WOLFRAM|DEMONSTRATIONS PROJECT

Contours of Constant Principal Angle in the Complex Dielectric Plane

​
ϕ
ψ
scale
small
medium
large
The contours of the constant principal angle
ϕ
in the complex dielectric
ϵ
plane can be determined by eliminating the principal azimuth
ψ
from the equation
ϵ=
2
sin
ϕ+
2
sin
ϕ
2
tan
ϕ
-j4ψ
e
. This gives
ϵ-
2
sin
ϕ=
2
sin
ϕ
2
tan
ϕ
, which is a circle with center at
2
sin
ϕ
on the real axis and radius
2
sin
ϕ
2
tan
ϕ
. The figure shows constant principal-angle contours for
0≤ϕ≤70°
. As
ϕ
approaches
90°
, these contours approach concentric circles with center at
ϵ=1
.