计算脉冲在非线性耦合器中演化的Matlab 程序 !e E;MaS> vn"+x_ % This Matlab script file solves the coupled nonlinear Schrodinger equations of
:+*q,lX8 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
i$ CN{c* % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
6G0Y ,B7& % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
YRRs bm{ TpIx!R9 %fid=fopen('e21.dat','w');
^]{m* bEkR N = 128; % Number of Fourier modes (Time domain sampling points)
|X6 /Y@N M1 =3000; % Total number of space steps
K}e:zR;;^ J =100; % Steps between output of space
&Ay[mZQ 7 T =10; % length of time windows:T*T0
'ugc=-0pd T0=0.1; % input pulse width
CaE1h9 MN1=0; % initial value for the space output location
/|MHZ$Y9w? dt = T/N; % time step
m( DJ6CSa n = [-N/2:1:N/2-1]'; % Index
4Fs5@@>X t = n.*dt;
B/F6WQdZ u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
m]Gxep0% u20=u10.*0.0; % input to waveguide 2
fWk,k*Z 9 u1=u10; u2=u20;
g:rjt1w`D U1 = u1;
]/ffA|"U` U2 = u2; % Compute initial condition; save it in U
XV %DhR= ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
2>+(OL4l w=2*pi*n./T;
1=U NA :t< g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
s:ZYiZ- L=4; % length of evoluation to compare with S. Trillo's paper
Q}6!t$Vk dz=L/M1; % space step, make sure nonlinear<0.05
@ ]F1J for m1 = 1:1:M1 % Start space evolution
h'm-]v u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
xP+`scv*m# u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
xmXuBp:M(R ca1 = fftshift(fft(u1)); % Take Fourier transform
rZ#ZY ca2 = fftshift(fft(u2));
='G-wX&k c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
}huFv*<@' c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
CR8szMa u2 = ifft(fftshift(c2)); % Return to physical space
ATzFs]~K; u1 = ifft(fftshift(c1));
V]Z!x.x"=y if rem(m1,J) == 0 % Save output every J steps.
RzOcz=A} U1 = [U1 u1]; % put solutions in U array
\@!"7._= U2=[U2 u2];
YM r2|VEU[ MN1=[MN1 m1];
euiP<[|h= z1=dz*MN1'; % output location
HE|XDcYO end
h
]6: `5- end
D8 BmC hg=abs(U1').*abs(U1'); % for data write to excel
M~ eXC ha=[z1 hg]; % for data write to excel
H5!e/4iz t1=[0 t'];
aDZ,9} hh=[t1' ha']; % for data write to excel file
'B\7P*L"p %dlmwrite('aa',hh,'\t'); % save data in the excel format
SUC' o" figure(1)
F?+\J =LT waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
mJNw<T4!/ figure(2)
'zhv#&O waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
E! GH$%:; ~J:]cy)Q 非线性超快脉冲耦合的数值方法的Matlab程序 cNl NJ >r\q6f#J4 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。
~YRG9TK 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
Bw /8-:eb 1Eh6ti 8_Nyy/K#F G_]zy mXQ % This Matlab script file solves the nonlinear Schrodinger equations
m gE
r+ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
%WF]mF T_ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
uL{CUt
% pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
2!Qg1h M Fs( FI\^ C=1;
BIh^b?:zU M1=120, % integer for amplitude
vzFo" M3=5000; % integer for length of coupler
p?2^JJpUb N = 512; % Number of Fourier modes (Time domain sampling points)
i_e%HG dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
s[bQO1g;* T =40; % length of time:T*T0.
;-AC}jG dt = T/N; % time step
46##(4RF n = [-N/2:1:N/2-1]'; % Index
=Hbf()cN) t = n.*dt;
v>0I =ut ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
C2 {*m{
D w=2*pi*n./T;
oy-y Q Y X g1=-i*ww./2;
MfZamu5+F g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
(YM2Cv{ 4 g3=-i*ww./2;
hVIv-> P1=0;
*#9?9SYSk P2=0;
;,/4Ry22j- P3=1;
{l"(EeW6) P=0;
zY9CoadZ for m1=1:M1
2]]}Xvx4# p=0.032*m1; %input amplitude
-AN5LE9- s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
n^|SN9 _r s1=s10;
^8 KxU s20=0.*s10; %input in waveguide 2
)#8}xAjV s30=0.*s10; %input in waveguide 3
d uP0US s2=s20;
"U!Vdt2vp s3=s30;
#(QS5J&Qq p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
NL,6<ZOon, %energy in waveguide 1
. ' >d7 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
=h xyR; %energy in waveguide 2
n&,X ']z. p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
P? ^%i %energy in waveguide 3
osc A\r for m3 = 1:1:M3 % Start space evolution
d_!}9 s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
!jf!\Uu[U s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
{#~A `crO s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
V-3 ;7 sca1 = fftshift(fft(s1)); % Take Fourier transform
AZf69z sca2 = fftshift(fft(s2));
YYL3a=;`a sca3 = fftshift(fft(s3));
c/^l2CJ0 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
+koW3> sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
ht#,v5oG>f sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
PjofW%7F s3 = ifft(fftshift(sc3));
H_ ,4N_hL s2 = ifft(fftshift(sc2)); % Return to physical space
Sk:x.oOZ s1 = ifft(fftshift(sc1));
0"Euf41 end
L1WvX6 p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
Xvk+ 1:D p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
^q`RaX) p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
V CVKh P1=[P1 p1/p10];
!Na@T]J P2=[P2 p2/p10];
X,c`,B03 P3=[P3 p3/p10];
yY{ P=[P p*p];
g6+5uvpd end
@-Y,9mM figure(1)
re,}}' plot(P,P1, P,P2, P,P3);
9R">l5u }u1h6rd ` 转自：
http://blog.163.com/opto_wang/
