计算脉冲在非线性耦合器中演化的Matlab 程序 8ZW?|-i JCNk\@0i* % This Matlab script file solves the coupled nonlinear Schrodinger equations of
Qww^P/vm % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
l0:5q?g % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
x^X$M$o,l % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Hsgy'X%om EavX8r %fid=fopen('e21.dat','w');
dHq# N = 128; % Number of Fourier modes (Time domain sampling points)
bs
BZ E M1 =3000; % Total number of space steps
bQ"N
;d)e J =100; % Steps between output of space
HS7_MGU T =10; % length of time windows:T*T0
@0D![ oA T0=0.1; % input pulse width
` zY!`G MN1=0; % initial value for the space output location
[g`, AmR\! dt = T/N; % time step
%E a E, n = [-N/2:1:N/2-1]'; % Index
d@ Q][7 t = n.*dt;
S+iP^*L,c u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
M7vj^mt? u20=u10.*0.0; % input to waveguide 2
Hit Ac8 u1=u10; u2=u20;
/K@$#x_{ U1 = u1;
ZtR&wk U2 = u2; % Compute initial condition; save it in U
||XIWKF<n2 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
D'n L w=2*pi*n./T;
~{P:sjsU g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
6"+8M 3M l L=4; % length of evoluation to compare with S. Trillo's paper
M/ } aq dz=L/M1; % space step, make sure nonlinear<0.05
pqH4w(; for m1 = 1:1:M1 % Start space evolution
EX+,:l\^ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
:/i~y $t u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
Mi?}S6bp ca1 = fftshift(fft(u1)); % Take Fourier transform
e C;!YG Z ca2 = fftshift(fft(u2));
Y&g&n o_ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
[%?y( q c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
\lW_f{ X) u2 = ifft(fftshift(c2)); % Return to physical space
'W(xgOP1 u1 = ifft(fftshift(c1));
!UcOl0"6 if rem(m1,J) == 0 % Save output every J steps.
4w;~4#ZPp U1 = [U1 u1]; % put solutions in U array
T
.hb#oO U2=[U2 u2];
$kl$D"*0 MN1=[MN1 m1];
%Hwbw],kl8 z1=dz*MN1'; % output location
-X8eabb end
LipxAE?O end
k}U
JVH21k hg=abs(U1').*abs(U1'); % for data write to excel
)88nMH- ha=[z1 hg]; % for data write to excel
Um\0i;7 ~4 t1=[0 t'];
;s }3e#$L hh=[t1' ha']; % for data write to excel file
Wcn[gn< %dlmwrite('aa',hh,'\t'); % save data in the excel format
3S ;N(A4 figure(1)
lQL:3U0DjU waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
R8 jovr figure(2)
($ S Lb6 waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
1eD.:_t4 /PW&$P1.]" 非线性超快脉冲耦合的数值方法的Matlab程序 S =PJhAF 6c & Y 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
^yJ:+m;6K Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
-TS?
fne) R04J3D| /WYh[XKe Q;wB{vr$ % This Matlab script file solves the nonlinear Schrodinger equations
!+KhFC&Py % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
f'_M 0x % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
anC+r(jjg9 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Dft%ip2 ;RHNRVP C=1;
hDvpOIUL1 M1=120, % integer for amplitude
C C#C M3=5000; % integer for length of coupler
,ux+Qz5( N = 512; % Number of Fourier modes (Time domain sampling points)
}dKLMNqPA dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
7xT[<?, T =40; % length of time:T*T0.
?(D}5`Nfu dt = T/N; % time step
"-0;#&! n = [-N/2:1:N/2-1]'; % Index
{ i;6vRr t = n.*dt;
* <q4S(l ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
J3IRP/*z w=2*pi*n./T;
'HB~Dbq`V g1=-i*ww./2;
^Plc}W7h g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
EY$?^iS g3=-i*ww./2;
61|B]ei/ P1=0;
C0(sAF@ P2=0;
>3P9 i ;W P3=1;
tT-=hDw P=0;
enumK\ for m1=1:M1
VY igxhP7 p=0.032*m1; %input amplitude
iC*U $+JG s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
41}/w3Z4 s1=s10;
/buW AX 1 s20=0.*s10; %input in waveguide 2
-)RJ\V^{9 s30=0.*s10; %input in waveguide 3
n_P(k-^U* s2=s20;
?!7
SzLll s3=s30;
#HG&[Ywi p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
f[}|rf %energy in waveguide 1
} #
Xi`<{ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
[+Un ^gD %energy in waveguide 2
RJPcn)@l p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
&^+3er rO %energy in waveguide 3
WHk/$7_"i for m3 = 1:1:M3 % Start space evolution
VDa|U9N s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
Nf5 WQTa4 s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
MA6P"? s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
KZ
)Ys sca1 = fftshift(fft(s1)); % Take Fourier transform
\ 3G*j` sca2 = fftshift(fft(s2));
MS {{R +& sca3 = fftshift(fft(s3));
:o$@F-$k sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
g@u ;Y5 sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
H"D 5 e sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
0!_*S ) s3 = ifft(fftshift(sc3));
(3O1?n [n s2 = ifft(fftshift(sc2)); % Return to physical space
(Y rR8 s1 = ifft(fftshift(sc1));
f3t. T=S end
~S;! T p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
b0YNac.l p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
/RqhykgZ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
=GTD"*vwr P1=[P1 p1/p10];
u-39r^`5 P2=[P2 p2/p10];
LzE/g)> P3=[P3 p3/p10];
`p1DaV P=[P p*p];
$3 vhddO end
9GPb$ gtx figure(1)
$ ',3Pv plot(P,P1, P,P2, P,P3);
!sG"n&uZq {+\'bIV[ 转自：
http://blog.163.com/opto_wang/
