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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2603.28962 |
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| _version_ | 1866918418875154432 |
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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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_28962 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| 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 |