计算脉冲在非线性耦合器中演化的Matlab 程序 BBev< 3qf
Y m}d % This Matlab script file solves the coupled nonlinear Schrodinger equations of
OOo3G~2r % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
sr{a(4*\ % 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
$ 69oV: a x<?GjpM %fid=fopen('e21.dat','w');
ATK_DE Au N = 128; % Number of Fourier modes (Time domain sampling points)
9J2NH|]c M1 =3000; % Total number of space steps
rp ;b" q J =100; % Steps between output of space
6 |PrX
L& T =10; % length of time windows:T*T0
xjKR R? T0=0.1; % input pulse width
fR(d MN1=0; % initial value for the space output location
0|{u{w@!` dt = T/N; % time step
TOB]IrW n = [-N/2:1:N/2-1]'; % Index
#
mV{#B= t = n.*dt;
Q|#W#LV,K u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
gMzcTmbc8 u20=u10.*0.0; % input to waveguide 2
)mF5Vw" u1=u10; u2=u20;
vzim<;i U1 = u1;
^rifRY-,yO U2 = u2; % Compute initial condition; save it in U
' /^q J7eb ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
)p<ExMIxd w=2*pi*n./T;
,g2ij g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
2#c<\s|C L=4; % length of evoluation to compare with S. Trillo's paper
^c9t'V`IWQ dz=L/M1; % space step, make sure nonlinear<0.05
ur:3W6ZKl for m1 = 1:1:M1 % Start space evolution
*%%g{
3$ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
^\4h<M u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
Z{]0jhUyNh ca1 = fftshift(fft(u1)); % Take Fourier transform
;V *l.gr'2 ca2 = fftshift(fft(u2));
Ab{ K<:l c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
v|dBSX9k0 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
tMf}
u2 = ifft(fftshift(c2)); % Return to physical space
Uq^#r iq u1 = ifft(fftshift(c1));
Y^$X*U/q%U if rem(m1,J) == 0 % Save output every J steps.
{>hC~L?6 U1 = [U1 u1]; % put solutions in U array
onz?_SAW U2=[U2 u2];
#h`
V>; MN1=[MN1 m1];
`p2+&&]S z1=dz*MN1'; % output location
;:\<gVi: end
VY
| _d k end
E &2OD [iX hg=abs(U1').*abs(U1'); % for data write to excel
UQ?XqgUM ha=[z1 hg]; % for data write to excel
nn@-W] t1=[0 t'];
0IBhb(X hh=[t1' ha']; % for data write to excel file
$w2u3 - %dlmwrite('aa',hh,'\t'); % save data in the excel format
J}v}~Cv figure(1)
J&W)(Cf waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
aX)I3^ar figure(2)
`6~Aoe waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
^c- =;Rtdy/Yn% 非线性超快脉冲耦合的数值方法的Matlab程序 +ElfZ4 J8uLJ 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。
5:Z0Pt 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
47+&L + B B@OW ?!A 7rb/tj ;oW 6 NJ % This Matlab script file solves the nonlinear Schrodinger equations
j*so9M6|c % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
q&s3wDl/ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
$rv8K j+ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Q=;U@k@> 2@'oe7E C=1;
]zE;Tw.S M1=120, % integer for amplitude
=,spvy'"*C M3=5000; % integer for length of coupler
WA)yfo0A N = 512; % Number of Fourier modes (Time domain sampling points)
y{ibO}s dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
3er nTD*` T =40; % length of time:T*T0.
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ml@@ dt = T/N; % time step
q rJ`1 n = [-N/2:1:N/2-1]'; % Index
G&D7a/G\ t = n.*dt;
;RDh ~EV ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
#lmB
AL~3 w=2*pi*n./T;
*scVJ g1=-i*ww./2;
q)X$^oE!6 g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
zi|+HM g3=-i*ww./2;
mn, =i P1=0;
Jj!v h{ P2=0;
F, W~,y P3=1;
v- T$:c L P=0;
z>58dA@f for m1=1:M1
nKPYOY8^ p=0.032*m1; %input amplitude
4r>6G/b8* s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
R.jIl@p s1=s10;
Zn&,
t &z s20=0.*s10; %input in waveguide 2
i6dHrx]:, s30=0.*s10; %input in waveguide 3
GPkmf%F J s2=s20;
HW3 }uP\c s3=s30;
c`J.Tm[_u p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
EYtL_hNp}I %energy in waveguide 1
7C,&*Ax,9 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
E27vR 7 %energy in waveguide 2
jF ^~p9z p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
fol,xMc& %energy in waveguide 3
S^-DK~Xt4 for m3 = 1:1:M3 % Start space evolution
x2OaPlG,&V s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
"'c
A2~ s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
RN$ 1bxY s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
E@@5BEB ~ sca1 = fftshift(fft(s1)); % Take Fourier transform
$Z.7zH sca2 = fftshift(fft(s2));
3LAIl913 sca3 = fftshift(fft(s3));
xbdN0MAU sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
YLqGRE`W sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
9>l*lCA sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
rSZd!OQ s3 = ifft(fftshift(sc3));
0H6(EzN s2 = ifft(fftshift(sc2)); % Return to physical space
ozmrw\_}[ s1 = ifft(fftshift(sc1));
}Mst jm end
F<n 3 p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
7|{}\w(I p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
+MR.>" p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
VPO
N-{=` P1=[P1 p1/p10];
uD\?(LM P2=[P2 p2/p10];
-=%@ L&y1 P3=[P3 p3/p10];
XG}C+;4Aw P=[P p*p];
;XF:\<+ end
{_7 i8c<s= figure(1)
a][f plot(P,P1, P,P2, P,P3);
,5i ` -OI JSkLEa~< 转自：
http://blog.163.com/opto_wang/
