Spheres

PEC/PMC Sphere

The perfectly electrically conducting (PEC) or perfectly magnetically conducting (PMC) sphere has radius $r$ and is assumed to be located in the origin. It is defined by PECSphere.

API

PECSphere(
    radius = error("missing argument `radius`"),
)

PECSphere is an alias of Sphere{PEC}: a sphere carrying the boundary condition PEC as its type parameter, see Scatterer.

Dielectric Sphere

The dielectric sphere has radius $r$ and is assumed to be located in the origin. It is defined by DielectricSphere, where the filling Medium(εᵢ, μᵢ) with permeability $\mu_\mathrm{i}$ and permittivity $\varepsilon_\mathrm{i}$ has to be defined.

API

DielectricSphere(
    radius      = error("missing argument `radius`"),
    filling     = error("missing argument `filling`")
)

Here radius is a Float and filling is of type Medium(εᵢ, μᵢ).

DielectricSphere is an alias of Sphere{<:Dielectric}: the filling is carried by the boundary condition Dielectric, which, in contrast to PEC, requires data and is therefore stored as a value as well, sp.boundary.filling.

Layered Dielectric Sphere

The layered dielectric sphere has radii $[r_1, r_2, \dots, r_N]$ and is assumed to be located in the origin. It is defined by LayeredSphere, where the vector of fillings [Medium(ε₁, μ₁), Medium(ε₂, μ₂), ..., Medium(εN, μN)] with permeability $\mu_n$ and permittivity $\varepsilon_n$ has to be defined.

API

LayeredSphere(
    radii   = error("Missing argument `radii`"),
    filling = error("`missing argument `filling`")
)

with, e.g., radii = SVector(0.25, 0.5, 1.0) and filling = SVector(Medium(ε1, μ1), Medium(ε2, μ2), Medium(ε3, μ3)).

LayeredSphere is an alias of Sphere{<:Layered{<:Dielectric}}. Seen from outside, the shells form a condition on the outer surface: the outermost radius $r_N$ is the radius of the Sphere, while the inner interfaces, the fillings of the shells, and the dielectric core are carried by the boundary condition Layered.

Layered Dielectric Sphere with PEC Core

The layered dielectric sphere has radii $[r_1, r_2, \dots, r_{N+1}]$ and is assumed to be located in the origin. It is defined by LayeredSpherePEC, where the vector of fillings [Medium(ε₁, μ₁), Medium(ε₂, μ₂), ..., Medium(εN, μN)] with permeability $\mu_n$ and permittivity $\varepsilon_n$ has to be defined.

API

LayeredSpherePEC(
    radii   = error("Missing argument `radii`"),
    filling = error("Missing argument `filling`")
)

with, e.g., radii = SVector(0.25, 0.5, 1.0) and filling = SVector(Medium(ε1, μ1), Medium(ε2, μ2)).

LayeredSpherePEC is an alias of Sphere{<:Layered{PEC}}: as for the LayeredSphere, the outermost radius is that of the sphere, and the condition Layered carries the rest, here with a PEC core.

Dielectric Sphere with Thin Impedance Layer

The dielectric sphere with a thin impedance layer of thickness $t$ has radius $r$ and is assumed to be located in the origin. It is defined by DielectricSphereThinImpedanceLayer. Unlike the LayeredSphere model, the solution is obtained by using an approximation: it is assumed that the impedance is so high that the displacement field is purely radial (see [Jon95, pp. 230ff]). This leads to a potential drop across the thin layer, while the displacement field is constant in radial direction. In addition to the filling Medium(εᵢ, μᵢ), the impedance layer must be specified, both the Medium(εₜ, μₜ) and its thickness.

API

DielectricSphereThinImpedanceLayer(
    radius    = error("missing argument `radius`"),
    thickness = error("missing argument `thickness` of the coating"),
    thinlayer = error("missing argument `thinlayer`"),
    filling   = error("missing argument `filling`")
)

Here radius and thickness are a Floats, filling and thinlayer are of type Medium.

DielectricSphereThinImpedanceLayer is an alias of Sphere{<:ThinImpedanceLayer}: the coating, being thin, is modelled as an effective condition on the surface of the sphere, see ThinImpedanceLayer, which carries the thickness, the thinlayer, and the filling.