计算脉冲在非线性耦合器中演化的Matlab 程序 %i) 0sE T `\r <3? % This Matlab script file solves the coupled nonlinear Schrodinger equations of
N*f ]NCSi % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
dsn(h5,Q' % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
_;,"!'R`f % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
d%K& }` YtXD-o %fid=fopen('e21.dat','w');
9vP#/ -g N = 128; % Number of Fourier modes (Time domain sampling points)
t$3B#= M1 =3000; % Total number of space steps
?3% r:g4 J =100; % Steps between output of space
0g2rajS T =10; % length of time windows:T*T0
rvacCwI T0=0.1; % input pulse width
\S_A e; MN1=0; % initial value for the space output location
>K<cc#Aa dt = T/N; % time step
lA` qB1x n = [-N/2:1:N/2-1]'; % Index
=$y;0]7Lwi t = n.*dt;
m T /^F{c u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
o)GesgxFa5 u20=u10.*0.0; % input to waveguide 2
CXBFR>" u1=u10; u2=u20;
)KY4 BBc U1 = u1;
fR b U2 = u2; % Compute initial condition; save it in U
o:B ?hr'\ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
6!HYx w=2*pi*n./T;
K 6 yD64 g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
$Xh5N3 L=4; % length of evoluation to compare with S. Trillo's paper
XmP,3KG2{S dz=L/M1; % space step, make sure nonlinear<0.05
"(iD Ul for m1 = 1:1:M1 % Start space evolution
9^&B.6! 6 u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
g~2= he\ C u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
}G "EdhSl ca1 = fftshift(fft(u1)); % Take Fourier transform
W!"Oho' ca2 = fftshift(fft(u2));
QnJLTBv c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
voFg6zoV_ c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
u_}UU
2 u2 = ifft(fftshift(c2)); % Return to physical space
},{sJ0To u1 = ifft(fftshift(c1));
)5 `~ WzA if rem(m1,J) == 0 % Save output every J steps.
iaJLIr l U1 = [U1 u1]; % put solutions in U array
j]U~ZAn,K U2=[U2 u2];
#Cx#U"~G` MN1=[MN1 m1];
[%P[ x]- z1=dz*MN1'; % output location
nly}ly Q/ end
}( ! rB#bf end
Kf6 D)B 26 hg=abs(U1').*abs(U1'); % for data write to excel
gi>W&6 ha=[z1 hg]; % for data write to excel
0Y'ow=8M t1=[0 t'];
l $ kO%E' hh=[t1' ha']; % for data write to excel file
Fn0 |v66 %dlmwrite('aa',hh,'\t'); % save data in the excel format
>oN Wf figure(1)
| &@`~OBa waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
4 aE{} jp1 figure(2)
W56VA>ia waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
4\ |/S@. q{%~(A5*H 非线性超快脉冲耦合的数值方法的Matlab程序 E,dUO; `EfF yhG$ 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。
3}8L!2_p 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
N ]14~r= `\P1Ff@z0 `Z#':0 Z .'. bokl/ % This Matlab script file solves the nonlinear Schrodinger equations
L& rtN@5; % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
pN_%>v"o % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
ll[&O4.F % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
itE/QB Wsp c ;]& C=1;
y\4/M6 M1=120, % integer for amplitude
.beqfcj" M3=5000; % integer for length of coupler
Q"uK6ANp' N = 512; % Number of Fourier modes (Time domain sampling points)
K'/if5>Bc dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
2 .= G T =40; % length of time:T*T0.
'@
p464 dt = T/N; % time step
%"=GQ 3u[ n = [-N/2:1:N/2-1]'; % Index
[ $ uKI,l t = n.*dt;
?S9vYaA$ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
H |7XfM w=2*pi*n./T;
*YX5bpR? g1=-i*ww./2;
= y(*?TZH g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
I(WIT=Wi< g3=-i*ww./2;
p-l FzNPc0 P1=0;
,`OQAJ)> P2=0;
SSbx[<E3 P3=1;
D SWmQQ P=0;
yyk@f% for m1=1:M1
I}f7|hYX p=0.032*m1; %input amplitude
,t;US.s([. s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
*0?@/2& s1=s10;
/2hRL yeAZ s20=0.*s10; %input in waveguide 2
j:>0XP s30=0.*s10; %input in waveguide 3
QoZZXCU s2=s20;
:>o 0zG[;f s3=s30;
FA;-D 5= p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
,%BDBZ %energy in waveguide 1
k.jBu p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
2`%a[t@M. %energy in waveguide 2
=9`UcTSi6p p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
i~AReJxt7 %energy in waveguide 3
0*9xau{( for m3 = 1:1:M3 % Start space evolution
[Y?Y@x"MZ s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
?FUK _] s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
ywk RH s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
h{H*k#> sca1 = fftshift(fft(s1)); % Take Fourier transform
Wv9L }@J sca2 = fftshift(fft(s2));
&cJ?mSI sca3 = fftshift(fft(s3));
[)dIt@Y&j sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
Lz p}<B sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
qX; F+~ sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
_ WPt
zL s3 = ifft(fftshift(sc3));
\x\N?$`ANc s2 = ifft(fftshift(sc2)); % Return to physical space
> M !LC s1 = ifft(fftshift(sc1));
'-J<ib
t end
_d!o,=} p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
^c >Bh[ p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
ZBFn p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
~b ! la P1=[P1 p1/p10];
vceD/ N8 P2=[P2 p2/p10];
/#&jF:h P3=[P3 p3/p10];
Z
h9D^ I P=[P p*p];
olA+B end
S-ZN}N{,6 figure(1)
JZ*.;}" plot(P,P1, P,P2, P,P3);
Q<g>WNb 5XzsqeG| 转自：
http://blog.163.com/opto_wang/
