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Bounds on Propagation Constants in Dielectric Gratings
Abstract
We establish analytical bounds on the normalized longitudinal propagation constants β=kz/k0 of modes in lossless dielectric diffraction gratings. If εmax denotes the maximum relative permittivity, we show that regular modes (β2∈ℝ) satisfy β2≤εmax despite the lack of a scalar dispersion relation. We further show that the so-called ghost modes (β2∉ℝ), admitted by the non-Hermitian nature of the associated eigenproblem, satisfy |Re(β)|≤√(εmax)/2. Both bounds are obtained directly from the Fourier-series formulation of the fully coupled vectorial eigenproblem.
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BibTeX
@misc{faghihifar2026bounds,
title = {{Bounds on Propagation Constants in Dielectric Gratings}},
author = {Ehsan Faghihifar},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.05052},
eprint = {2609.05052},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.05052},
}
RIS
TY - UNPB
TI - Bounds on Propagation Constants in Dielectric Gratings
AU - Ehsan Faghihifar
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2609.05052
UR - https://arxiv.org/abs/2609.05052
AB - 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∈ℝ) satisfy β^2≤ε_max despite the lack of a scalar dispersion relation. We further show that the so-called ghost modes (β^2∉ℝ), admitted by the non-Hermitian nature of the associated eigenproblem, satisfy |Re(β)|≤√(ε_max)/2. Both bounds are obtained directly from the Fourier-series formulation of the fully coupled vectorial eigenproblem.
ER -