计算脉冲在非线性耦合器中演化的Matlab 程序 UQ8bN I7 ;4 ~U,+Av % This Matlab script file solves the coupled nonlinear Schrodinger equations of
r6.N4eW.L % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
Kn}ub+
"J % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
^^?q$1k6r* % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
\ L] |-f(4 mP}#Ccji? %fid=fopen('e21.dat','w');
T~>#2N-Z N = 128; % Number of Fourier modes (Time domain sampling points)
(.X]F_ *sc M1 =3000; % Total number of space steps
d>i13d AI J =100; % Steps between output of space
_a
-]?R T =10; % length of time windows:T*T0
]n
v( aM?d T0=0.1; % input pulse width
Fvl`2W94; MN1=0; % initial value for the space output location
d/U."V} dt = T/N; % time step
jPJAWXB4a n = [-N/2:1:N/2-1]'; % Index
] |Z b\{
t = n.*dt;
%|IUq jg
u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
M7dU@ Ag u20=u10.*0.0; % input to waveguide 2
isK;mU?< u1=u10; u2=u20;
P%>?[9!Nt U1 = u1;
]H[8Z|i"" U2 = u2; % Compute initial condition; save it in U
*Xr$/N ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
rY}B-6qJn w=2*pi*n./T;
P:!) 9/.2 g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
oyeG$mpg L=4; % length of evoluation to compare with S. Trillo's paper
_m'ysCjA dz=L/M1; % space step, make sure nonlinear<0.05
,0? !ov| for m1 = 1:1:M1 % Start space evolution
ujzW|HW^v u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
1 /iE`Si u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
bXdY\&fE ca1 = fftshift(fft(u1)); % Take Fourier transform
m4/er539T ca2 = fftshift(fft(u2));
La,QB3K/ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
AR B7>" c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
F[E? A95W u2 = ifft(fftshift(c2)); % Return to physical space
^Kq|ID
AP u1 = ifft(fftshift(c1));
;e{5)@h$ if rem(m1,J) == 0 % Save output every J steps.
e f]B9J~h U1 = [U1 u1]; % put solutions in U array
fE25(wCz7 U2=[U2 u2];
}T(z4P3 MN1=[MN1 m1];
SG'JE}jzO z1=dz*MN1'; % output location
])T/sO#' end
%+tV/7|F end
bBE+jqi 2 hg=abs(U1').*abs(U1'); % for data write to excel
[ ]p"3 i ha=[z1 hg]; % for data write to excel
dHII.=l T t1=[0 t'];
&8?`< hh=[t1' ha']; % for data write to excel file
G$=-,6kZO %dlmwrite('aa',hh,'\t'); % save data in the excel format
WZ~> BM figure(1)
=*MR(b> waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
Z)9R9 s figure(2)
}~I|t!GL waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
g(m_yXIx ti_u!kNv 非线性超快脉冲耦合的数值方法的Matlab程序 KD*O%@X5C ecFi (eMD 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。
1f//wk | 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
3%
vis\~^ )%j" tOg=zXm YoSQN/Z % This Matlab script file solves the nonlinear Schrodinger equations
b! tludb % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
,2zKQ2 z % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
jnBC;I[: % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
X;EJ&g/ { ;n0/
C=1;
p;->hn~D'5 M1=120, % integer for amplitude
?qT( 3C9p M3=5000; % integer for length of coupler
-c={ +z " N = 512; % Number of Fourier modes (Time domain sampling points)
A*0*sZ0 dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
GX38~pq T =40; % length of time:T*T0.
A ,<@m2 dt = T/N; % time step
HdCk!Fv n = [-N/2:1:N/2-1]'; % Index
&?T $ {*~ t = n.*dt;
UrK"u{ G ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
GOr}/y; w=2*pi*n./T;
K&S@F!#g g1=-i*ww./2;
rPTfpeqN) g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
cU | _ g3=-i*ww./2;
+x]e-P % P1=0;
E fSMFPM
P2=0;
Qj!d ^8 P3=1;
5$^c@ 0 P=0;
i+ic23$4M for m1=1:M1
'j# a%j@{ p=0.032*m1; %input amplitude
78w4IICk s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
m+T2vi s1=s10;
/v$]X4 S` s20=0.*s10; %input in waveguide 2
(Y;'[. s30=0.*s10; %input in waveguide 3
SALCuo"L s2=s20;
`7_n}8NVC s3=s30;
M?hFCt3Y p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
8S= c^_PJ %energy in waveguide 1
rC rr"O#j p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
%zQ2:iT5@= %energy in waveguide 2
% kW3hQ<$ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
Y_lCcu#OA %energy in waveguide 3
mxhW|}_-j for m3 = 1:1:M3 % Start space evolution
4#@0T"T~M s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
!Bncx`pl s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
S41)l!+2 s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
\S5V}!_ sca1 = fftshift(fft(s1)); % Take Fourier transform
O 3}P07 sca2 = fftshift(fft(s2));
H nK/A0j M sca3 = fftshift(fft(s3));
2K~tDNv7 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
44|03Ty sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
+ 1f{ _v sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
:|fl?{E s3 = ifft(fftshift(sc3));
_! ;\R7] s2 = ifft(fftshift(sc2)); % Return to physical space
{4)5]62>u s1 = ifft(fftshift(sc1));
J\GKqt;5@ end
TP^\e_k p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
NIL^UN} p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
N$ *>suQ, p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
T/ Ez*iQW P1=[P1 p1/p10];
Y?e3B x7*b P2=[P2 p2/p10];
uTUa4 ^]* P3=[P3 p3/p10];
nu(eLUU P=[P p*p];
wEv*1y4 end
DW 4MA<UQ figure(1)
m9cj7 plot(P,P1, P,P2, P,P3);
|:/ @t *<;&>w8 转自：
http://blog.163.com/opto_wang/
