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Main Authors: Fikioris, George, Koutserimpas, Theodoros T., Glytsis, Elias N.
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2603.28962
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author Fikioris, George
Koutserimpas, Theodoros T.
Glytsis, Elias N.
author_facet Fikioris, George
Koutserimpas, Theodoros T.
Glytsis, Elias N.
contents We develop a general framework for the electrostatic analysis of point charges in multilayer planar structures with arbitrary layer thicknesses and material parameters. Starting from a Hankel-transform analysis, we derive alternative representations of the solution and establish a Stokes-like formulation based on ``generalized reflection coefficients,'' yielding a systematic and physically transparent treatment of multilayer media. This approach extends classical image theory to parameter regimes in which the conventional image-charge series (which has an infinite number of terms) diverges. The formulation applies to arbitrary permittivity values, including negative permittivities, where overscreening effects and plasmon-resonant conditions may occur. In these regimes, we show that the boundary-value problem no longer has a unique solution because homogeneous (source-free) modes appear; and we derive Cauchy-principal-value integral representations for the particular solution. We also introduce an asymptotic ``phantom-image'' method that replaces a divergent infinite image series by a finite set of effective sources, thus providing a computationally efficient approximation in large-reflection regimes. These results furnish both practical computational tools and additional mathematical insight into the structure of electrostatic image theory in layered media.
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publishDate 2026
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spellingShingle A general framework for the study of electrostatic point charges in multilayer planar structures
Fikioris, George
Koutserimpas, Theodoros T.
Glytsis, Elias N.
Applied Physics
We develop a general framework for the electrostatic analysis of point charges in multilayer planar structures with arbitrary layer thicknesses and material parameters. Starting from a Hankel-transform analysis, we derive alternative representations of the solution and establish a Stokes-like formulation based on ``generalized reflection coefficients,'' yielding a systematic and physically transparent treatment of multilayer media. This approach extends classical image theory to parameter regimes in which the conventional image-charge series (which has an infinite number of terms) diverges. The formulation applies to arbitrary permittivity values, including negative permittivities, where overscreening effects and plasmon-resonant conditions may occur. In these regimes, we show that the boundary-value problem no longer has a unique solution because homogeneous (source-free) modes appear; and we derive Cauchy-principal-value integral representations for the particular solution. We also introduce an asymptotic ``phantom-image'' method that replaces a divergent infinite image series by a finite set of effective sources, thus providing a computationally efficient approximation in large-reflection regimes. These results furnish both practical computational tools and additional mathematical insight into the structure of electrostatic image theory in layered media.
title A general framework for the study of electrostatic point charges in multilayer planar structures
topic Applied Physics
url https://arxiv.org/abs/2603.28962