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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Mauricio Garcia-Vergara & Guillaume Demésy & André Nicolet & Frédéric Zolla, 2024. "Polyharmonic Representation of the Electromagnetic Field Generated by an Oscillating Particle near a Dispersive Bulk," Mathematics, MDPI, vol. 12(2), pages 1-46, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:2:p:321-:d:1321937
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