计算脉冲在非线性耦合器中演化的Matlab 程序 n
'P: sn5N9=\+T % This Matlab script file solves the coupled nonlinear Schrodinger equations of
*uA?}XEfi % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
<Cg;l<$`b % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
1G .+)*:3 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
5CU< ? g+ 2SB5 2D %fid=fopen('e21.dat','w');
T 2Y`q' N = 128; % Number of Fourier modes (Time domain sampling points)
OiM{@ M1 =3000; % Total number of space steps
ni2H~{]z
J =100; % Steps between output of space
&sS k~ : T =10; % length of time windows:T*T0
T?AGQcG T0=0.1; % input pulse width
Kw!`u^> MN1=0; % initial value for the space output location
Z"Et]xSU%$ dt = T/N; % time step
Mh~T.;f.qq n = [-N/2:1:N/2-1]'; % Index
$X yGCn t = n.*dt;
R)<Fqa7Tm u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
YQQ!1 hw u20=u10.*0.0; % input to waveguide 2
I=(O,*+PQ u1=u10; u2=u20;
KOi%zE% U1 = u1;
}-r"W7]k U2 = u2; % Compute initial condition; save it in U
CvbY2_>Nh ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
/ jj!DO# w=2*pi*n./T;
U}gYZi;;$ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
Qbv)(&i# ~ L=4; % length of evoluation to compare with S. Trillo's paper
(]7@0d88 dz=L/M1; % space step, make sure nonlinear<0.05
p-*BB_ J" for m1 = 1:1:M1 % Start space evolution
B@iIj<p~ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
z h/+1 u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
HowlJ[ km% ca1 = fftshift(fft(u1)); % Take Fourier transform
D|=QsWZI ca2 = fftshift(fft(u2));
Y Nq<%i!> c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
5+ fS$Q
c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
/)oxuk&}c u2 = ifft(fftshift(c2)); % Return to physical space
!Id F6 % u1 = ifft(fftshift(c1));
QtN 0|q{af if rem(m1,J) == 0 % Save output every J steps.
V 8n}" U1 = [U1 u1]; % put solutions in U array
"K\ Rq+si U2=[U2 u2];
lPFMNRt~8 MN1=[MN1 m1];
KpwUp5K z1=dz*MN1'; % output location
>@oO7<WB end
E"L'm0i[[ end
D(h|r^5 hg=abs(U1').*abs(U1'); % for data write to excel
%' g/4I ha=[z1 hg]; % for data write to excel
Uj!L:u2b t1=[0 t'];
^' [ | hh=[t1' ha']; % for data write to excel file
DcOu =Y> 1 %dlmwrite('aa',hh,'\t'); % save data in the excel format
!2{MWj figure(1)
9R ugkGy waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
|#-Oz#Eg' figure(2)
u"|.]r waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
J41Z Q p n
=S%Qf] 非线性超快脉冲耦合的数值方法的Matlab程序 ^8MgNVoJ) .S5&M NE 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。
eGguq~s` 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
pbgCcO~xm 4cV(Z-\ x`o_&09;CG x1Si&0T0P< % This Matlab script file solves the nonlinear Schrodinger equations
el[6 E0!@ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
#vDe/o+= % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
wwp vmb % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
k XOlZ C |20p#]0E+ C=1;
90ORx\Oeo M1=120, % integer for amplitude
:^ cA\2= M3=5000; % integer for length of coupler
UhEnW8^bz1 N = 512; % Number of Fourier modes (Time domain sampling points)
lq%s/l dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
Gm6^BYCk T =40; % length of time:T*T0.
QTLO P~^ dt = T/N; % time step
_Y~+ #Vc n = [-N/2:1:N/2-1]'; % Index
a{-}8f 6 t = n.*dt;
JgxOxZS`@ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
2^:5aABQ w=2*pi*n./T;
;e[-t/SI g1=-i*ww./2;
1= <Qnmw g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
k*n5+[U^tP g3=-i*ww./2;
z{%G P1=0;
bF} ~9WEa P2=0;
XS1>ti|< P3=1;
7,(:vjIXd P=0;
X GO_n{ x for m1=1:M1
|~Z+Xl a p=0.032*m1; %input amplitude
0<P
-` |X s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
:|fzG f s1=s10;
9p k<=F s20=0.*s10; %input in waveguide 2
qvab >U` s30=0.*s10; %input in waveguide 3
|\b*p:e l s2=s20;
-Ol/r=/& s3=s30;
7d9%L}+q p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
Gb MSO %energy in waveguide 1
k'S/nF A p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
"4ovMan %energy in waveguide 2
l9SbuT$U p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
(IEtjv}D %energy in waveguide 3
EmH2 Dbw for m3 = 1:1:M3 % Start space evolution
K\;b3 s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
S(rA96n s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
.=K@M"5& s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
3
D+dM0wM sca1 = fftshift(fft(s1)); % Take Fourier transform
8-po| sca2 = fftshift(fft(s2));
hB|L W^@v sca3 = fftshift(fft(s3));
Rr:,'cXGi sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
cQN}z
Ke sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
cl{;%4$9 sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
)WBTqML[ s3 = ifft(fftshift(sc3));
M#2DI?S@ s2 = ifft(fftshift(sc2)); % Return to physical space
3g} ]nj:N s1 = ifft(fftshift(sc1));
CM~)\prks end
OHH wcJ 7N p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
&%INfl>o7. p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
nC2A&n &> p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
4Kx;F
9!%~ P1=[P1 p1/p10];
~KCOCtiD P2=[P2 p2/p10];
U*,5t81 P3=[P3 p3/p10];
&
XcY|y=W P=[P p*p];
3VKA rv- end
!R4`ihi1 figure(1)
+Pn+&o ;D plot(P,P1, P,P2, P,P3);
+ ]Ydf^rF 9r8*'.K`Z 转自：
http://blog.163.com/opto_wang/
