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arXiv · 2608.18872

A Weyl-type law for surface-localized eigenfunctions of the Maxwell transmission problem

Yan Jiang·Hongyu Liu·Kai Zhang·Haoran Zheng
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Abstract

This work studies surface-localized transmission eigenfunctions for time-harmonic electromagnetic scattering. Prior results on this phenomenon are mostly qualitative, proving existence without quantifying distribution. Here we provide a quantitative analysis for the Maxwell transmission eigenvalue problem, covering both TE and TM modes. We first establish a Weyl asymptotic law for the full counting function, with cubic growth with respect to the radius $R$. We then prove Weyl-type upper and lower bounds for the counting functions restricted to surface-localized modes, and demonstrate that they share the same growth order three. To our knowledge, this is the first quantitative result of its kind, demonstrating that surface-localized eigenfunctions form a non-negligible fraction of the high-frequency spectrum.

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Yan Jiang, Hongyu Liu, Kai Zhang, Haoran Zheng. 2026-08-19. A Weyl-type law for surface-localized eigenfunctions of the Maxwell transmission problem. https://arxiv.org/abs/2608.18872

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