General Usage

The basic building blocks are introduced in the following simple example; more details are provided afterwards:

Introductory Example: Plane Wave

using SphericalScattering, StaticArrays

# define excitation: plane wave travelling in positive z-direction with x-polarization
ex = planeWave(frequency=10e6) # Hz

# define scatterer: PEC sphere
sp = PECSphere(radius = 1.0)

# define an observation point
point_cart = [SVector(2.0, 2.0, 3.2)]

# compute scattered fields
E  = scatteredfield(sp, ex, ElectricField(point_cart))
H  = scatteredfield(sp, ex, MagneticField(point_cart))
FF = scatteredfield(sp, ex, FarField(point_cart))

Defining Observation Points

In order to define points the StaticArrays package has to be used.

using StaticArrays

# defining a single point
point_cart = [SVector(2.0, 2.0, 3.2)]

# defining multiple points (along a line)
point_cart = [SVector(5.0, 5.0, z) for z in -2:0.2:2]

Defining an Excitation

For all available excitations a simple constructor with keyword arguments and default values is available. For more details see the APIs of the

• Plane wave
• Dipoles
• Ring currents
• Spherical modes
• Uniform static field

Defining a Scatterer

For all available scatteres a simple constructor with keyword arguments and default values is available. For more details see the APIs of the

• PEC sphere
• PMC sphere
• Dielectric sphere
• Multilayer dielectric sphere
• Multilayer dielectric sphere with PEC core
• Dielectric sphere with thin impedance layer

Computing Fields

The incident, scattered, and total fields can be computed.

Incident Fields

For each excitation the far-field, the electric, and the magnetic near-field without a scatterer can be determined:

E  = field(ex, ElectricField(point_cart))

H  = field(ex, MagneticField(point_cart))

FF = field(ex, FarField(point_cart))

For the uniform field excitation, only the electric field as well as the scalar potential can be calculated:

Φ = field(ex, ScalarPotential(point_cart))

Scattered Fields

For each excitation the scattered fields from a given sphere can be determined as:

E  = scatteredfield(sp, ex, ElectricField(point_cart))

H  = scatteredfield(sp, ex, MagneticField(point_cart))

FF = scatteredfield(sp, ex, FarField(point_cart))

For the uniform static field excitation, only the electric field as well as the scalar potential can be calculated:

Φ = scatteredfield(sp, ex, ScalarPotential(point_cart))

For the dielectric sphere with thin impedance layer two additional quantities are available:

Φ = scatteredfield(sp, ex, ScalarPotentialJump(point_cart))

E = scatteredfield(sp, ex, DisplacementField(point_cart))

Total Fields

For each excitation the total fields in the presence of a given sphere can be determined as:

E  = field(sp, ex, ElectricField(point_cart))

H  = field(sp, ex, MagneticField(point_cart))

FF = field(sp, ex, FarField(point_cart))

For the uniform field excitation, only the electric field as well as the scalar potential can be calculated:

Φ = field(sp, ex, ScalarPotential(point_cart))

Radar Cross Section

To compute the bistatic radar cross section (RCS), the function

σ = rcs(sp, ex, points_cart)

is provided. For the monostatic RCS, the function

σ = rcs(sp, ex)

is provided.

Conversion Between Bases

Methods are provided to convert between Cartesian and spherical coordinates:

point_cart = SphericalScattering.sph2cart.(point_sph)

point_sph  = SphericalScattering.cart2sph.(point_cart)

Converting fields:

F_cart = SphericalScattering.convertSpherical2Cartesian.(F_sph,  point_sph)

F_sph  = SphericalScattering.convertCartesian2Spherical.(F_cart, point_sph)

Plotting Fields

To visualize far-fields and near-fields the functions

patternPoints(;r=1.0, resolution=5)

phiCutPoints(ϕ; r=1.0, resolution=1)

thetaCutPoints(ϑ; r=1.0, resolution=1)

as well as the functions

plotff(F, points_sph; scale="log", normalize=true, type="abs")

plotffcut(F, points; scale="log", normalize=true, format="polar")

are provided (after loading the PlotlyJS package). For more details see the visualization of fields examples.