计算脉冲在非线性耦合器中演化的Matlab 程序 )wU.|9o]M _I;+p eq % This Matlab script file solves the coupled nonlinear Schrodinger equations of
F<8Rr#Z % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
1( V>8}zn % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
esCm`?qCP % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
xpo<1Sr>S klC;fm2C %fid=fopen('e21.dat','w');
b-}nv`9C N = 128; % Number of Fourier modes (Time domain sampling points)
|1d;0*HIgX M1 =3000; % Total number of space steps
a`.] 8Jy) J =100; % Steps between output of space
cP[3p : T =10; % length of time windows:T*T0
lWj|7 T0=0.1; % input pulse width
R:+2}kS5e{ MN1=0; % initial value for the space output location
2mVcT3 dt = T/N; % time step
74*1|S < n = [-N/2:1:N/2-1]'; % Index
(eS/Q%ZGK t = n.*dt;
K-Bf=7F, u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
b2;+a( u20=u10.*0.0; % input to waveguide 2
SJY<#_b u1=u10; u2=u20;
HJl$v#]#+ U1 = u1;
(1 7%/80-J U2 = u2; % Compute initial condition; save it in U
$~UQKv> ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
e %VJ:Dj w=2*pi*n./T;
MS{pur D g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
\VmqK&9 L=4; % length of evoluation to compare with S. Trillo's paper
HJ pkR<h dz=L/M1; % space step, make sure nonlinear<0.05
9z9z:PU for m1 = 1:1:M1 % Start space evolution
:O:Rfmr ~ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
a\an u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
$x&@!/&|pv ca1 = fftshift(fft(u1)); % Take Fourier transform
/{pVYY ca2 = fftshift(fft(u2));
41luFtE9 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
(fON\ )l c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
+RexQE u2 = ifft(fftshift(c2)); % Return to physical space
xEBiBsk d u1 = ifft(fftshift(c1));
2`(-l{3 if rem(m1,J) == 0 % Save output every J steps.
Uq /#\7/rL U1 = [U1 u1]; % put solutions in U array
\tFg10 U2=[U2 u2];
d#:&Uw MN1=[MN1 m1];
+pU\;x z1=dz*MN1'; % output location
r(` ;CY]@ end
j&(2ze:=*$ end
#~um F%# hg=abs(U1').*abs(U1'); % for data write to excel
A:Z$i5%' ha=[z1 hg]; % for data write to excel
0-~Y[X"9. t1=[0 t'];
J_tj9+r^ hh=[t1' ha']; % for data write to excel file
eCB(!Y| %dlmwrite('aa',hh,'\t'); % save data in the excel format
q0Fq7rWP figure(1)
]@OGp:Hz waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
O[Xl*9P figure(2)
usi v`.
waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
Dt,b\6 5Cxh >,k 非线性超快脉冲耦合的数值方法的Matlab程序 BC V<( @c W jZJQK 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。
Wr h C
q6 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
6'y+Ev$9 zAEq)9Y"l' %Kd&A * dzDh V{ % This Matlab script file solves the nonlinear Schrodinger equations
i:`ur % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
lcgT9 m# % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
MdK!Y % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
.+3= H@8h GSg|Gz""J0 C=1;
Z qX U M1=120, % integer for amplitude
FUzIuz 6 M3=5000; % integer for length of coupler
6GCwc1g N = 512; % Number of Fourier modes (Time domain sampling points)
BQWEC,*N dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
lTe}[@( T =40; % length of time:T*T0.
o Xwoi ! dt = T/N; % time step
P_+S;(QQ~d n = [-N/2:1:N/2-1]'; % Index
md7Aqh t = n.*dt;
7"F
w8 ;k ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
D+{h@^C9Z w=2*pi*n./T;
9_'xq.uP g1=-i*ww./2;
L%`~`3%n- g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
(gBP` *2 g3=-i*ww./2;
r{qM!(T P1=0;
E",s ] P2=0;
9
O| "Ws>{ P3=1;
)#[?pYd P=0;
\FN"0P(G for m1=1:M1
m`C (y$8fU p=0.032*m1; %input amplitude
jLC,<V * s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
FH}n]T s1=s10;
b)@%gS\F s20=0.*s10; %input in waveguide 2
KquHc-fzqr s30=0.*s10; %input in waveguide 3
kXS_:f;M s2=s20;
j Efrxlj s3=s30;
pc&/'zb p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
aNb=gj Lpt %energy in waveguide 1
Ixm< wKwW# p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
LFy5tX# %energy in waveguide 2
}Q_IqI[7 p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
CYrVP%xRA %energy in waveguide 3
`L`*jA+_ for m3 = 1:1:M3 % Start space evolution
!o~% F5|t s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
Acr\2!)) s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
9,Zg'4",d s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
PCnE-$QH sca1 = fftshift(fft(s1)); % Take Fourier transform
W"4E0!r sca2 = fftshift(fft(s2));
# 'G/&&< sca3 = fftshift(fft(s3));
6gwjrGje\ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
BZEY^G sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
@PuJre4!;L sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
RL |.y~ s3 = ifft(fftshift(sc3));
)0`; leli s2 = ifft(fftshift(sc2)); % Return to physical space
6NJ"ty9Bp s1 = ifft(fftshift(sc1));
!> b>"\b end
q a#Fa)g* p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
6PT ,m p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
K"Vv= p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
c#nFm&}dm P1=[P1 p1/p10];
HZCEr6}( P2=[P2 p2/p10];
Nkn0G _ P3=[P3 p3/p10];
I<|)uK7 P=[P p*p];
w=d#y
)1 end
uS bOGhP figure(1)
,@%1q)S?A plot(P,P1, P,P2, P,P3);
r~F T, GdEkA 转自：
http://blog.163.com/opto_wang/
