计算脉冲在非线性耦合器中演化的Matlab 程序 'r'=%u$1C gx\V)8Zr % This Matlab script file solves the coupled nonlinear Schrodinger equations of
0%xk tf % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
V[ UOl J % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
D5zc{) / % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
k-$Acv( e\)%<G5 %fid=fopen('e21.dat','w');
b:1B
> N = 128; % Number of Fourier modes (Time domain sampling points)
[*% lm9 x M1 =3000; % Total number of space steps
T!
}G 51 J =100; % Steps between output of space
<Qq
{&,Le T =10; % length of time windows:T*T0
)Rr6@o T0=0.1; % input pulse width
#rHMf%0 MN1=0; % initial value for the space output location
<5Vf3KoC& dt = T/N; % time step
v }>g* @ n = [-N/2:1:N/2-1]'; % Index
D ksYKv t = n.*dt;
g5BL"Dn u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
[[T7s(3 u20=u10.*0.0; % input to waveguide 2
oKGH|iVEe u1=u10; u2=u20;
r$<!?Z U1 = u1;
|:)Bo<8 U2 = u2; % Compute initial condition; save it in U
iBE|6+g~Cj ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
'O%*:'5k w=2*pi*n./T;
k_g@4x1y* g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
o sc8;B/ L=4; % length of evoluation to compare with S. Trillo's paper
tmGh JZ2j dz=L/M1; % space step, make sure nonlinear<0.05
/.:1Da for m1 = 1:1:M1 % Start space evolution
74_ ?@Z( u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
$$AZ)#t[ u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
Fd8nR9A ca1 = fftshift(fft(u1)); % Take Fourier transform
n'rq ca2 = fftshift(fft(u2));
yf{\^^ i( c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
U=v>gNba c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
lU 9o"2 u2 = ifft(fftshift(c2)); % Return to physical space
"t2T* 'j{ u1 = ifft(fftshift(c1));
hyxv+m[ if rem(m1,J) == 0 % Save output every J steps.
e_-g|ukC U1 = [U1 u1]; % put solutions in U array
#kQ! GMZH U2=[U2 u2];
~#g c{ C@ MN1=[MN1 m1];
&UDbH* !4= z1=dz*MN1'; % output location
qJ" (:~ end
zDg* ds\ end
R/u0, hg=abs(U1').*abs(U1'); % for data write to excel
4n#u?) ha=[z1 hg]; % for data write to excel
Iq|h1ie
m+ t1=[0 t'];
{ UH45#Ua hh=[t1' ha']; % for data write to excel file
?`TQ!m6y %dlmwrite('aa',hh,'\t'); % save data in the excel format
]xf89[ ;0 figure(1)
:F d1k
Jm waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
QXI~Toddj figure(2)
[KUkv waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
t{,$?} 1uo | a 非线性超快脉冲耦合的数值方法的Matlab程序 58?WO} 7L+Wj }m 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。
\Vv)(/q { 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
$d1ow#ROgy }51QU FhL0 }[% F ]:ca=&> % This Matlab script file solves the nonlinear Schrodinger equations
9f['TG," % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
aT/2 rMKPF % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
zt2# K % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
DN9x<%/- d% @0xsU1 C=1;
6rS
? FG= M1=120, % integer for amplitude
W}F~vx. M3=5000; % integer for length of coupler
[6@bsXiw N = 512; % Number of Fourier modes (Time domain sampling points)
eDo4>k"5 dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
*K>2B99TXu T =40; % length of time:T*T0.
F_u ?.6e] dt = T/N; % time step
bSM|" n = [-N/2:1:N/2-1]'; % Index
W)`>'X` t = n.*dt;
|yN yk7~ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
4 JBfA, w=2*pi*n./T;
oCwep^P(v g1=-i*ww./2;
$_% g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
?:q"qwt$F g3=-i*ww./2;
gISA13 P1=0;
H/f}t w P2=0;
zt((TD2 P3=1;
mj9|q8v{+ P=0;
4o''C |ND for m1=1:M1
WKr4S<B8mr p=0.032*m1; %input amplitude
;[zZ I~wh s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
@#"K 6 s1=s10;
qHrIs-NR s20=0.*s10; %input in waveguide 2
?,v@H$)3_ s30=0.*s10; %input in waveguide 3
J bim a> s2=s20;
>$<Q:o}^ s3=s30;
sS)tSt{C p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
T5@t_D>8 %energy in waveguide 1
vr>J$(F p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
3F6'3NvVc2 %energy in waveguide 2
AzGbvBI&V p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
Z(E .F,k %energy in waveguide 3
9( &$Gwi for m3 = 1:1:M3 % Start space evolution
aF=;v* s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
1_~'?'&^ s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
E?0RR' s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
/|Gz<nSc sca1 = fftshift(fft(s1)); % Take Fourier transform
Q<osYO{l sca2 = fftshift(fft(s2));
}k1[Fc | sca3 = fftshift(fft(s3));
7|m{hSc sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
9 Up> e sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
.Gno K? sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
e mq%"
;. s3 = ifft(fftshift(sc3));
=0@ o(#gM s2 = ifft(fftshift(sc2)); % Return to physical space
}Ny~.EV5^ s1 = ifft(fftshift(sc1));
IxP$ lx end
(_q&QI0{ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
QK~>KgVi p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
'?|.#D#-c p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
5o|u!#6 P1=[P1 p1/p10];
~ "~uXNd P2=[P2 p2/p10];
bF@iO316H P3=[P3 p3/p10];
{-IRX)m* P=[P p*p];
R[lA@q:
end
m<9W# figure(1)
z Hj_q%A plot(P,P1, P,P2, P,P3);
4_eF c$^ {XS2<!D 转自：
http://blog.163.com/opto_wang/
