API reference

All distances are in meters and frequencies are in hertz. Geometries list regions from the center outward. Each region includes its inner radius and excludes its outer radius; adjacent regions must share a boundary exactly. The final region represents the exterior and must extend to positive infinity.

Materials

Material takes relative permittivity and permeability. Either may be complex for lossy or dispersive material models:

from scatsol import Material

vacuum = Material.vacuum()
dielectric = Material(epsilon_r=2.5, mu_r=1.0)
pec = Material.PEC()

epsilon, mu, and eta return absolute permittivity, permeability, and wave impedance. k(frequency) returns the wavenumber. Material.PEC() creates the perfect electric conductor used for an innermost region.

Material

epsilon property

Calculate the material's real or complex electric permittivity.

Returns:

• epsilon ( float | complex ) –

  electric permittivity.

mu property

Calculate the material's real or complex magnetic permeability.

Returns:

• mu ( float | complex ) –

  magnetic permeability.

is_pec property

Whether this material was created as a perfect electric conductor.

eta property

Calculate the material's electromagnetic impedance.

Returns:

• eta ( float | complex ) –

  electromagnetic impedance.

__init__(epsilon_r=1.0, mu_r=1.0)

Representation of a material with electromagnetic properties.

Parameters:

• epsilon_r (float | complex, default: 1.0 ) –

  relative electric permittivity.

• mu_r (float | complex, default: 1.0 ) –

  relative magnetic permeability.

k(frequency)

Calculate the material's electromagnetic wavenumber.

Parameters:

• frequency ((float, Hz)) –

  frequency.

Returns:

• k ( float | complex ) –

  electromagnetic wavenumber.

vacuum() classmethod

Create a vacuum material.

Returns:

• Material ( Material ) –

  vacuum material.

PEC() classmethod

Create a perfect electric conductor material.

Returns:

• Material ( Material ) –

  perfect electric conductor material.

Cylindrical regions and geometry

The first cylindrical region starts at radius zero. Later regions form concentric annuli; the exterior region ends at infinity.

from scatsol import CylindricalGeometry, CylindricalRegion, Material

geometry = CylindricalGeometry([
    CylindricalRegion(0.0, 0.2, Material(epsilon_r=3.0)),
    CylindricalRegion(0.2, 0.4, Material(epsilon_r=2.0)),
    CylindricalRegion(0.4, float("inf"), Material.vacuum()),
])

CylindricalRegion

__init__(inner_radius, outer_radius, material)

Cylindrical region representation.

Parameters:

• inner_radius (Annotated[float, m]) –

  inner radius of the cylindrical region in meters.

• outer_radius (Annotated[float, m]) –

  outer radius of the cylindrical region in meters.

• material (Material) –

  material of the cylindrical region.

check_within(radius)

Check if a radius is within the region not including the outer radius.

Parameters:

• radius (Annotated[float, m]) –

  radius in meters to check.

Returns:

• bool –

  True if the radius is within the region, False otherwise.

CylindricalGeometry

Representation of a cylindrical geometry.

Attributes:

• regions –

  sequence of cylindrical regions.

Cylindrical solver and solution

The cylindrical solver models a plane wave traveling along +x. Select TM for longitudinal E_z, or TE for longitudinal H_z:

from scatsol import CylindricalSolver, Polarization

solution = CylindricalSolver(geometry, frequency=300e6).solve(
    n=50, polarization=Polarization.TE
)

n is the maximum number of modes requested. The solver may use fewer based on the interface size parameters; solution.n gives the count used. PEC is supported in the innermost region, with finite-material layers around it.

total_field(points) returns (electric, magnetic) complex arrays of shape (N, 3). Input points must have shape (N, 3) in Cartesian x, y, z order. incident_field(points) returns the incident plane-wave fields in the exterior material. Component methods such as e_z(points) and h_y(points) return one-dimensional complex arrays.

CylindricalSolver

solve(n=50, polarization=Polarization.TM)

Solve for up to n cylindrical modes.

CylindricalSolution

e_x(xyz)

Return the x component of the total electric field at xyz.

e_y(xyz)

Return the y component of the total electric field at xyz.

e_z(xyz)

Return the z component of the total electric field at xyz.

h_x(xyz)

Return the x component of the total magnetic field at xyz.

h_y(xyz)

Return the y component of the total magnetic field at xyz.

h_z(xyz)

Return the z component of the total magnetic field at xyz.

Spherical regions and geometry

Spherical regions are concentric shells. The first starts at radius zero, and the exterior region extends to infinity.

from scatsol import Material, SphericalGeometry, SphericalRegion

geometry = SphericalGeometry([
    SphericalRegion(0.0, 1.0, Material(epsilon_r=2.56)),
    SphericalRegion(1.0, float("inf"), Material.vacuum()),
])

SphericalRegion

A homogeneous spherical shell, bounded by two radii.

SphericalGeometry

Concentric spherical regions, ordered from the core to the exterior.

Spherical solver and solution

The spherical solver uses an x-polarized plane wave traveling along +z. It solves both electric and magnetic multipole channels for each order:

from scatsol import SphericalSolver

solution = SphericalSolver(geometry, frequency=300e6).solve(n=50)

n is the maximum multipole order. As for the cylindrical solver, the mode count may be reduced using the interface size parameters. The scattered coefficients are available as solution.an (electric channel) and solution.bn (magnetic channel). There is no Polarization argument because both channels contribute to the returned fields.

The spherical total_field, incident_field, and component methods use the same Cartesian input and output layout as the cylindrical solution. PEC is supported as the innermost spherical region only.

SphericalSolver

Mie solver for any number of concentric spherical material regions.

SphericalSolution

Fields and modal coefficients for concentric spherical regions.