计算脉冲在非线性耦合器中演化的Matlab 程序 l{hO"fzy C%AN4Mo % This Matlab script file solves the coupled nonlinear Schrodinger equations of
*`V r P % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
!%/(a)B$^$ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
h=d FSK?*D % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
G| qsJ ]BfJ~+ N %fid=fopen('e21.dat','w');
8JU{]Z!G<; N = 128; % Number of Fourier modes (Time domain sampling points)
_eUd
RL> M1 =3000; % Total number of space steps
a!\^O).pA J =100; % Steps between output of space
S>y}|MG T =10; % length of time windows:T*T0
z4JhLef % T0=0.1; % input pulse width
X- `PF MN1=0; % initial value for the space output location
t4+bRmS`_ dt = T/N; % time step
H Em XB= n = [-N/2:1:N/2-1]'; % Index
;nKhmcQ4 t = n.*dt;
p']{WLDj2 u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
>9t+lr1 u20=u10.*0.0; % input to waveguide 2
u^( s0q u1=u10; u2=u20;
fwv.^k x U1 = u1;
t!o=-k U2 = u2; % Compute initial condition; save it in U
%XH%.Ps/ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
IgPU^?sp w=2*pi*n./T;
jfp bD
/ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
i&0Zli L=4; % length of evoluation to compare with S. Trillo's paper
|N:kf&]b dz=L/M1; % space step, make sure nonlinear<0.05
C;oO=R3r for m1 = 1:1:M1 % Start space evolution
#2;8 /"v u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
LrdX^_,nt u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
_^`TG ]F ca1 = fftshift(fft(u1)); % Take Fourier transform
Tfw5i,{ ca2 = fftshift(fft(u2));
76b2 3| c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
w exa\o c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
U3t) yr h u2 = ifft(fftshift(c2)); % Return to physical space
Pa "[&{ : u1 = ifft(fftshift(c1));
K [i&!Z&
if rem(m1,J) == 0 % Save output every J steps.
BQ(sjJ$v6F U1 = [U1 u1]; % put solutions in U array
';I(#J6 U2=[U2 u2];
w$ jq2?l MN1=[MN1 m1];
)u]1j@Id z1=dz*MN1'; % output location
ZV$!dHW/ end
yD Avl+
end
$LOf2 kn hg=abs(U1').*abs(U1'); % for data write to excel
dm"|\ 7 ha=[z1 hg]; % for data write to excel
~{q;
- & t1=[0 t'];
L\ \'n ) hh=[t1' ha']; % for data write to excel file
S y^et %dlmwrite('aa',hh,'\t'); % save data in the excel format
Nl9}*3r figure(1)
pf#~ |n#t waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
I?CfdI figure(2)
Aq_?8 Cd waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
bDnT><eH [>|6qY$D 非线性超快脉冲耦合的数值方法的Matlab程序 '-_tF3x p?sFX$S 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
4q\gFFV4 Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
G@rV9 RU\MT'E>( nBzju?X)I O[z-K K< % This Matlab script file solves the nonlinear Schrodinger equations
o(g}eP,g } % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
ogG:Ai)90 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
As(6E}{S % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
z
9~|Su r_pZK(G % C=1;
M)CQ|P M1=120, % integer for amplitude
lLN5***47J M3=5000; % integer for length of coupler
wQ '_ , d N = 512; % Number of Fourier modes (Time domain sampling points)
fn Pej?f: dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
q=;U(,Y T =40; % length of time:T*T0.
x, #? dt = T/N; % time step
'v%v*Ujf[ n = [-N/2:1:N/2-1]'; % Index
sDjbvC0 t = n.*dt;
(4C_Ft*~j ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
HA ~BXxa/ w=2*pi*n./T;
p
s_o:*$l g1=-i*ww./2;
\ 8/$ZEom g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
XF`?5G~~# g3=-i*ww./2;
nmClP P1=0;
CMU\DO P2=0;
7$7#z\VWu P3=1;
L^??*XEUJ P=0;
'(SqHP|8&g for m1=1:M1
-x+K#T0Z p=0.032*m1; %input amplitude
yX CJ? s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
2(25IYMS8 s1=s10;
g.COKA s20=0.*s10; %input in waveguide 2
Ev,b5KelD s30=0.*s10; %input in waveguide 3
tWA<OOl
s2=s20;
J@o$V- KK s3=s30;
Q,n X c p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
AV;x'H7G %energy in waveguide 1
Zn] !*} p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
oTk?a!Q %energy in waveguide 2
=S|dzgS/ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
cR!Mn$m %energy in waveguide 3
|[MtUWEW for m3 = 1:1:M3 % Start space evolution
~)
vz`bD1 s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
*q0 vp^? s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
5`{u! QE s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
oZw #]Q@ sca1 = fftshift(fft(s1)); % Take Fourier transform
hGj`IAW sca2 = fftshift(fft(s2));
^) 5*?8# sca3 = fftshift(fft(s3));
<MgC7S2I sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
>5j&Q #Bu sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
7X/KQ97 sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
D9higsN s3 = ifft(fftshift(sc3));
-~&T 0dt~ s2 = ifft(fftshift(sc2)); % Return to physical space
;I]$N]8YI s1 = ifft(fftshift(sc1));
\04 (V'`U end
^2"3h$DJfS p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
M Jtn)gXb p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
mC ./,a[ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
Io]KlR@!T P1=[P1 p1/p10];
8RU91H8fE P2=[P2 p2/p10];
-5MQ/ujQ P3=[P3 p3/p10];
[ *^ rH: P=[P p*p];
k:*vD" end
]w~ECP(ap figure(1)
eOs 4c` plot(P,P1, P,P2, P,P3);
v6O5n(5,, l#rr--]; 转自：
http://blog.163.com/opto_wang/
