计算脉冲在非线性耦合器中演化的Matlab 程序 prIJjy-F V 1G5Kph % This Matlab script file solves the coupled nonlinear Schrodinger equations of
0lcwc"_DZX % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
ov\%*z2= % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
c^&:':Z%' % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
QZO<'q`L L+lye Ir' %fid=fopen('e21.dat','w');
K&=6DvfR N = 128; % Number of Fourier modes (Time domain sampling points)
v] Xy^7? M1 =3000; % Total number of space steps
y|9 LtQ J =100; % Steps between output of space
i
!SN"SY T =10; % length of time windows:T*T0
^;\6 ju2 T0=0.1; % input pulse width
rXe+#`m2 MN1=0; % initial value for the space output location
K
#J O# dt = T/N; % time step
abEdZ)$ n = [-N/2:1:N/2-1]'; % Index
NB( GE t = n.*dt;
b+CvA(* u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
N a.e1A&?j u20=u10.*0.0; % input to waveguide 2
)^E6VD&6 u1=u10; u2=u20;
f|yq~3x) U1 = u1;
REk^pZ3B U2 = u2; % Compute initial condition; save it in U
X Fww|SG$ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
Fy_~~nI0 w=2*pi*n./T;
x^pHP|<3` g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
5(Xq58nhxI L=4; % length of evoluation to compare with S. Trillo's paper
g^\>hjNX dz=L/M1; % space step, make sure nonlinear<0.05
x_4{MD^% for m1 = 1:1:M1 % Start space evolution
%.{xo.`a[ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
ap rgThoD u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
[ID#P Ule ca1 = fftshift(fft(u1)); % Take Fourier transform
8Y;>3z th7 ca2 = fftshift(fft(u2));
o 7 &q c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
|q q29dS? c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
h#|A c>fz u2 = ifft(fftshift(c2)); % Return to physical space
) f%Q7 u1 = ifft(fftshift(c1));
M3)Id?|]6 if rem(m1,J) == 0 % Save output every J steps.
+2 s][^-KV U1 = [U1 u1]; % put solutions in U array
cW^u4%f't' U2=[U2 u2];
oR<;Tr~{q MN1=[MN1 m1];
N$8"X-na ? z1=dz*MN1'; % output location
$[(FCS end
qKuHd~M{ 1 end
mi sPJO&QD hg=abs(U1').*abs(U1'); % for data write to excel
M; @/697G ha=[z1 hg]; % for data write to excel
\3j4=K'nE t1=[0 t'];
93Q x+oK] hh=[t1' ha']; % for data write to excel file
*eUxarI %dlmwrite('aa',hh,'\t'); % save data in the excel format
]=]`Mnuxb figure(1)
`SYq/6$VEH waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
0:>C v <N figure(2)
'[[*(4 a3 waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
^c>ROpic `%0k\,}V 非线性超快脉冲耦合的数值方法的Matlab程序 O'W[/\A56M 8PW3x-+ 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。
=,W~^<\" 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
Y2y =
P mC`U"rlK~ _We4% BH?fFe&J:` % This Matlab script file solves the nonlinear Schrodinger equations
OV $ |!n % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
T7 XbbU % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
a[V 4EX1E % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
J`A )WsKkb 'Z^KpW C=1;
&uu69)u M1=120, % integer for amplitude
A)o%\j M3=5000; % integer for length of coupler
bRc ~e@ N = 512; % Number of Fourier modes (Time domain sampling points)
p/&s-G F dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
K>`*J J, T =40; % length of time:T*T0.
1 |#j/ dt = T/N; % time step
1`EkN0iZ n = [-N/2:1:N/2-1]'; % Index
vtf`+q t = n.*dt;
m9 f[nT ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
|K$EUL zz w=2*pi*n./T;
::G0v g1=-i*ww./2;
#N|A@B5 x g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
Gv }~ g3=-i*ww./2;
VWE`wan< P1=0;
qu0dWgK P2=0;
uF\f>E)/N% P3=1;
ln=:E$jX P=0;
*[wj ) for m1=1:M1
[%BWCd8Q~P p=0.032*m1; %input amplitude
n%:& N s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
#jR1ti)p s1=s10;
Ng<oz*>U s20=0.*s10; %input in waveguide 2
H=7Nh6v s30=0.*s10; %input in waveguide 3
-Mufo.Jz1o s2=s20;
}h_=
n> s3=s30;
-#"7F:N1 p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
Z "g6z#L& %energy in waveguide 1
*v9 {f? p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
GF awmNZ %energy in waveguide 2
7W\aX*] p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
E,:E u< %energy in waveguide 3
0@PI=JZ% for m3 = 1:1:M3 % Start space evolution
i ?pC[Ao-_ s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
V(6ovJpA0 s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
LDv>hz o s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
+%RB&:K7, sca1 = fftshift(fft(s1)); % Take Fourier transform
v?(9ZY] sca2 = fftshift(fft(s2));
8 n)3'ok sca3 = fftshift(fft(s3));
gpzZs<ST sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
!7 fVO2m T sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
LuW^Ga"E sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
1q;r 4$n s3 = ifft(fftshift(sc3));
B#;0 { s2 = ifft(fftshift(sc2)); % Return to physical space
d<B=p&~ s1 = ifft(fftshift(sc1));
M- += t8 end
#sp8 !8|y p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
WL/9r
*jW p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
b_j8g{/9 p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
|F^h >^
x P1=[P1 p1/p10];
AIa#t#8${ P2=[P2 p2/p10];
n"c3C) P3=[P3 p3/p10];
~`Xu 6+1o P=[P p*p];
2k3 yf_N end
TdH~ s z figure(1)
4 Z< plot(P,P1, P,P2, P,P3);
\H5{[ZUn T hLR<\ 转自：
http://blog.163.com/opto_wang/
