计算脉冲在非线性耦合器中演化的Matlab 程序 o^+2%S`] 4} . PQ { % This Matlab script file solves the coupled nonlinear Schrodinger equations of
XB0G7o%1 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
M~+}ss % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
1K{u>T % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
( f]@lN mx E.LD1Pm0 %fid=fopen('e21.dat','w');
KTtB!4by
N = 128; % Number of Fourier modes (Time domain sampling points)
Bm"-X:=' M1 =3000; % Total number of space steps
? TWve)U J =100; % Steps between output of space
R RRF/Z;)) T =10; % length of time windows:T*T0
! $n@- T0=0.1; % input pulse width
J,(@1R]KF: MN1=0; % initial value for the space output location
<fS WX>pR dt = T/N; % time step
Y=83r ]% n = [-N/2:1:N/2-1]'; % Index
=
y @*vl t = n.*dt;
Eqizx~e qq u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
kx{LY`pY u20=u10.*0.0; % input to waveguide 2
#ME!G/ u1=u10; u2=u20;
= -bGH
U1 = u1;
$|"Y|3&X U2 = u2; % Compute initial condition; save it in U
d?ru8 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
ml,FBBGq|- w=2*pi*n./T;
$Z|HFV{ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
/aTW X L=4; % length of evoluation to compare with S. Trillo's paper
JkShtLEr dz=L/M1; % space step, make sure nonlinear<0.05
Nwwn #+ for m1 = 1:1:M1 % Start space evolution
MpK3 +4UMa u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
~ECI L7, u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
8NnGN( a*D ca1 = fftshift(fft(u1)); % Take Fourier transform
O:E0htdWr ca2 = fftshift(fft(u2));
{' 8td^JEE c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
|E?PQ?P c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
3#A 4A0 u2 = ifft(fftshift(c2)); % Return to physical space
Iip%er%b u1 = ifft(fftshift(c1));
]SC|%B _* if rem(m1,J) == 0 % Save output every J steps.
cs lZ; U1 = [U1 u1]; % put solutions in U array
&2,3R}B/ U2=[U2 u2];
O*7vmPy MN1=[MN1 m1];
_lG|t6 y z1=dz*MN1'; % output location
~] &yHzp2 end
Kpg?'
!I end
6o0 }7T%6 hg=abs(U1').*abs(U1'); % for data write to excel
efr 9 ha=[z1 hg]; % for data write to excel
_`I}"`2H t1=[0 t'];
yJK:4af;. hh=[t1' ha']; % for data write to excel file
[I?[N.v %dlmwrite('aa',hh,'\t'); % save data in the excel format
de/ oK c figure(1)
f\;w(_ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
Wsb>3J figure(2)
=,b6yV+$D waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
Q7.jSL6 $Ge0<6/ 非线性超快脉冲耦合的数值方法的Matlab程序 3,'L W} v M'!WVs 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
z]2MR2W@X Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
S{m:Iij[; (|\%)v H- 0tz? sN RNF%i~nhO % This Matlab script file solves the nonlinear Schrodinger equations
?y-@c] % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
,\?s=D{ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
|< Y~\ | % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
U! {~L$S (mr*Thy`@ C=1;
s 3Wjhw/ M1=120, % integer for amplitude
v#lrF\G5 M3=5000; % integer for length of coupler
d"yJ0F N = 512; % Number of Fourier modes (Time domain sampling points)
u6 QW*8b4 dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
We++ DWp T =40; % length of time:T*T0.
,.kmUd dt = T/N; % time step
/ Xq |S O n = [-N/2:1:N/2-1]'; % Index
`_f&T} ] t = n.*dt;
aGOS 9 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
&q&~&j'[ w=2*pi*n./T;
#zv&h`gY g1=-i*ww./2;
,)uW`7 g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
: t9sAD g3=-i*ww./2;
Wks zN h P1=0;
ow P2=0;
9M^5<8: P3=1;
7;c^*"Ud P=0;
L 8q#_k for m1=1:M1
u -)ED p=0.032*m1; %input amplitude
GSs?!BIC s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
S\ ]9mHJI s1=s10;
N d ]RbX s20=0.*s10; %input in waveguide 2
(t){o> l s30=0.*s10; %input in waveguide 3
;HBKOe_3 s2=s20;
zB`J+r;LU s3=s30;
:f:&B8 p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
H E{UgU:tY %energy in waveguide 1
rizjH+ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
CDF;cM"td %energy in waveguide 2
eIy:5/ s p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
o~9sO=-O %energy in waveguide 3
EX F]y}n for m3 = 1:1:M3 % Start space evolution
>0[:uu,'> s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
TQ:h[6v s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
[m4M#Lg\0 s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
=E$bZe8 sca1 = fftshift(fft(s1)); % Take Fourier transform
Qn|8Ic` * sca2 = fftshift(fft(s2));
AOkG.u-k sca3 = fftshift(fft(s3));
~3-"1E>Rgy sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
q sUBvq sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
p s?su` sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
m]*a;a'}# s3 = ifft(fftshift(sc3));
}D+ b`, s2 = ifft(fftshift(sc2)); % Return to physical space
.%dGSDru s1 = ifft(fftshift(sc1));
Nmd{C(^o end
3Z`"k2k p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
S(U9Dlyarg p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
j'Jb+@W? p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
gG@ 4MXq. P1=[P1 p1/p10];
u Fw1% P2=[P2 p2/p10];
6`iYIXnz P3=[P3 p3/p10];
8ki3>"!A P=[P p*p];
b%*`}B end
u,nn\>Y figure(1)
qo u\4YZ plot(P,P1, P,P2, P,P3);
r73W. & Qd\ ='*:! 转自：
http://blog.163.com/opto_wang/
