计算脉冲在非线性耦合器中演化的Matlab 程序 5(q\x(N cE nkt= % This Matlab script file solves the coupled nonlinear Schrodinger equations of
>Bq;Z}EV % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
e] !Vxn3 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
L7_(KC h % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
q<o*rcwf ^ Nt,)5_K < %fid=fopen('e21.dat','w');
@/ l { N = 128; % Number of Fourier modes (Time domain sampling points)
(l{+ T# M1 =3000; % Total number of space steps
F#7ZR*ZB1 J =100; % Steps between output of space
V^QKn+/ T =10; % length of time windows:T*T0
J5)e 7 T0=0.1; % input pulse width
)|@b
GEk MN1=0; % initial value for the space output location
%/>\`d? dt = T/N; % time step
LO[1xE9 n = [-N/2:1:N/2-1]'; % Index
yc|C}oQF t = n.*dt;
l
" pCxA u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
^ 'FC. u20=u10.*0.0; % input to waveguide 2
%E?:9. :NJ u1=u10; u2=u20;
7s; <5xc U1 = u1;
m(q6Xe:Vc U2 = u2; % Compute initial condition; save it in U
FXV=D_G} ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
Wg[?i C*~ w=2*pi*n./T;
V. )y7B g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
qF`;xa% ,} L=4; % length of evoluation to compare with S. Trillo's paper
O_K@\<;~ dz=L/M1; % space step, make sure nonlinear<0.05
/%po@Pm#I for m1 = 1:1:M1 % Start space evolution
`!S5FE"- u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
V9-pY/v 9 u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
#pBAGm 3 ca1 = fftshift(fft(u1)); % Take Fourier transform
Fkuq'C<|Y ca2 = fftshift(fft(u2));
X_C9Z c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
:^0g}8$< c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
-}%'I ]R= u2 = ifft(fftshift(c2)); % Return to physical space
N[^% | u1 = ifft(fftshift(c1));
< /t_<I0{ if rem(m1,J) == 0 % Save output every J steps.
E$.|h;i]Q U1 = [U1 u1]; % put solutions in U array
FH)bE#4 U2=[U2 u2];
kuu9'Sqc'b MN1=[MN1 m1];
3:<+9X z1=dz*MN1'; % output location
kMKI=>s+ end
)wP0U{7?v end
Odxq ]HlbO hg=abs(U1').*abs(U1'); % for data write to excel
x,E#+
m ha=[z1 hg]; % for data write to excel
:{h,0w'd t1=[0 t'];
< Xm5re. hh=[t1' ha']; % for data write to excel file
9<kKno %dlmwrite('aa',hh,'\t'); % save data in the excel format
k^Tu9}[W1 figure(1)
?)<zrE5p waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
_bqiS]: figure(2)
%=/Y~ml? waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
h #zx ^F1 ~^lQ[ x 非线性超快脉冲耦合的数值方法的Matlab程序 +1Si>I $JqdI/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。
)~_!u}+:( 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\Hck=P[$3
~ i1w,;( KD$ P\(5# W2|*:<Jt % This Matlab script file solves the nonlinear Schrodinger equations
nf,>l0 ,,' % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
$^I uE0. % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
<E$P % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
3
C=nC n]a r\f C=1;
tH 5f;mY, M1=120, % integer for amplitude
P0RM df M3=5000; % integer for length of coupler
\>cZ = N = 512; % Number of Fourier modes (Time domain sampling points)
|?s %8c'w= dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
'gUHy1p T =40; % length of time:T*T0.
TnL%_!V! dt = T/N; % time step
$MKx\qx} n = [-N/2:1:N/2-1]'; % Index
s.1(- "DU t = n.*dt;
AbZ:AJ(
ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
~Az20RrK) w=2*pi*n./T;
6]T02;b>/, g1=-i*ww./2;
EM vV g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
A&$!s)8 z g3=-i*ww./2;
`C=!8q P1=0;
8Qu7x[tK? P2=0;
$7TYix8= P3=1;
8 PXleAn P=0;
oVoTnGNM6 for m1=1:M1
}O2hhh_ p=0.032*m1; %input amplitude
w a<@bub s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
-5p=gO s1=s10;
U~Ni2|}\C9 s20=0.*s10; %input in waveguide 2
[+{ ot
s30=0.*s10; %input in waveguide 3
bT[Q:#GL s2=s20;
J9/9k s3=s30;
]_d(YHYf p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
kC|tv{g#> %energy in waveguide 1
K_]LK p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
Ip8 Ap$ %energy in waveguide 2
+ ;Cq>1x, p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
6 Y&OG >_\ %energy in waveguide 3
<FS/'[P for m3 = 1:1:M3 % Start space evolution
>P\T nb"Q\ s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
DbPw) aCj s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
jt3s;U* s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
S wC, =S sca1 = fftshift(fft(s1)); % Take Fourier transform
En5Bsz ! sca2 = fftshift(fft(s2));
l-t:7`=| sca3 = fftshift(fft(s3));
M*t@Q|$: sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
><\mt sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
C9gF2ii|? sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
LE1&atq s3 = ifft(fftshift(sc3));
z+wV (i97 s2 = ifft(fftshift(sc2)); % Return to physical space
8"o S1W s1 = ifft(fftshift(sc1));
5 Nl>4d` end
q n =6>wP p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
nn#A-x}~;b p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
&[ 3y_, p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
_<t3~{qUT P1=[P1 p1/p10];
7:x.08 P2=[P2 p2/p10];
gl]{mUZz} P3=[P3 p3/p10];
i Y;)R|6 P=[P p*p];
yaR|d3ef?4 end
fD,#z& figure(1)
'd(}bYr) plot(P,P1, P,P2, P,P3);
R0. `2= kdxs {b"t 转自：
http://blog.163.com/opto_wang/
