计算脉冲在非线性耦合器中演化的Matlab 程序 RzSN,bL R ' :] w % This Matlab script file solves the coupled nonlinear Schrodinger equations of
`+@%l*TQ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
`V0]t_*D % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
%}&9[# % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
}@ A~a`9g Ix5yQgnB}j %fid=fopen('e21.dat','w');
8c$Isv Jg N = 128; % Number of Fourier modes (Time domain sampling points)
d{GXFT;0 M1 =3000; % Total number of space steps
c Ky%0oTla J =100; % Steps between output of space
J.`.lQ$z T =10; % length of time windows:T*T0
CUw
9aH T0=0.1; % input pulse width
I `KN8ll MN1=0; % initial value for the space output location
!*#=7^# dt = T/N; % time step
IWpUbD|kC n = [-N/2:1:N/2-1]'; % Index
WCWBvw4&"{ t = n.*dt;
XJOo. Y u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
]X _& u20=u10.*0.0; % input to waveguide 2
p|bpE F=U u1=u10; u2=u20;
CGg6n CB U1 = u1;
)5V1H WjU U2 = u2; % Compute initial condition; save it in U
Cw^)}23R ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
d ly 08 74 w=2*pi*n./T;
C"mb-n 7s g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
#QDV_ziE5 L=4; % length of evoluation to compare with S. Trillo's paper
%r,2ZLZ dz=L/M1; % space step, make sure nonlinear<0.05
(}qLxZ/U for m1 = 1:1:M1 % Start space evolution
1Q;` <= u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
@' ,;/j80 u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
"I i!)n, ca1 = fftshift(fft(u1)); % Take Fourier transform
(c*Dvpo1 ca2 = fftshift(fft(u2));
bKaV]Uy c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
>)
:d3 8M c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
O@Kr}8^, u2 = ifft(fftshift(c2)); % Return to physical space
-jw=I yv u1 = ifft(fftshift(c1));
6qA{l_V if rem(m1,J) == 0 % Save output every J steps.
t[
MRyi)LF U1 = [U1 u1]; % put solutions in U array
aY+>85?g U2=[U2 u2];
=UP)b9*h MN1=[MN1 m1];
hP#&]W3: z1=dz*MN1'; % output location
JuI,wA end
f3 h9CV end
J/*[wj hg=abs(U1').*abs(U1'); % for data write to excel
nBj7 Q!lW ha=[z1 hg]; % for data write to excel
QBo^{], t1=[0 t'];
<z4!m/f [( hh=[t1' ha']; % for data write to excel file
#sHP\|rA %dlmwrite('aa',hh,'\t'); % save data in the excel format
MdfkC6P figure(1)
\5l}5<| waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
%?$"oWmenS figure(2)
,J#5Y. waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
1|89-Ii] Z n!SHj 非线性超快脉冲耦合的数值方法的Matlab程序 ljCgIfZ_4 n(+:l'#HJ 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
ZtT`_G& Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
rYqvG Y#5S;?bR Q&LkST-i +Sn jb0 % This Matlab script file solves the nonlinear Schrodinger equations
(^4%Fk&I- % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
eyWwE% % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
fe$WR~ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
/L
4WWQ5 Glr.)PA C=1;
1$W!<:uh M1=120, % integer for amplitude
/ u{r5`4
M3=5000; % integer for length of coupler
_ Owz% N = 512; % Number of Fourier modes (Time domain sampling points)
J5"*OH:f dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
xVP GlU T =40; % length of time:T*T0.
& Hqu`A/^ dt = T/N; % time step
V+q RDQ n = [-N/2:1:N/2-1]'; % Index
re*/JkDq3K t = n.*dt;
1XKk~G"D ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
^b#E%Rd w=2*pi*n./T;
@wPmx*SF g1=-i*ww./2;
5W48z%MN
g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
9.B7Owgr89 g3=-i*ww./2;
.wSAysiQ|P P1=0;
pf_ /jR P2=0;
S7vE[VF5 P3=1;
Y 4O L 82Y P=0;
;a` X|N9 for m1=1:M1
>A/=eW/q p=0.032*m1; %input amplitude
\v_C7R;& s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
ik*_,51Zj s1=s10;
J Nz 0!wi s20=0.*s10; %input in waveguide 2
`dZ| }4[1 s30=0.*s10; %input in waveguide 3
$%-?S ]6) s2=s20;
:Mk}Suf&H s3=s30;
v(O.GhJ@ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
= )8Ct %energy in waveguide 1
#`$7$Y~] p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
v2' J L(= %energy in waveguide 2
gib]#n1!p p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
'Ap 5Aq %energy in waveguide 3
%U 7B0- for m3 = 1:1:M3 % Start space evolution
@gc"- V*-/ s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
Vvj]2V3 s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
Tjqn::~D s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
%K7}yy&9C sca1 = fftshift(fft(s1)); % Take Fourier transform
h~p}08 sca2 = fftshift(fft(s2));
?s]`G'=>V` sca3 = fftshift(fft(s3));
F{ ,O+\ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
P +0xi sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
`9l\ ~t(M
sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
KF)i6 6 s3 = ifft(fftshift(sc3));
,GIqRT4K s2 = ifft(fftshift(sc2)); % Return to physical space
&?6w 2[} s1 = ifft(fftshift(sc1));
t,,^^ll end
mtHz6+ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
~~,<+X: p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
)[*O^bPowI p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
k Dt)S$N4n P1=[P1 p1/p10];
ex458^N_ P2=[P2 p2/p10];
}i:'f 2/ P3=[P3 p3/p10];
*lAdS]I P=[P p*p];
uw! |G> end
(xed(uFEK figure(1)
H)Ge#=;ckQ plot(P,P1, P,P2, P,P3);
:\_MA^< 6,1|y%(f 转自：
http://blog.163.com/opto_wang/
