SphericalScattering.jl

This package provides semi-analytical solutions to the scattering of time-harmonic and static electromagnetic fields as well as time-harmonic acoustic fields from spherical objects (amongst others known as Mie solutions or Mie scattering). To this end, series expansions are evaluated. Special care is taken to obtain accurate solutions down to the static limit.

Note

A time convention of $\mathrm{e}^{\,\mathrm{j}\omega t}$ and SI units are used everywhere.

Note

If you use this software, please cite our JOSS article:

B. Hofmann, P. Respondek, and S. B. Adrian, Sphericalscattering: a Julia package for electromagnetic scattering from spherical objects, Journal of Open Source Software, vol. 8, no. 91, Nov. 2023, doi: 10.21105/joss.05820.

Installation

To install julia, you can follow these instructions. Installing SphericalScattering is done by entering the package manager (enter ] at the julia REPL) and issuing:

pkg> add SphericalScattering

Feature Overview

The following aspects are implemented (✔) and planned (⌛):

object	boundary	electromagnetic excitation
object	boundary	plane wave	el. ring current	mag. ring current	el. dipole	mag. dipole	TE/TM modes	uniform static field	static charge(s)
Spheres
	PEC	✔	✔	✔	✔	✔	✔	✔	⌛
	PMC	⌛	⌛	⌛	⌛	⌛	⌛	⌛	⌛
	dielectric	✔	⌛	⌛	⌛	⌛	⌛	✔	⌛
	multilayer dielectric	⌛	⌛	⌛	⌛	⌛	⌛	✔	⌛
	multilayer dielectric with PEC core	⌛	⌛	⌛	⌛	⌛	⌛	✔	⌛
	dielectric with thin impedance layer	➖	➖	➖	➖	➖	➖	✔	➖
Spheroids
prolate	PEC	⌛	⌛	⌛	⌛	⌛	⌛	⌛	⌛
prolate	PMC	⌛	⌛	⌛	⌛	⌛	⌛	⌛	⌛
oblate	PEC	⌛	⌛	⌛	⌛	⌛	⌛	⌛	⌛
oblate	PMC	⌛	⌛	⌛	⌛	⌛	⌛	⌛	⌛
disc flat oblate spheroid	PEC	⌛	⌛	⌛	⌛	⌛	⌛	⌛	⌛
disc flat oblate spheroid	PMC	⌛	⌛	⌛	⌛	⌛	⌛	⌛	⌛

object	boundary	acoustic excitation
object	boundary	plane wave	monopole
Spheres
	sound-hard	✔	✔
	sound-soft	✔	✔
Spheroids
prolate	sound-hard	✔	✔
prolate	sound-soft	✔	✔
oblate	sound-hard	✔	✔
oblate	sound-soft	✔	✔
disc flat oblate spheroid	sound-hard	✔	✔
disc flat oblate spheroid	sound-soft	✔	✔

Available quantities

The quantities which can be computed for these setups, among them near fields, far fields, potentials, and surface traces, are listed under Quantities. The surface currents of the electromagnetic scatterers are planned (⌛).