计算脉冲在非线性耦合器中演化的Matlab 程序 b]+F/@h~] WVy'f|3; % This Matlab script file solves the coupled nonlinear Schrodinger equations of
/8h=6" % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
ssi7)0 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
LSJ?;Zg(=z % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
6@J=n@J$p c0@8KW[, %fid=fopen('e21.dat','w');
~.m<`~u N = 128; % Number of Fourier modes (Time domain sampling points)
#dA$k+3 M1 =3000; % Total number of space steps
vjGQ! xF J =100; % Steps between output of space
)#}>,,S T =10; % length of time windows:T*T0
-1g:3'%
P T0=0.1; % input pulse width
3yZmW$E. MN1=0; % initial value for the space output location
DYD<?._I
dt = T/N; % time step
V0\[|E;F n = [-N/2:1:N/2-1]'; % Index
smQ^(S^ t = n.*dt;
Iry$z^ u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
*glZb;_
u20=u10.*0.0; % input to waveguide 2
18>cfDh;N u1=u10; u2=u20;
Z',!LK! U1 = u1;
u*l|MIi6J U2 = u2; % Compute initial condition; save it in U
$1an#~ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
/~[Lr
w=2*pi*n./T;
S\e&xUA;| g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
Z4j6z>q E L=4; % length of evoluation to compare with S. Trillo's paper
t;&XIG~ dz=L/M1; % space step, make sure nonlinear<0.05
&_ekA44E for m1 = 1:1:M1 % Start space evolution
I &t~o u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
g{65 QP u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
,fVD`RR(W? ca1 = fftshift(fft(u1)); % Take Fourier transform
wHc
my ca2 = fftshift(fft(u2));
$cCC
1=dW c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
\*xB<mq c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
~U9K<_U u2 = ifft(fftshift(c2)); % Return to physical space
0s#72}n u1 = ifft(fftshift(c1));
%@/^UE: if rem(m1,J) == 0 % Save output every J steps.
m~ tvuz I U1 = [U1 u1]; % put solutions in U array
sHP-@ U2=[U2 u2];
~Iu! B
Y MN1=[MN1 m1];
z$32rt8{`v z1=dz*MN1'; % output location
gE-y`2SU end
WSkGVQu end
_u`YjzK hg=abs(U1').*abs(U1'); % for data write to excel
O !L`0
=%c ha=[z1 hg]; % for data write to excel
+L(amq;S t1=[0 t'];
+eM${JyXH hh=[t1' ha']; % for data write to excel file
)ZJvx%@i %dlmwrite('aa',hh,'\t'); % save data in the excel format
^QB[;g.O figure(1)
C6_(j48& waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
vJkc/7 figure(2)
7|P
kc(O waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
Y::0v@&( Ykbg5Z 非线性超快脉冲耦合的数值方法的Matlab程序 ^URCnJ67Se 4`IM[DIG~ 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。
t8Zo9q> 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
Hd|l6/[xz W?
iA P i=8iK#2 h v<qh;2 % This Matlab script file solves the nonlinear Schrodinger equations
z*y!Ml1 % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
5jdZC(q5a % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
^4y]7p % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
S;Bk/\2 [uq>b|`RG C=1;
R$a<= M1=120, % integer for amplitude
AKNx~!%2 M3=5000; % integer for length of coupler
XC4Z ,,ah" N = 512; % Number of Fourier modes (Time domain sampling points)
K~x,so dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
8!g
`bC#% T =40; % length of time:T*T0.
^S9y7b^;r dt = T/N; % time step
VSj!Gm0LB n = [-N/2:1:N/2-1]'; % Index
B~Q-V&@o t = n.*dt;
/'O8RUjN ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
XX;4A w=2*pi*n./T;
^?69|, g1=-i*ww./2;
$EMOz=)I# g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
adON&< g3=-i*ww./2;
?mQ^"9^XS P1=0;
G4&s_M$ P2=0;
ZO}Og&% P3=1;
_`$LdqgE P=0;
q!c(~UVw for m1=1:M1
0bNvmZ$ p=0.032*m1; %input amplitude
6 Z/`p~e s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
]`E+HLEQ' s1=s10;
Nz{dnV{&x; s20=0.*s10; %input in waveguide 2
OI R5QH s30=0.*s10; %input in waveguide 3
;?6vKpj; s2=s20;
WKf<%
E$ s3=s30;
#F*|@ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
K,f:X g!: %energy in waveguide 1
mgxIxusR p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
w7nt $L5 %energy in waveguide 2
Zw]`z*,yRA p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
@0`A!5h?u %energy in waveguide 3
e_BG%+;G, for m3 = 1:1:M3 % Start space evolution
$o"nTl s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
^}3^|jF s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
,m=F
H?5 s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
*2X6;~ sca1 = fftshift(fft(s1)); % Take Fourier transform
8$Q`wRt(% sca2 = fftshift(fft(s2));
HN47/]"* sca3 = fftshift(fft(s3));
WSThhI sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
x_PO; sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
Z1Qz
LvWs sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
^<]'?4m] s3 = ifft(fftshift(sc3));
e r"
w{ s2 = ifft(fftshift(sc2)); % Return to physical space
(su,=Z s1 = ifft(fftshift(sc1));
y48]|%73 end
Nk~}aj p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
J5@08bZm p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
)W@ug,y p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
Xo^8o0xi P1=[P1 p1/p10];
+^I0>\ P2=[P2 p2/p10];
6K2e]r P3=[P3 p3/p10];
p_r` " P=[P p*p];
4Z)4WGp! end
3WV(Ok figure(1)
|%_C$s% plot(P,P1, P,P2, P,P3);
{N(qS'N \BOoY# !a 转自:
http://blog.163.com/opto_wang/