计算脉冲在非线性耦合器中演化的Matlab 程序 *F_ dP *'BA#
/@ % This Matlab script file solves the coupled nonlinear Schrodinger equations of
!}+rg2 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
/a'c P % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
@0v%5@ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
H 0 %;t c;M&;'#x %fid=fopen('e21.dat','w');
GM{J3O= N = 128; % Number of Fourier modes (Time domain sampling points)
S|_} 0 M1 =3000; % Total number of space steps
m h5ozv$ J =100; % Steps between output of space
zfexaf! T =10; % length of time windows:T*T0
)^D:VY9 2 T0=0.1; % input pulse width
` 6'dhB MN1=0; % initial value for the space output location
C{5^UCJkg dt = T/N; % time step
o 5;V=8T; n = [-N/2:1:N/2-1]'; % Index
"&@v[O)!xu t = n.*dt;
p3f>;|uh_ u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
8B|qNf `Yi u20=u10.*0.0; % input to waveguide 2
XZ3)gYQi u1=u10; u2=u20;
%XU V[L} U1 = u1;
'9w.~@7 U2 = u2; % Compute initial condition; save it in U
--t5jSS44 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
FlqE!6[[ w=2*pi*n./T;
83| 7#L g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
'7j!B1K- L=4; % length of evoluation to compare with S. Trillo's paper
Dj K dz=L/M1; % space step, make sure nonlinear<0.05
c!2j+ORz for m1 = 1:1:M1 % Start space evolution
(: TZ~"VY u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
q |r/%[[!o u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
L{i,.aE/nO ca1 = fftshift(fft(u1)); % Take Fourier transform
kCuIEv@ ca2 = fftshift(fft(u2));
m :sT) c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
sC ^9 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
iuxS=3lT"K u2 = ifft(fftshift(c2)); % Return to physical space
.dr-I7&! u1 = ifft(fftshift(c1));
<h vVh9 if rem(m1,J) == 0 % Save output every J steps.
;`(l)X+7 U1 = [U1 u1]; % put solutions in U array
FFvF4]|L U2=[U2 u2];
h G8 !aJo MN1=[MN1 m1];
< "SOH; w z1=dz*MN1'; % output location
KK|AXoBf end
13lJq:bM end
$QbaPmHW hg=abs(U1').*abs(U1'); % for data write to excel
0~;Owu ha=[z1 hg]; % for data write to excel
@h91: hb t1=[0 t'];
VD).UdUn hh=[t1' ha']; % for data write to excel file
gTby%6- \| %dlmwrite('aa',hh,'\t'); % save data in the excel format
ov@N13 ,$ figure(1)
ar#Xe;T! waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
Alh"ZT^ * figure(2)
!
,*4d $ waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
Q^_*&},V i!U,qV1 非线性超快脉冲耦合的数值方法的Matlab程序 #*"5F* lls-Nir% 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。
L]_1z 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
o2J-& |;[%ZE " Fhr5)Z ;@&mR <5j % This Matlab script file solves the nonlinear Schrodinger equations
%xH2jf % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
];n 3H~2 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
7"iUyZ( % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
)uJu .foE , (Bo .(] C=1;
eOdB<He36 M1=120, % integer for amplitude
oOj7y>Nm M3=5000; % integer for length of coupler
#"6O3.P N = 512; % Number of Fourier modes (Time domain sampling points)
K< ;I*cAX dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
p}r1@L s T =40; % length of time:T*T0.
3a_=e
B dt = T/N; % time step
$XOs(>~"r n = [-N/2:1:N/2-1]'; % Index
?df*Y5I2 t = n.*dt;
v_7?Zik8E ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
1_aUU,|. w=2*pi*n./T;
5R?[My g1=-i*ww./2;
u3Qm"? $` g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
{ !;I4W%! g3=-i*ww./2;
=gYKAr^ p5 P1=0;
U< aT%^_ P2=0;
h yPVt6Gkj P3=1;
&ml7368@ P=0;
@5i m*ubzM for m1=1:M1
DF>LN%a~ p=0.032*m1; %input amplitude
tcm?qro) s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
" G&S`8 s1=s10;
?c$z? QTMJ s20=0.*s10; %input in waveguide 2
zHEH?xZ6sD s30=0.*s10; %input in waveguide 3
C }= *%S s2=s20;
d5hYOh O[ s3=s30;
\m\E*c
): p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
m7|}PH" 7 %energy in waveguide 1
N3Yf 3rK p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
2EU((Q`>=( %energy in waveguide 2
Ep.Q&(D
> p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
3. c0P RZ %energy in waveguide 3
gHB*u!w7Z for m3 = 1:1:M3 % Start space evolution
gE_i#=bw s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
/p& V7 2 s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
\ fk%^1XY s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
+kMVl_` V sca1 = fftshift(fft(s1)); % Take Fourier transform
H;eGBVi sca2 = fftshift(fft(s2));
O>h,u[0 sca3 = fftshift(fft(s3));
X *Qt bm, sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
0pC}+
+ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
s"7$SxMT sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
i xf~3Y8 s3 = ifft(fftshift(sc3));
cg]\R1Gm s2 = ifft(fftshift(sc2)); % Return to physical space
7;w x,7CUq s1 = ifft(fftshift(sc1));
+J`H I1 end
FS(bEAk} p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
'pa>;{ p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
-F-RWs{yS p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
e\[z Q
2Z3 P1=[P1 p1/p10];
<fZ?F= P2=[P2 p2/p10];
/CE]7m,7~K P3=[P3 p3/p10];
e
Qz_,vTk P=[P p*p];
P_ [A end
U@ 6bH@v5 figure(1)
g?}$"=B plot(P,P1, P,P2, P,P3);
+p:?blG }:b6WN;c 转自：
http://blog.163.com/opto_wang/
