+ Summary
+ When electromagnetic fields are impinging on objects of various
+ kinds, determining the scattered field as a solution to Maxwell’s
+ equations is crucial for many applications. For example, when
+ monitoring the position of an airplane by a radar, the scattering
+ behavior of the airplane plays a pivotal role and, thus, needs to be
+ studied. Analytical approaches, however, to characterize such
+ scattering behavior are rarely known. Some of the few exceptions where
+ at least semi-analytical descriptions are available are metallic or
+ dielectric spherical objects excited by time-harmonic or static fields
+ (Jin,
+ 2015;
+ Ruck
+ et al., 1970). In some applications, these canonical scattering
+ problems are the study subject of interest. In other areas, solutions
+ to the scattering from spherical objects rather serve as a means to
+ verify the correctness of more involved numerical techniques, which
+ allow to analyze the scattering from real-world objects, for instance,
+ via finite element or integral equation methods
+ (Adrian
+ et al., 2021;
+ Harrington,
+ 1993;
+ Jin,
+ 2015;
+ Rao
+ et al., 1982). Hence, semi-analytical descriptions for the
+ scattering from spherical objects facilitate a reproducible and
+ comparable verification of approaches to solve electromagnetic
+ scattering problems.
+
+
+ Statement of need
+ SphericalScattering is a Julia package
+ (Bezanson
+ et al., 2017) providing semi-analytical solutions to the
+ scattering of time-harmonic as well as static electromagnetic fields
+ from spherical objects (including the Mie solutions for plane wave
+ excitations). To this end, series expansions are evaluated with
+ special care to obtain accurate solutions down to the static limit.
+ The series expansions are based on expressing the incident and
+ scattered fields in terms of spherical wave functions such that the
+ boundary conditions can be enforced at interfaces of different
+ materials yielding the expansion coefficients of the spherical wave
+ functions of the scattered field
+ (Jin,
+ 2015;
+ Ruck
+ et al., 1970).
+ Other available implementations have a different focus, that is,
+ specific 2D scenarios are addressed
+ (Blankrot
+ & Heitzinger, 2018), T-matrices are employed for general
+ shaped objects
+ (Egel
+ et al., 2017-09;
+ Art
+ Gower & Deakin, 2018;
+ Parker,
+ 2022;
+ Schebarchov
+ et al., 2021), ensemble averaged waves are obtained
+ (Artur
+ Gower, 2020), spontaneous decay rates of a dipole are studied
+ (Rasskazov
+ et al., 2020), light scattering is considered employing only
+ plane waves as excitations
+ (chillin-capybara,
+ 2022;
+ Ladutenko
+ et al., 2017;
+ Leinonen,
+ 2016;
+ Prahl,
+ 2023;
+ Schäfer,
+ 2023;
+ Walter,
+ 2023;
+ Wu,
+ 2023), or only far-field quantities are computed.
+ In contrast, in SphericalScattering a
+ variety of excitations is available, that is,
+
+
+ plane waves,
+
+
+ fields of electric/magnetic ring currents,
+
+
+ fields of electric/magnetic dipoles,
+
+
+ transverse electric (TE) and transverse magnetic (TM) spherical
+ vector waves, and
+
+
+ uniform static electric fields,
+
+
+ where several parameters including the orientation, direction, or
+ polarization of the sources can be set by the user and are not
+ predefined. The scattered far- and near-fields are then obtained
+ following
+ (Hansen,
+ 1988;
+ Jackson,
+ 1999;
+ Jin,
+ 2015;
+ Jones,
+ 1995;
+ Ruck
+ et al., 1970;
+ Sihvola
+ & Lindell, 1988) for
+
+
+ perfectly electrically conducting (PEC) spheres and
+
+
+ dielectric spheres
+
+
+ all via a unified interface. In consequence,
+ SphericalScattering is a useful (code-)
+ verification tool in the area of electromagnetic scattering for a wide
+ range of scenarios. For this purpose, it has already been employed in
+ scientific publications
+ (Hofmann
+ et al., 2022a,
+ 2023a,
+ 2021,
+ 2022b,
+ 2023b,
+ 2023c,
+ 2023d).
+
+