https://doi.org/10.1140/epjp/s13360-020-00117-0
Regular Article
On the reflection, diffraction and refraction of a spherical wave of parallel polarization by a sphere of electrically long radius
, Athens, Greece
Received:
17
September
2019
Accepted:
12
December
2019
Published online:
10
February
2020
A novel mathematical approach is proposed for the analysis of the reflection, diffraction and refraction of spherical waves from curved material interfaces. As a paradigm, this approach is applied to the radiation of a vertical electric dipole over an electrically homogenous sphere. The material of the sphere can be dielectric or conducting. The radius of the sphere is assumed to be much greater than the wavelength in its less dense exterior. The formulation is developed for any height of the dipole above the sphere and for any radial distance of the point of observation from the center of the sphere. Novel expansions are applied to the integral representations of the resulting fields. It is shown that contributions to the value of the fields can be produced either from stationary-phase points of the integrands that are generated by such expansions or from any of the two strings of poles of these integrands. Contributions from rapidly converging residue series, as opposed to those coming from stationary-phase points, correspond to wave trajectories containing a curved path in addition to rectilinear paths. For the sake of demonstration, approximate analytical formulas for computation are derived for a number of select cases. The method yields leading-order approximations for the reflected and refracted fields. The affinity with the reflection from a planar interface is analysed.
This paper is dedicated to the memory of my father Athanassios Houdzoumis.
The original online version of this article was revised: “In formula (5.18), last line, inside the radical it should be k2r, instead of k2b. In formula (5.91), in the first term on the right-hand side, the last index of Φ should be +, not +/-. In the legend of Fig. 19, the integration should be Ι2,3, not l2,3 (uppercase I, instead of lowercase L). In the middle of p.99 instead of "as shown is the Fig. 25", it should be read "as shown in Fig. 25”.
A correction to this article is available online at https://doi.org/10.1140/epjp/s13360-023-04587-w.
Copyright comment corrected publication 2023
Copyright comment Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
© Società Italiana di Fisica (SIF) and Springer-Verlag GmbH Germany, part of Springer Nature 2020. corrected publication 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
