计算脉冲在非线性耦合器中演化的Matlab 程序 3T4HX|rC &oy')\H % This Matlab script file solves the coupled nonlinear Schrodinger equations of
v_WQ<G? % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
}N$f=:iI % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
)58~2vR % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
|d*a~T0 =6Gn?
/{ %fid=fopen('e21.dat','w');
MtN!Xx N = 128; % Number of Fourier modes (Time domain sampling points)
-V[x
q M1 =3000; % Total number of space steps
af9KtX+ J =100; % Steps between output of space
lI.oyR' T =10; % length of time windows:T*T0
|5X[/Q*K`W T0=0.1; % input pulse width
$AE5n>ZD$ MN1=0; % initial value for the space output location
1+XM1(|c` dt = T/N; % time step
Y#~A":A n = [-N/2:1:N/2-1]'; % Index
e"NP]_vh, t = n.*dt;
]t`SCsoo u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
$gD8[NAIx= u20=u10.*0.0; % input to waveguide 2
; D/6e6 u1=u10; u2=u20;
UXJblo# U1 = u1;
q^Oj/ws U2 = u2; % Compute initial condition; save it in U
0BhcXHt ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
%DXBl:!Y` w=2*pi*n./T;
q#8yU\J|, g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
'@Rk#=85Z L=4; % length of evoluation to compare with S. Trillo's paper
BI %XF
9{ dz=L/M1; % space step, make sure nonlinear<0.05
vB{iw}Hi! for m1 = 1:1:M1 % Start space evolution
Y_!+Y<x7v u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
dr: x0>
u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
m;MJ{"@A' ca1 = fftshift(fft(u1)); % Take Fourier transform
18QqZ,t ca2 = fftshift(fft(u2));
CEc(2q+%i c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
]S[?tn c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
L+<h5>6 u2 = ifft(fftshift(c2)); % Return to physical space
m6n%?8t u1 = ifft(fftshift(c1));
~"SQwE| if rem(m1,J) == 0 % Save output every J steps.
)E>yoUhN U1 = [U1 u1]; % put solutions in U array
n-l_PhPQ` U2=[U2 u2];
vIOGDI> MN1=[MN1 m1];
-bHlFNRm z1=dz*MN1'; % output location
%N fpEo end
Z_m<x! end
m:[I$b6AY hg=abs(U1').*abs(U1'); % for data write to excel
=f{v:n6 ha=[z1 hg]; % for data write to excel
AguE)I&m t1=[0 t'];
vJ^~J2#5 hh=[t1' ha']; % for data write to excel file
}P.Z}n;Uj %dlmwrite('aa',hh,'\t'); % save data in the excel format
A`Y^qXFb` figure(1)
PDuBf&/e waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
D_czUM figure(2)
SM4`Hys;p waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
3-{BXht) PRaVe,5a 非线性超快脉冲耦合的数值方法的Matlab程序 `Y4K w kex V~Q 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。
52tc|j6~# 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
Q/
.LDye8 9|Jv>Ur=)2 |y eQz zHX\h[0f % This Matlab script file solves the nonlinear Schrodinger equations
PD.$a-t % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
$$1t4=Pz % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
rVNx2 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
fP|[4 ku )c' 45bD C=1;
7N[".V]c M1=120, % integer for amplitude
wPjq
B{!Q M3=5000; % integer for length of coupler
Rq5'=L N = 512; % Number of Fourier modes (Time domain sampling points)
:! oJmvy dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
yef\Y3X T =40; % length of time:T*T0.
~. vridH dt = T/N; % time step
EXr2d" n = [-N/2:1:N/2-1]'; % Index
%(/E
` t = n.*dt;
cE
'LE1DK ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
nWIZ0Nde' w=2*pi*n./T;
nJN-U+)u g1=-i*ww./2;
W{"sB:E g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
\~E?;q! g3=-i*ww./2;
$e7%>*?m P1=0;
_)
x{TnK P2=0;
P|$n P3=1;
U`qC.s(L P=0;
g&xj(SMj-$ for m1=1:M1
6-_g1vq p=0.032*m1; %input amplitude
%%s)D4sW s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
<.n,:ir s1=s10;
9,INyEyAL s20=0.*s10; %input in waveguide 2
rz%~=Ca2j s30=0.*s10; %input in waveguide 3
)-)rL@s. s2=s20;
x:MwM? s3=s30;
5:IDl1f5 p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
F%|P#CaB %energy in waveguide 1
*zrGrk:l p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
8>eYM %energy in waveguide 2
HfVHjF) p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
@Z
==B%` %energy in waveguide 3
9m)$^U>oz for m3 = 1:1:M3 % Start space evolution
?K[Y"*y2 s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
,XEIg s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
mcd{:/^? s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
zK5&,/ sca1 = fftshift(fft(s1)); % Take Fourier transform
?;CIS$$r sca2 = fftshift(fft(s2));
V
,p~,rC sca3 = fftshift(fft(s3));
):G%o sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
=SLG N`m3 sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
metn& sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
W:RjWn @< s3 = ifft(fftshift(sc3));
p6<JpW5@_ s2 = ifft(fftshift(sc2)); % Return to physical space
b_~XTWP$l s1 = ifft(fftshift(sc1));
LRu,_2" end
>k\pSV[ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
'r]6 GC8Z$ p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
F}u'A,Hc p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
Q&]|W
Xv P1=[P1 p1/p10];
z;1dMQ,# P2=[P2 p2/p10];
a*5KUj6/TL P3=[P3 p3/p10];
*ai~!TR P=[P p*p];
u @Ze@N% end
$vu*# .w figure(1)
q*
R}yt5 plot(P,P1, P,P2, P,P3);
9-T<gYl T&'Jc 转自:
http://blog.163.com/opto_wang/