Chapter 5
An Electromagnetic Model
for Anisotropic Media: Green’s Dyad
for Plane-Layered Media
5.1 Theory
The Green’s dyad, which is the electric-field response to a delta-function vector
current source, plays a principal role in volume-integral equations. In this chapter
we sketch the theory of the Green’s dyad for plane-parallel layered media as it is
applied to titanium and titanium-like alloys that possess 6 mm symmetry.
Eigenmodes of Anisotropic Media
We will consider plane-parallel bodies of infinite extent in the (x, y) plane, which
are made up of layers of homogeneous, anisotropic material. To be specific, we
consider host materials that are characterized by the following biaxial generalized
electrical permittivity matrix:
h =
⎡
⎣
x xy 0
yx y 0
0 0 z
⎤
⎦ ,
(5.1)
where the entries are generalized permittivities + σ/j ω.
Maxwell’s equations for an electrically anisotropic body are
∇ × E = −jωμ h H − jω(μ(r) − μ h )H
= −jωμ h H + J m
∇ × H = jω h · E + jω( − h ) · E
= jω h · E + J e ,
(5.2)
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
H. A. Sabbagh et al., Advanced Electromagnetic Models for Materials
Characterization and Nondestructive Evaluation, Scientific Computation,
https://doi.org/10.1007/978-3-030-67956-9_5
123
An Electromagnetic Model
for Anisotropic Media: Green’s Dyad
for Plane-Layered Media
5.1 Theory
The Green’s dyad, which is the electric-field response to a delta-function vector
current source, plays a principal role in volume-integral equations. In this chapter
we sketch the theory of the Green’s dyad for plane-parallel layered media as it is
applied to titanium and titanium-like alloys that possess 6 mm symmetry.
Eigenmodes of Anisotropic Media
We will consider plane-parallel bodies of infinite extent in the (x, y) plane, which
are made up of layers of homogeneous, anisotropic material. To be specific, we
consider host materials that are characterized by the following biaxial generalized
electrical permittivity matrix:
h =
⎡
⎣
x xy 0
yx y 0
0 0 z
⎤
⎦ ,
(5.1)
where the entries are generalized permittivities + σ/j ω.
Maxwell’s equations for an electrically anisotropic body are
∇ × E = −jωμ h H − jω(μ(r) − μ h )H
= −jωμ h H + J m
∇ × H = jω h · E + jω( − h ) · E
= jω h · E + J e ,
(5.2)
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
H. A. Sabbagh et al., Advanced Electromagnetic Models for Materials
Characterization and Nondestructive Evaluation, Scientific Computation,
https://doi.org/10.1007/978-3-030-67956-9_5
123