计算脉冲在非线性耦合器中演化的Matlab 程序 #/& q YQfZiz}Fv % This Matlab script file solves the coupled nonlinear Schrodinger equations of
RN cI]oJ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
DI2S
%N l % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
A61-AwvF8- % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
qqO10~Xc v]d?6g %fid=fopen('e21.dat','w');
B <|q{D$N/ N = 128; % Number of Fourier modes (Time domain sampling points)
f6/\JVi) - M1 =3000; % Total number of space steps
N?`GZ +5 J =100; % Steps between output of space
u:{.
Hn` T =10; % length of time windows:T*T0
NZi'eZ{^` T0=0.1; % input pulse width
5BGv^Qb_2 MN1=0; % initial value for the space output location
[\ w>{ dt = T/N; % time step
+wPvQKVfI n = [-N/2:1:N/2-1]'; % Index
ej??j<] t = n.*dt;
U 8 .0 L u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
l zQ&)7 ` u20=u10.*0.0; % input to waveguide 2
@N:3`[oB u1=u10; u2=u20;
QKL]O* U1 = u1;
pqNoL*
H U2 = u2; % Compute initial condition; save it in U
ua. 6?W) ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
+ $pO w=2*pi*n./T;
E!(`275s g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
'
m# Ymp L=4; % length of evoluation to compare with S. Trillo's paper
`zvT5=*-# dz=L/M1; % space step, make sure nonlinear<0.05
@?($j)9} for m1 = 1:1:M1 % Start space evolution
`(w kqa u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
0 ^-b} u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
f|HgLFx ca1 = fftshift(fft(u1)); % Take Fourier transform
OkO@BWL ca2 = fftshift(fft(u2));
36 D,el In c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
"}azC |:5 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
EzY
scX.[ u2 = ifft(fftshift(c2)); % Return to physical space
T J"{nB u1 = ifft(fftshift(c1));
B1AF4}~5 if rem(m1,J) == 0 % Save output every J steps.
D-;43>yi< U1 = [U1 u1]; % put solutions in U array
[$ Xu U2=[U2 u2];
lf7H8k, - MN1=[MN1 m1];
gs2&0rnOy\ z1=dz*MN1'; % output location
4 9+}OIX end
;-P:$zw9c end
G#=b6DB hg=abs(U1').*abs(U1'); % for data write to excel
:d/:Ga5v! ha=[z1 hg]; % for data write to excel
^c:eXo U t1=[0 t'];
,'@ISCK^ hh=[t1' ha']; % for data write to excel file
hc~#l # %dlmwrite('aa',hh,'\t'); % save data in the excel format
?\ i,JJO figure(1)
;:K?7w fXn waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
)-7( Hv1 figure(2)
Ub-k<]yZ waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
?eZ"UGZg' bgx5{!A
非线性超快脉冲耦合的数值方法的Matlab程序 N6 Cc%, 085 ^!AZ 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
)Z`viT Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Z_TbM^N [+5S Er} SZ 1pf#w! C X@H G)l % This Matlab script file solves the nonlinear Schrodinger equations
yyYbB ]D % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
<GU(/S!} % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
=dJEcC_J % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
'Y/V9;`)s P<w>1
= C=1;
vmQ
DcCw M1=120, % integer for amplitude
Vf* B1Zb M3=5000; % integer for length of coupler
pLFL6\{g N = 512; % Number of Fourier modes (Time domain sampling points)
[AK %~Kg9 dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
`[R:L.H1 T =40; % length of time:T*T0.
E?W!.hbA dt = T/N; % time step
y#SD-# I- n = [-N/2:1:N/2-1]'; % Index
' [M2Q"X t = n.*dt;
Xwqf Wd_ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
fxCPGj w=2*pi*n./T;
F_
lj>;}a5 g1=-i*ww./2;
J*kzJ{vwy* g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
3R96;d; g3=-i*ww./2;
)e$-B]>7z P1=0;
+=F);;! P2=0;
`E%d $ P3=1;
o ML
K!]a P=0;
MhXm-<4
for m1=1:M1
A&|(% p=0.032*m1; %input amplitude
GAe_Z( T s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
rAi!'vIE s1=s10;
; bu;t# s20=0.*s10; %input in waveguide 2
9U%}" uE s30=0.*s10; %input in waveguide 3
j;c ^pLUP s2=s20;
o lW`.3f s3=s30;
>@\?\!Go p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
I;PO$T %energy in waveguide 1
Pt xc9~k p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
v}t :}M< ; %energy in waveguide 2
E8V\J p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
v8M#%QoA %energy in waveguide 3
U\plt%2m> for m3 = 1:1:M3 % Start space evolution
-"b3q s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
x6mq['_ s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
Qpu2RfP s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
Wam?(!{mOf sca1 = fftshift(fft(s1)); % Take Fourier transform
iV$75Atk sca2 = fftshift(fft(s2));
\^Q)`Lqp:g sca3 = fftshift(fft(s3));
Fd=`9 N9 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
`SpS?mWA sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
eyp\h8!u_ sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
bao5^t} s3 = ifft(fftshift(sc3));
]fmf X s2 = ifft(fftshift(sc2)); % Return to physical space
?v*7!2; s1 = ifft(fftshift(sc1));
6>^k9cJp end
jtJ8r5j 1 p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
FO3*[O p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
"+C\f) p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
/ 1@m#ZxA: P1=[P1 p1/p10];
>dH*FZ:c P2=[P2 p2/p10];
\?I wR]@y P3=[P3 p3/p10];
gDBQ\vM8 P=[P p*p];
#GJh:# tt^ end
f@X*Tlx^| figure(1)
qOanu plot(P,P1, P,P2, P,P3);
F#R\Ot,hv ph+tk5k 转自：
http://blog.163.com/opto_wang/
