计算脉冲在非线性耦合器中演化的Matlab 程序 )E @ A0 W i;LXu%3\ % This Matlab script file solves the coupled nonlinear Schrodinger equations of
'EDda % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
?7<JQh)"e % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
S;$-''o?9 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
s l]_M t2,A@2DU 2 %fid=fopen('e21.dat','w');
QFYWA1<pDh N = 128; % Number of Fourier modes (Time domain sampling points)
}:X*7 n(& M1 =3000; % Total number of space steps
d
,4]VE J =100; % Steps between output of space
&boOtl^
T =10; % length of time windows:T*T0
_?OW0x 4 T0=0.1; % input pulse width
='`/BY(m[ MN1=0; % initial value for the space output location
At-U2a#J{ dt = T/N; % time step
IiY/(N+J n = [-N/2:1:N/2-1]'; % Index
tjup J*Rt t = n.*dt;
S30?VG9U0f u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
(M*FIX u20=u10.*0.0; % input to waveguide 2
cWoPB
_ u1=u10; u2=u20;
UK<Nj<-'t U1 = u1;
Zos P(Td q U2 = u2; % Compute initial condition; save it in U
G 6T_O ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
c-B
cA w=2*pi*n./T;
$0 vb^ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
ee yHy"@ L=4; % length of evoluation to compare with S. Trillo's paper
!o:f$6EA~C dz=L/M1; % space step, make sure nonlinear<0.05
{phNds% for m1 = 1:1:M1 % Start space evolution
1v71rf&w u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
bD/~eIcWL u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
Y;?{| ca1 = fftshift(fft(u1)); % Take Fourier transform
9I6a"PGDb ca2 = fftshift(fft(u2));
mIK7p 6 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
eEuvl`& c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
zd @m~V u2 = ifft(fftshift(c2)); % Return to physical space
\ExMk<y_& u1 = ifft(fftshift(c1));
,6-:VIHQ if rem(m1,J) == 0 % Save output every J steps.
Tj:B!>> U1 = [U1 u1]; % put solutions in U array
D)L+7N0D~ U2=[U2 u2];
U4d:] z MN1=[MN1 m1];
Qk:Y2mL z1=dz*MN1'; % output location
XD.)Dl8 end
<
jJ end
gt@m?w( hg=abs(U1').*abs(U1'); % for data write to excel
uG,5BV .M ha=[z1 hg]; % for data write to excel
f|\onHI)> t1=[0 t'];
RW<D<5C hh=[t1' ha']; % for data write to excel file
)h7<?@wv& %dlmwrite('aa',hh,'\t'); % save data in the excel format
vSEuk}pk figure(1)
jYk&/@`Ly waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
|olA9mp|] figure(2)
<0X f9a8> waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
;lE% M ,J+}rPe"sf 非线性超快脉冲耦合的数值方法的Matlab程序 Zy`m!]G]80 LY%WD%pL 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
aAD^^l# Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
4K\G16'$v e|"WQ> 6 (]Dh;gC \NPmym_ 6J % This Matlab script file solves the nonlinear Schrodinger equations
oKuI0-*mR % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
'=b/6@& % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
V<GHpFi0 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
R!}H;[c dYJ(!V& C=1;
EJMM9(DQ7 M1=120, % integer for amplitude
8A##\j ) M3=5000; % integer for length of coupler
Te"ioU?. N = 512; % Number of Fourier modes (Time domain sampling points)
p{r}?a dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
>;e~ WF>+K T =40; % length of time:T*T0.
]Sf ]J4eQ dt = T/N; % time step
KcWN,!G n = [-N/2:1:N/2-1]'; % Index
Va"0 >KX t = n.*dt;
d; boIP`M; ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
TM%| '^) w=2*pi*n./T;
"\: `/k3 g1=-i*ww./2;
=$' 6(aDH g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
]_ f_w 9] g3=-i*ww./2;
j()7_ P1=0;
p`olCp' P2=0;
u^^[Q2LDU} P3=1;
NcBIg:V\c P=0;
rV ` #[d for m1=1:M1
DX#Nf""Pw p=0.032*m1; %input amplitude
Ag-(5: s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
p|U?86 t s1=s10;
+}Dw3;W}m s20=0.*s10; %input in waveguide 2
Y vaK0p0Z s30=0.*s10; %input in waveguide 3
'OITI TM s2=s20;
<FV1Wz s3=s30;
.s?L^Z^ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
_>&X\`D %energy in waveguide 1
=W(Q34 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
- YEZ]:" %energy in waveguide 2
q+yQwX{ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
V(H1q`ao9 %energy in waveguide 3
BX`{73sw for m3 = 1:1:M3 % Start space evolution
i1 }:8Unxf s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
^UP`%egR s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
0yk] o5a++ s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
X8Bd3-B sca1 = fftshift(fft(s1)); % Take Fourier transform
Dj"F\j 1 sca2 = fftshift(fft(s2));
;AG8C#_ sca3 = fftshift(fft(s3));
01 }D,W` sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
Cjn#00 sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
%z=le7 sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
Q *D;U[ s3 = ifft(fftshift(sc3));
Kg{+T` s2 = ifft(fftshift(sc2)); % Return to physical space
{&&z-^ s1 = ifft(fftshift(sc1));
=x/X:; )> end
R$R *'l p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
\j$&DCv p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
Y`~Ut:fZ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
'{cIAw/"n P1=[P1 p1/p10];
L^1NY3=$ P2=[P2 p2/p10];
(d(CT; P3=[P3 p3/p10];
]% ;:7? 5l P=[P p*p];
)v'WWwXY> end
6fkRrD figure(1)
y6g&Y. :o plot(P,P1, P,P2, P,P3);
g_;\iqxL fBU`k_ 转自：
http://blog.163.com/opto_wang/
