计算脉冲在非线性耦合器中演化的Matlab 程序 S=)
c7t?a <!>\
n\A % This Matlab script file solves the coupled nonlinear Schrodinger equations of
EB!ne)X % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
37kFbR@x % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
Jg=!GU/:: % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
g?"QahH G o 7kg.w| %fid=fopen('e21.dat','w');
W=^.s> 7G N = 128; % Number of Fourier modes (Time domain sampling points)
K\9 CW%W M1 =3000; % Total number of space steps
m_0y ]RfG J =100; % Steps between output of space
``jNj1t{} T =10; % length of time windows:T*T0
[k%hl`} T0=0.1; % input pulse width
YOLzCnI4 MN1=0; % initial value for the space output location
+U<YM 94? dt = T/N; % time step
asYk #;z\" n = [-N/2:1:N/2-1]'; % Index
i,ZEUdd*_ t = n.*dt;
uFSU |SDd. u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
}#D=Rf?2\P u20=u10.*0.0; % input to waveguide 2
>R] M:Wx u1=u10; u2=u20;
082iE G U1 = u1;
{ DP9^hg U2 = u2; % Compute initial condition; save it in U
Ga02Z k ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
-W^{)%4g w=2*pi*n./T;
=QVk Y7 g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
'u v=D L=4; % length of evoluation to compare with S. Trillo's paper
<!RkkU&
6 dz=L/M1; % space step, make sure nonlinear<0.05
R&(OWF;~, for m1 = 1:1:M1 % Start space evolution
ZT!8h$SE: u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
j
H2)8~P u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
&Iy5@8 ca1 = fftshift(fft(u1)); % Take Fourier transform
N8Rq7i3F?a ca2 = fftshift(fft(u2));
rZdOU?U c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
2LUsqL\m}. c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
{H[N|\ u2 = ifft(fftshift(c2)); % Return to physical space
;=0mL, u1 = ifft(fftshift(c1));
M^oL.' if rem(m1,J) == 0 % Save output every J steps.
6vbKKn`ST U1 = [U1 u1]; % put solutions in U array
(n7xY GfYS U2=[U2 u2];
N 5Om~D MN1=[MN1 m1];
EF:ec9 . z1=dz*MN1'; % output location
;iX~3[] end
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bI2 end
sc+%v1Y#} hg=abs(U1').*abs(U1'); % for data write to excel
*d=}HO/ ha=[z1 hg]; % for data write to excel
HL"c yxe t1=[0 t'];
V WZpEi hh=[t1' ha']; % for data write to excel file
G@ ot^n3 %dlmwrite('aa',hh,'\t'); % save data in the excel format
b>p_w%d[[J figure(1)
9*s8%pL waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
G 0pq'7B figure(2)
05ClPT\BCr waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
n(N u El9T>!Z 非线性超快脉冲耦合的数值方法的Matlab程序 :'w xm3f wic sf <] 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
c\o_U9=n Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
@>46.V{P}B Wo&22,EB h?dSn:Y\? MV$E_@pg % This Matlab script file solves the nonlinear Schrodinger equations
]>)shH=Yx % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
^V; r % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
o`Z3} % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
`uPO+2 I-!7 EC2{! C=1;
>4wigc M1=120, % integer for amplitude
OAq-(_H M3=5000; % integer for length of coupler
S>x@9$( ym N = 512; % Number of Fourier modes (Time domain sampling points)
Y<W9L F dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
Xxh^4vKjX T =40; % length of time:T*T0.
!b!An; ', dt = T/N; % time step
16Ka>=G n = [-N/2:1:N/2-1]'; % Index
T U_' 1 t = n.*dt;
bX38=.up ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
#0r^<Yn w=2*pi*n./T;
[x 7Rq_^ g1=-i*ww./2;
h *;c"/7 g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
'{c ND g3=-i*ww./2;
U3Gg:onuE P1=0;
4 `l$0m@> P2=0;
y g(N a P3=1;
g0biw? P=0;
[p'2# Et for m1=1:M1
a7_Q 8iMe p=0.032*m1; %input amplitude
90+V w`Gz= s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
4S 4MQ s1=s10;
prS%lg>
s20=0.*s10; %input in waveguide 2
> )Qq^?U s30=0.*s10; %input in waveguide 3
1d49&-N s2=s20;
2* `kkS s3=s30;
NaoOgZ? p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
/x gC`]- %energy in waveguide 1
t9<BQg p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
$ 9\8?gS %energy in waveguide 2
l5 ^Q p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
`_LQs9J0J %energy in waveguide 3
Bkq4V$D_ for m3 = 1:1:M3 % Start space evolution
7n .A QII s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
c [M4 l s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
YYI0iM> s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
n, 2 p)#? sca1 = fftshift(fft(s1)); % Take Fourier transform
[4qvQ7Y
! sca2 = fftshift(fft(s2));
uYs45 G sca3 = fftshift(fft(s3));
DH n\ =M sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
,~$sJ2
g7 sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
CaCApL sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
P 2y Sjgd s3 = ifft(fftshift(sc3));
~-sgk"$ s2 = ifft(fftshift(sc2)); % Return to physical space
<^;~8 :0] s1 = ifft(fftshift(sc1));
B_Gcz 5 end
aO |@w"p8 p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
?8grK p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
_0naqa!JyH p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
z I9jxwXU P1=[P1 p1/p10];
=1>G *
, P2=[P2 p2/p10];
s +S6'g-- P3=[P3 p3/p10];
8}[<3K%*g P=[P p*p];
ok ,O/|E}? end
ByoI+n* U figure(1)
nY;Sk #9 plot(P,P1, P,P2, P,P3);
~,F]~|U7l y<IHZq`C3 转自：
http://blog.163.com/opto_wang/
