计算脉冲在非线性耦合器中演化的Matlab 程序 7x ?2(( (Rt jD`e} % This Matlab script file solves the coupled nonlinear Schrodinger equations of
7\e96+j|f % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
sKU?"|G81G % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
v?S~ =$. % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
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;p U=> %fid=fopen('e21.dat','w');
'CkN N = 128; % Number of Fourier modes (Time domain sampling points)
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_Uy]_ M1 =3000; % Total number of space steps
;?`l1:C5) J =100; % Steps between output of space
<Z6tRf;B T =10; % length of time windows:T*T0
jh|4 Y( T0=0.1; % input pulse width
nL[ zXl MN1=0; % initial value for the space output location
v7kR]HU[y dt = T/N; % time step
tq^d1b(j4 n = [-N/2:1:N/2-1]'; % Index
o"5[~$O t = n.*dt;
=Lyo]8>,X u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
PiTe/ u20=u10.*0.0; % input to waveguide 2
/Wqx@# u1=u10; u2=u20;
qp6*v& U1 = u1;
Bt\z0*t=s U2 = u2; % Compute initial condition; save it in U
eJm7}\/6` ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
FYtf<C+ w=2*pi*n./T;
_a e&@s1 g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
y_Tc$g ~ L=4; % length of evoluation to compare with S. Trillo's paper
7KzMa%= dz=L/M1; % space step, make sure nonlinear<0.05
\h&ui]V for m1 = 1:1:M1 % Start space evolution
%j*i= u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
,*w u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
V&>\U?q: ca1 = fftshift(fft(u1)); % Take Fourier transform
h)746T ) ca2 = fftshift(fft(u2));
ZX
Sl+k . c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
#ErIot c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
OSsxO(;g u2 = ifft(fftshift(c2)); % Return to physical space
nfV32D|3 u1 = ifft(fftshift(c1));
d'yA" b] if rem(m1,J) == 0 % Save output every J steps.
az=(6PX U1 = [U1 u1]; % put solutions in U array
I
)LO @ U2=[U2 u2];
?(!<m'jEy MN1=[MN1 m1];
0B;cQSH!q z1=dz*MN1'; % output location
H"g$qSx end
q:9#Vcw end
{ta0dS;1 hg=abs(U1').*abs(U1'); % for data write to excel
?<#2raH- ha=[z1 hg]; % for data write to excel
i(k]}Di: t1=[0 t'];
c T!L+z g hh=[t1' ha']; % for data write to excel file
RRBokj)] %dlmwrite('aa',hh,'\t'); % save data in the excel format
v FL\O figure(1)
i{$h]D_fD waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
Po: )b figure(2)
+C(v4@=nd waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
t#0/ _tD $m:4'r 非线性超快脉冲耦合的数值方法的Matlab程序 %!>~2=Q2* #''q :^EQ 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
K^_Mt!% Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
1{.=T&eG# Viu+#J; l +gQn, HX c<8RRYs % This Matlab script file solves the nonlinear Schrodinger equations
( _{\t gSm % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
onuhNn_=> % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
MR/8 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
{Y% X E!eBQ [@ C=1;
73 C M1=120, % integer for amplitude
U1>VKP;5Nn M3=5000; % integer for length of coupler
~$zod rS9 N = 512; % Number of Fourier modes (Time domain sampling points)
:V%XEN) dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
F_Q?0 Do0' T =40; % length of time:T*T0.
c==` r
C dt = T/N; % time step
^r7-| n = [-N/2:1:N/2-1]'; % Index
W|PKcZ ]Uc t = n.*dt;
4}~zVT0'~ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
l1|z;
$_z w=2*pi*n./T;
r] +V:l3 g1=-i*ww./2;
)7e[o8O_6 g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
DJtKLG0 g3=-i*ww./2;
ml |[x M8 P1=0;
95,{40; X7 P2=0;
-1Luyuy/` P3=1;
0an g^v;q P=0;
u= | hRTD= for m1=1:M1
.Jt&6N p=0.032*m1; %input amplitude
SOyE$GoOsx s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
3zO'=g wJ s1=s10;
*CA7
{2CX s20=0.*s10; %input in waveguide 2
);^]
is~ s30=0.*s10; %input in waveguide 3
dn by &-+T s2=s20;
FuZ7xM, s3=s30;
M~/%V NX p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
HqW| %energy in waveguide 1
{-sy,EYc w p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
w%no6 ; %energy in waveguide 2
N {]|!# p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
w,\#)<boyb %energy in waveguide 3
Kf XE=v{t for m3 = 1:1:M3 % Start space evolution
<uugT9By s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
|]5g+sd s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
,3k"J4|d s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
* q8L$D sca1 = fftshift(fft(s1)); % Take Fourier transform
x,\PV> sca2 = fftshift(fft(s2));
hCX}* sca3 = fftshift(fft(s3));
y[*Bw)F\N sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
-ISI!EU$ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
%bnDxCj" sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
nj*B-M\p s3 = ifft(fftshift(sc3));
eCY gi7? s2 = ifft(fftshift(sc2)); % Return to physical space
#'Q_eBX s1 = ifft(fftshift(sc1));
+"!,rZ7,A end
t@Qs&DZ7k p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
_MZq H8 p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
PrIS L[@ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
N#')Qz: P P1=[P1 p1/p10];
Hnwir!=7 P2=[P2 p2/p10];
;r[@;2p*( P3=[P3 p3/p10];
*/Oq$3QGsV P=[P p*p];
:^DuB_ end
S6 F28 d[j figure(1)
R{~Yh.)~ plot(P,P1, P,P2, P,P3);
xf8C$ |, Aw )='&;^z 转自：
http://blog.163.com/opto_wang/
