计算脉冲在非线性耦合器中演化的Matlab 程序 P_.zp5> W_L;^5Y;m % This Matlab script file solves the coupled nonlinear Schrodinger equations of
B'-n
^'; % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
r'< !wp@ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
S[e> 8 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
&a 'mh q\G7T{t$. %fid=fopen('e21.dat','w');
?&JK q^9\I N = 128; % Number of Fourier modes (Time domain sampling points)
cB 6LJ}R M1 =3000; % Total number of space steps
Gm[XnUR7V J =100; % Steps between output of space
BC)1FxsGf T =10; % length of time windows:T*T0
IP!`;?T= T0=0.1; % input pulse width
]64pb;w"$D MN1=0; % initial value for the space output location
Xd@ d$ dt = T/N; % time step
l @ 5kw]6 n = [-N/2:1:N/2-1]'; % Index
ckkm}|&m t = n.*dt;
,R}9n@JI^Y u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
6J<R;g23R] u20=u10.*0.0; % input to waveguide 2
gn:&akg u1=u10; u2=u20;
U E- 1p U1 = u1;
W+i&!' U2 = u2; % Compute initial condition; save it in U
R9-Uoc/ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
F):1@.S w=2*pi*n./T;
'd]t@[# g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
+' SG$<Xv L=4; % length of evoluation to compare with S. Trillo's paper
wln"g,ct dz=L/M1; % space step, make sure nonlinear<0.05
EvptGM for m1 = 1:1:M1 % Start space evolution
?h:xO\h8 u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
Tq,dlDDOR u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
moCR64n ca1 = fftshift(fft(u1)); % Take Fourier transform
ap<r )<u ca2 = fftshift(fft(u2));
;0o%
hx c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
g~XR#vl$ c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
p^s:s-"f\ u2 = ifft(fftshift(c2)); % Return to physical space
m[nrr6 G" u1 = ifft(fftshift(c1));
OCu/w1 bc if rem(m1,J) == 0 % Save output every J steps.
y9 ~:[ jB U1 = [U1 u1]; % put solutions in U array
K(AZD&D U2=[U2 u2];
6J <.i MN1=[MN1 m1];
Ud_0{%@ z1=dz*MN1'; % output location
{$I1(DYN end
t;}`~B end
lv #L+} T hg=abs(U1').*abs(U1'); % for data write to excel
;( (|0Xa ha=[z1 hg]; % for data write to excel
Q>I7.c-M| t1=[0 t'];
Jo\karpb hh=[t1' ha']; % for data write to excel file
F{E`MK~f_ %dlmwrite('aa',hh,'\t'); % save data in the excel format
C8O<fwNM
figure(1)
p2h PLq waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
3F$N@K~s figure(2)
A+Kp ECP waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
%GGSd0
g jd.w7 .8 非线性超快脉冲耦合的数值方法的Matlab程序 Zd]ua_)I%[ MaZV GrcC 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。
lL,0IfC, 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
s8;*Wt $XcuU
sG Y+gNi_dE A#gy[.Bb % This Matlab script file solves the nonlinear Schrodinger equations
6('CB|ga % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
!O4)Y M % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
GQYB2{e> % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
@xr}(. @[#)zO C=1;
mOJ-M@ME M1=120, % integer for amplitude
K@?K4o
M3=5000; % integer for length of coupler
C YdYa| N = 512; % Number of Fourier modes (Time domain sampling points)
7 iQa)8, dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
v7<r- <I[ T =40; % length of time:T*T0.
WH<\ f |xR dt = T/N; % time step
bp'\nso/ n = [-N/2:1:N/2-1]'; % Index
k/i&e~! \ t = n.*dt;
>6|Xvtf ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
FAq9G-\B w=2*pi*n./T;
@DKph!c r g1=-i*ww./2;
(d['f]S+& g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
!.7m4mKzo g3=-i*ww./2;
Jm 1n|f P1=0;
lt%9Zgr[u P2=0;
_Nf%x1m5s P3=1;
!Y*O0_ P=0;
{5 (M for m1=1:M1
|N|[E5Cn p=0.032*m1; %input amplitude
!gi3J @ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
REPI >-| s1=s10;
I.p "8I; s20=0.*s10; %input in waveguide 2
o4,9jk$ s30=0.*s10; %input in waveguide 3
a``Q}.ST s2=s20;
;".]W;I*O s3=s30;
B-wF1! Jv p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
vb$i00? %energy in waveguide 1
GD4+f|1.* p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
j|VX6U
%energy in waveguide 2
Wqe0m_7 p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
]3
76F7 %energy in waveguide 3
OKnpG*)u=g for m3 = 1:1:M3 % Start space evolution
9
xFX"_J s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
7|<-rjz^ s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
e09QaY s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
~I@ % ysR sca1 = fftshift(fft(s1)); % Take Fourier transform
k;HI -v sca2 = fftshift(fft(s2));
_8wT4|z5 sca3 = fftshift(fft(s3));
kZ=yb-~ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
,S1'SCwVdJ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
yJ!,>OQ%' sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
\F<C$cys\ s3 = ifft(fftshift(sc3));
-pQ0,/}K s2 = ifft(fftshift(sc2)); % Return to physical space
h_B
nQZ\ s1 = ifft(fftshift(sc1));
`&J=3x end
wvH*<,8V q p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
;W3c|5CE p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
9Yji34eDZ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
q5 .5 %W P1=[P1 p1/p10];
B
\.0 5< P2=[P2 p2/p10];
@ e+ qe9A| P3=[P3 p3/p10];
64SRW8AH P=[P p*p];
! ~+mf^D end
FB
O_B figure(1)
bK|nx L plot(P,P1, P,P2, P,P3);
_ !k\~4U e*39/B0S 转自：
http://blog.163.com/opto_wang/
