计算脉冲在非线性耦合器中演化的Matlab 程序 ^W-03 .iFd % This Matlab script file solves the coupled nonlinear Schrodinger equations of
r:u, % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
`4E6&&E+S % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
nzI}w7>VU % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
_ _jFSa`at 6@_Vg ~=S %fid=fopen('e21.dat','w');
u`Kj s}F' N = 128; % Number of Fourier modes (Time domain sampling points)
l n}2 M1 =3000; % Total number of space steps
0^htwec! J =100; % Steps between output of space
)r _zM~jI T =10; % length of time windows:T*T0
wIT0A-Por4 T0=0.1; % input pulse width
9
z_9yT MN1=0; % initial value for the space output location
i}mvKV?!|1 dt = T/N; % time step
sG{hUsPa n = [-N/2:1:N/2-1]'; % Index
@ m14x}H t = n.*dt;
~$7fU u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
%G!BbXlz u20=u10.*0.0; % input to waveguide 2
V6%J9+DK u1=u10; u2=u20;
m}Z=m8 U1 = u1;
A
i` U2 = u2; % Compute initial condition; save it in U
bbevy!m ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
}$-;P=k w=2*pi*n./T;
f{=0-%dA g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
G|5M~zP L=4; % length of evoluation to compare with S. Trillo's paper
~ x`BV+R dz=L/M1; % space step, make sure nonlinear<0.05
kae &,'@JF for m1 = 1:1:M1 % Start space evolution
C FqteY" u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
9L+dN%C u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
]A jDe] ca1 = fftshift(fft(u1)); % Take Fourier transform
;Js-27_0 ca2 = fftshift(fft(u2));
Y> }[c
c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
"?E>rWz c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
w>M8 FG(4] u2 = ifft(fftshift(c2)); % Return to physical space
$ K>.|\ u1 = ifft(fftshift(c1));
<C0~7]XO if rem(m1,J) == 0 % Save output every J steps.
9\F:<Bf$# U1 = [U1 u1]; % put solutions in U array
I8=p_Ie U2=[U2 u2];
EN^C'n MN1=[MN1 m1];
l_
/q/8-l z1=dz*MN1'; % output location
t)Q6A@$: end
*T (z4RVg end
sBozz # hg=abs(U1').*abs(U1'); % for data write to excel
NijvFT$V1 ha=[z1 hg]; % for data write to excel
FOz7W t1=[0 t'];
EMy Med_ hh=[t1' ha']; % for data write to excel file
no_(J>p^& %dlmwrite('aa',hh,'\t'); % save data in the excel format
5c*kgj:x figure(1)
'urn5[i waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
4N&4TUIM figure(2)
+
k1|+zzS waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
rv/O^aL`Y W10=SM } 非线性超快脉冲耦合的数值方法的Matlab程序 )%D2J C 59e q"08 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
04eE\%? Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
^_dYE]t q.]>uBAQ? Sl @$ +r0ItqkM % This Matlab script file solves the nonlinear Schrodinger equations
3\J-=U % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
kaBP& 6|Z
% Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
}%z {tn % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
F2QX ^* iQry X(z C=1;
hq}kAv4B= M1=120, % integer for amplitude
_=ani9E]uF M3=5000; % integer for length of coupler
+S!gS|8P N = 512; % Number of Fourier modes (Time domain sampling points)
ESdjDg$[u dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
\nQV{J T =40; % length of time:T*T0.
/Yk4%ZJ{ dt = T/N; % time step
q cYF& n = [-N/2:1:N/2-1]'; % Index
2 , bo t = n.*dt;
*`]LbS ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
R0>GM`{ w=2*pi*n./T;
6$#p}nE g1=-i*ww./2;
".Lwq_ g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
~&bn}
M>W g3=-i*ww./2;
` d rds P1=0;
eJWcr Vpn P2=0;
O>P792) P3=1;
)HPt(Ck P=0;
Y*!J +A# for m1=1:M1
Gj Ds,9@f p=0.032*m1; %input amplitude
! /pE6)a s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
#=~n>qn] s1=s10;
!RX7TYf s20=0.*s10; %input in waveguide 2
< PCa37 s30=0.*s10; %input in waveguide 3
D[d +lq#p s2=s20;
]w2nVC 3 s3=s30;
//9M~qHa" p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
<[7
b UB %energy in waveguide 1
4.?tP7UE p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
3LT[?C]H$ %energy in waveguide 2
_T,X z_ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
O3Jp:.ps %energy in waveguide 3
|3tq.JU for m3 = 1:1:M3 % Start space evolution
eC+S'Jgf s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
x8L$T (^ s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
][Ne ;F6 s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
}bwH(OOS sca1 = fftshift(fft(s1)); % Take Fourier transform
?!PpooYK sca2 = fftshift(fft(s2));
<B,z)c sca3 = fftshift(fft(s3));
#
tN#_<W sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
`/WX!4eR, sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
$w,&h:.p sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
d9' gH#f? s3 = ifft(fftshift(sc3));
P)VysYb? s2 = ifft(fftshift(sc2)); % Return to physical space
$+#Lq. 3, s1 = ifft(fftshift(sc1));
>Q159qZ end
ZM:!LkK p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
tS1(.CRk p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
B]):$#{Rxl p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
-ti
nL(?3 P1=[P1 p1/p10];
^pAgo B P2=[P2 p2/p10];
gEFs4;
CN P3=[P3 p3/p10];
/uXEh61$8 P=[P p*p];
f@:.bp8VB8 end
B2}|b^ 'I figure(1)
58T<~u 7 plot(P,P1, P,P2, P,P3);
q |Oz |2oCEb1 转自：
http://blog.163.com/opto_wang/
