Array Antenna Animation

T. Hirano

F(r)=A ((Exp[-I k r])/r)
f(r,t)=Re[ F(r) Exp[I ω t] ]=Re[ A ((Exp[-I (k r-ω t)])/r) ]
λ=1 として、
k r-ω t=((2 π)/λ) r-ω t
ω=2 π f, T=(1/f)=((2 π)/ω)
[k r-ω t=k(r-ct)=2 π (r-ct)と表現することもできる]

a point source

n=1;
a[1]=1.; xs[1]=0.; ys[1]=0.;

2-element array

n=2;
a[1]=1.; xs[1]=-2.; ys[1]=0.;
a[2]=1.; xs[2]=2.; ys[2]=0.;

4-element array

n=4;
a[1]=1.; xs[1]=0.; ys[1]=0.;
a[2]=1.; xs[2]=0.5; ys[2]=0.;
a[3]=1.; xs[3]=1.0; ys[3]=0.;
a[4]=1.; xs[4]=1.5; ys[4]=0.;

Graphics and Animation

ω=2*π;
r[x_,y_,i_]:=(Sqrt[(((x-xs[i]))^2)+(((y-ys[i]))^2)]);
Fc[x_,y_]:=Sum[a[i]*((Exp[-I*2*π*r[x,y,i]])/(r[x,y,i])),{i,1,n}]
f[x_,y_,t_]:=Re[ Fc[x,y]*Exp[I*ω*t] ];

DensityPlot[f[x,y,0],{x,-3.75,5.25},{y,-4.5,4.5},Mesh->False,PlotPoints->100,FrameTicks->None]

Table[DensityPlot[f[x,y,t],{x,-3.75,5.25},{y,-4.5,4.5},
Mesh->False,
PlotPoints->20,
FrameTicks->None],
{t,0,1-0.001,1/8}]