Bounds on Propagation Constants in Dielectric Gratings

Ehsan Faghihifar

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arXiv · 2609.05052

Bounds on Propagation Constants in Dielectric Gratings

Ehsan Faghihifar

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Abstract

We establish analytical bounds on the normalized longitudinal propagation constants $β=k_z/k_0$ of modes in lossless dielectric diffraction gratings. If $ε_{\max}$ denotes the maximum relative permittivity, we show that regular modes ($β^2\in\mathbb{R}$) satisfy $β^2\leε_{\max}$ despite the lack of a scalar dispersion relation. We further show that the so-called ghost modes ($β^2\notin\mathbb{R}$), admitted by the non-Hermitian nature of the associated eigenproblem, satisfy $|\mathrm{Re}(β)|\le\sqrt{ε_{\max}}/2$. Both bounds are obtained directly from the Fourier-series formulation of the fully coupled vectorial eigenproblem.

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Ehsan Faghihifar. 2026-09-04. Bounds on Propagation Constants in Dielectric Gratings. https://arxiv.org/abs/2609.05052

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