Polyharmonic Representation of the Electromagnetic Field Generated by an Oscillating Particle near a Dispersive Bulk

Mauricio Garcia-Vergara, Guillaume Demésy, André Nicolet and Frédéric Zolla ()
Additional contact information
Mauricio Garcia-Vergara: Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, Av. Universidad 3000, Mexico City 04510, Mexico
Guillaume Demésy: Aix Marseille Univ, CNRS, Centrale Med, Institut Fresnel, Marseille, France
André Nicolet: Aix Marseille Univ, CNRS, Centrale Med, Institut Fresnel, Marseille, France
Frédéric Zolla: Aix Marseille Univ, CNRS, Centrale Med, Institut Fresnel, Marseille, France

Mathematics, 2024, vol. 12, issue 2, 1-46

Abstract: This study introduces a polyharmonic framework for analyzing the electromagnetic (EM) field generated by an oscillating point charge near a dispersive bulk of size comparable to the wavelength under study. We critically evaluate traditional approaches such as Liénard-Wiechert, Landau, and Raimond, and propose a Fourier representation of sources that simplifies numerical implementation and enhances analytical clarity. Our method effectively addresses the limitations of conventional models and is applicable to both relativistic and non-relativistic scenarios. It includes the oscillating point dipole fields, providing a comprehensive understanding of the EM field behavior. The Finite Element Method (FEM) is employed for numerical analysis, demonstrating the method’s adaptability to complex geometries. While offering significant insights, this study acknowledges certain limitations and outlines directions for future research.

Keywords: electromagnetic waves; finite element method; harmonic decomposition; nanophotonics; numerical methods in electrodynamics (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/2/321/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/2/321/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:2:p:321-:d:1321937

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().