Plane Wave
Definition
A plane wave with amplitude $a$, wave vector $\bm k = k \hat{\bm k}$, and polarization $\hat{\bm p}$ (vectors with a hat denote unit vectors) is defined by the field
\[\bm e_\mathrm{PW}(\bm r) = a \hat{\bm p} \, \mathrm{e}^{-\mathrm{j} \bm k \cdot \bm r} \,,\]
where the polarization and wave vector are orthogonal, that is,
\[\bm k \cdot \hat{\bm p} = 0\]
holds.
API
The API provides the following constructor with default values:
SphericalScattering.planeWave
— Functionex = planeWave(;
embedding = Medium(ε0, μ0),
frequency = error("missing argument `frequency`"),
amplitude = 1.0,
direction = SVector{3,typeof(frequency)}(0.0, 0.0, 1.0),
polarization = SVector{3,typeof(frequency)}(1.0, 0.0, 0.0),
)
The provided direction
and the polarization
vectors have to be orthogonal. This is checked during initialization.
The direction
and the polarization
vectors are each automatically normalized to unit vectors during the initialization.
Incident Field
The electric field of the plane wave is as given above. The magnetic field is given by
\[\bm h_\mathrm{PW}(\bm r) = \cfrac{a}{Z_\mathrm{F}} (\hat{\bm k} \times \hat{\bm p}) \mathrm{e}^{-\mathrm{j} \bm k \cdot \bm r}\]
with $Z_\mathrm{F} = \sqrt{\mu / \varepsilon}$.
API
The general API is employed:
E = field(ex, ElectricField(point_cart))
H = field(ex, MagneticField(point_cart))
The far-field of a plane wave is not defined.
Scattered Field
The scattered field computation follows [1, pp. 347ff].
Internal details of the computations: Following [1, pp. 347ff] the plane wave is initially assumed to travel in positive $z$-axis direction and to have a polarization along the positive $x$-axis. Arbitrary directions and orientations (forming a valid pair) are obtained via rotations.
API
The general API is employed:
E = scatteredfield(sp, ex, ElectricField(point_cart))
H = scatteredfield(sp, ex, MagneticField(point_cart))
FF = scatteredfield(sp, ex, FarField(point_cart))
Total Field
API
The general API is employed:
E = field(sp, ex, ElectricField(point_cart))
H = field(sp, ex, MagneticField(point_cart))
The total far-field is not defined (since the incident far-field is not defined).
Radar Cross Section
To compute the bistatic radar cross section (RCS) [1, pp. 350ff]
\[\sigma (\vartheta, \varphi) = \lim_{r\rightarrow \infty} \left( 4 \pi r^2 \frac{{|e^\mathrm{sc}|}^2}{{|e^\mathrm{inc}|}^2} \right)\]
the function
σ = rcs(sp, ex, points_cart)
is provided. For the monostatic RCS, the function
σ = rcs(sp, ex)
is provided.