Analytical Modeling of the Admittance Tensor of Periodic Elliptical Meta-Atoms
Abstract
A metasurface is an electrically thin interface that controls the phase, amplitude and polarization of a wave, upon reflection or transmission. Printed on a grounded dielectric substrate and spatially modulated across the aperture, it converts a guided surface wave into a radiated leaky wave, a mechanism used in holographic metasurface antennas. Controlling this conversion requires synthesizing a prescribed distribution of admittance tensors, each derived from the homogenization of a subwavelength unit cell. Many numerical and semi-analytical methods have been proposed to relate the geometry of a meta-atom to the tensor it produces. This paper presents, to the author's knowledge, the first analytical model, restricted to elliptical meta-atoms on a uniform lattice. The Galerkin method is applied directly to the geometry of the patches, without spatial meshing. An affine transformation maps any rotated ellipse onto the unit disk, so that a single formulation covers every configuration. A wideband response takes from minutes to tens of minutes with a periodic full-wave solver, while the proposed model evaluates it in a few tens of milliseconds on the same workstation, roughly three orders of magnitude faster. The predicted admittance agrees with a method-of-moments reference up to the fundamental resonance and captures the guided-mode anomaly of the substrate. Beyond the physical insight it brings, the model is a differentiable function of the geometry, which makes the quasi-real-time design of optimized metasurfaces possible.
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BibTeX
@misc{fromenteze2026analytical,
title = {{Analytical Modeling of the Admittance Tensor of Periodic Elliptical Meta-Atoms}},
author = {Thomas Fromentèze},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.08166},
eprint = {2611.08166},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.08166},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Analytical Modeling of the Admittance Tensor of Periodic Elliptical Meta-Atoms
AU - Thomas Fromentèze
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.08166
UR - https://arxiv.org/abs/2611.08166
AB - A metasurface is an electrically thin interface that controls the phase, amplitude and polarization of a wave, upon reflection or transmission. Printed on a grounded dielectric substrate and spatially modulated across the aperture, it converts a guided surface wave into a radiated leaky wave, a mechanism used in holographic metasurface antennas. Controlling this conversion requires synthesizing a prescribed distribution of admittance tensors, each derived from the homogenization of a subwavelength unit cell. Many numerical and semi-analytical methods have been proposed to relate the geometry of a meta-atom to the tensor it produces. This paper presents, to the author's knowledge, the first analytical model, restricted to elliptical meta-atoms on a uniform lattice. The Galerkin method is applied directly to the geometry of the patches, without spatial meshing. An affine transformation maps any rotated ellipse onto the unit disk, so that a single formulation covers every configuration. A wideband response takes from minutes to tens of minutes with a periodic full-wave solver, while the proposed model evaluates it in a few tens of milliseconds on the same workstation, roughly three orders of magnitude faster. The predicted admittance agrees with a method-of-moments reference up to the fundamental resonance and captures the guided-mode anomaly of the substrate. Beyond the physical insight it brings, the model is a differentiable function of the geometry, which makes the quasi-real-time design of optimized metasurfaces possible.
ER -