计算脉冲在非线性耦合器中演化的Matlab 程序 &D, Iwq wQ_4_W % This Matlab script file solves the coupled nonlinear Schrodinger equations of
#M,&g{ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
N5Js.j>z % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
/K=OsMl2b8 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
x/|W;8g4 ?
SFBUX(p %fid=fopen('e21.dat','w');
6h 0qtXn- N = 128; % Number of Fourier modes (Time domain sampling points)
{)YbksrJ{ M1 =3000; % Total number of space steps
uLhGp@Dx J =100; % Steps between output of space
; pnF%co9 T =10; % length of time windows:T*T0
Z,& O8Jelf T0=0.1; % input pulse width
iw@rW5% '~ MN1=0; % initial value for the space output location
qeZ G/\, dt = T/N; % time step
|v&)O) Jg n = [-N/2:1:N/2-1]'; % Index
7?P'f3)fG t = n.*dt;
|IgR1kp+. u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
l.Q u20=u10.*0.0; % input to waveguide 2
i7x &[b u1=u10; u2=u20;
n,N->t$ i U1 = u1;
v{u3[c
U2 = u2; % Compute initial condition; save it in U
fSo8O ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
]OAU&t { w=2*pi*n./T;
\CB^9-V3 g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
_4 {0He`q L=4; % length of evoluation to compare with S. Trillo's paper
'gwh: dz=L/M1; % space step, make sure nonlinear<0.05
u 3WU0Z` for m1 = 1:1:M1 % Start space evolution
^<;W+dWdU u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
)nUdU
= m u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
r!r08y f ca1 = fftshift(fft(u1)); % Take Fourier transform
~ua( Qm ca2 = fftshift(fft(u2));
}$ y.q qG c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
OC ! {8MR c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
pdu1 kL u2 = ifft(fftshift(c2)); % Return to physical space
$LP(\T([ u1 = ifft(fftshift(c1));
2&6D`{"P if rem(m1,J) == 0 % Save output every J steps.
>A Ep\ * U1 = [U1 u1]; % put solutions in U array
K\xz|Gq U2=[U2 u2];
w,%"+ tY_ MN1=[MN1 m1];
*5'8jC"2g z1=dz*MN1'; % output location
[(X~C*VdxM end
Z+xk N end
5Tsz|k hg=abs(U1').*abs(U1'); % for data write to excel
y?s z&*: ha=[z1 hg]; % for data write to excel
pa-*&p t1=[0 t'];
Xo PJ?6 3 hh=[t1' ha']; % for data write to excel file
}8'_M/u\ %dlmwrite('aa',hh,'\t'); % save data in the excel format
j{C~wy!J figure(1)
#2=l\y-# waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
757&bH|a figure(2)
8mX!mYO3c waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
|d0 X1( 01(U)F\ 非线性超快脉冲耦合的数值方法的Matlab程序 p$,7qGST ;~3;CijJ8 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。
k>i88^ kPV 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
pH~\~ {i>AQ+z61f M$x,B#b (Mv~0ShakO % This Matlab script file solves the nonlinear Schrodinger equations
Dj/Hz\ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
L15)+^ 4n % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
`E~"T0RX % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
1^_W[+<S/ Z~:)hwF C=1;
lDS y$ M1=120, % integer for amplitude
)U/Kz1U M3=5000; % integer for length of coupler
XX=OyDLqP N = 512; % Number of Fourier modes (Time domain sampling points)
:6n4i$ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
Wvb ~ j T =40; % length of time:T*T0.
'a(y]QG dt = T/N; % time step
=CzGI|pb n = [-N/2:1:N/2-1]'; % Index
+9/K|SB{ $ t = n.*dt;
r1~W(r.x ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
0hY3vBQ! w=2*pi*n./T;
(N/u@ M g1=-i*ww./2;
4m~y%>
& g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
O%%Q./oh g3=-i*ww./2;
65Z}Hf P1=0;
+ 149 o2 P2=0;
^*jw e^ P3=1;
hy / g*> P=0;
y,?=,x}o# for m1=1:M1
HO i~eX1d p=0.032*m1; %input amplitude
p,=IL_ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
=2q#- ,t s1=s10;
Up
Z 9g" s20=0.*s10; %input in waveguide 2
4EYD5 s30=0.*s10; %input in waveguide 3
auI`'O`/ s2=s20;
E"}%$=yK s3=s30;
!S~)U{SSK p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
7,)E1dx -V %energy in waveguide 1
A":=-$) p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
OcB&6!1u %energy in waveguide 2
G! %m~+", p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
*mV?_4!,f7 %energy in waveguide 3
Z71 _D for m3 = 1:1:M3 % Start space evolution
(YJ2-
X~ s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
23|JgKuA s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
f0eQq;D$K s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
hq4&<Zr( sca1 = fftshift(fft(s1)); % Take Fourier transform
5]mH.{$x$? sca2 = fftshift(fft(s2));
1G A.c: sca3 = fftshift(fft(s3));
/$93#$ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
wmpQF< sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
uj;i E
9 sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
HF B> 0<$ s3 = ifft(fftshift(sc3));
y%|E z s2 = ifft(fftshift(sc2)); % Return to physical space
L@RnLaoQ s1 = ifft(fftshift(sc1));
C;ab -gh end
O0y0'P-rJq p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
;{8 X+H p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
RrLj5 Jq p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
Dj= {% P1=[P1 p1/p10];
3 85qQppz P2=[P2 p2/p10];
[#wt3<d`) P3=[P3 p3/p10];
b73} |4v P=[P p*p];
W +Piqf* end
C!_=L?QT^ figure(1)
c}v8j2{ plot(P,P1, P,P2, P,P3);
[-`s`g- ^?|4<Rm 转自：
http://blog.163.com/opto_wang/
