 3
5]1h8PW!Y s2=s20;
`: G % s3=s30;
l"zUv p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
X}6#II %energy in waveguide 1
B,(H eg p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
.~gl19#:T %energy in waveguide 2
<d7V<&@o= p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
2sp g?] %energy in waveguide 3
Sm2>'C for m3 = 1:1:M3 % Start space evolution
Fequm + s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
do
^RF<G s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
S? 0)1 O s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
<[/%{sUNC sca1 = fftshift(fft(s1)); % Take Fourier transform
}p9F#gr sca2 = fftshift(fft(s2));
] fI/(e_U sca3 = fftshift(fft(s3));
7a$ G@ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
ksjUr 1o sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
9><mp]E4 sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
-6Mm#sX s3 = ifft(fftshift(sc3));
@oG )LT s2 = ifft(fftshift(sc2)); % Return to physical space
9%iFV
N' s1 = ifft(fftshift(sc1));
cxYfZ4++m end
!z
zW2> p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
s/1 #DM" p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
oT|m1aGE p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
bO/*2oau P1=[P1 p1/p10];
2PSTGG8JV P2=[P2 p2/p10];
xqHL +W P3=[P3 p3/p10];
:'r6 TVDW P=[P p*p];
~mN% (w!^ end
zG
c[Z3N figure(1)
HpexH{.u) plot(P,P1, P,P2, P,P3);
~tGCLf]c\ xkA2g[ 转自：
http://blog.163.com/opto_wang/
