Möbius Reparametrization of Multiport-Network Models of PIN-Diode-Programmable Metasurfaces for Accurate Low-Order Neumann Approximations
Abstract
Accurate models of programmable metasurfaces based on multiport-network theory (MNT) account for mutual coupling (MC) through a configuration-dependent matrix inversion. The latter's high computational cost during gradient-based optimization (GBO) can be alleviated via a finite-order Neumann approximation. We show that the accuracy of this approximation depends strongly on the (tacitly) chosen MNT parametrization. For 1-bit-programmable meta-elements (e.g., meta-elements based on PIN diodes), we identify a closed-form Möbius reparametrization that depends only on the meta-element's two load states and requires neither training data nor numerical optimization. For an experimentally estimated proxy MNT model of a fabricated 96-element 19-GHz dynamic metasurface antenna with strong MC, a second-order Neumann approximation with our reparametrization achieves forward and control-gradient accuracies of 21.68 and 21.70 dB, respectively. Relative to the full proxy MNT, it reduces the runtime of a combined forward and control-gradient evaluation by a third and the saved-tensor memory by a factor of ten. In a prototypical GBO problem of end-to-end optimization for DMA-based scene classification, it achieves 94.97% test accuracy vs. 95.57% with the full model. We further note that MC-strength metrics and MC-unaware benchmarks should be parametrization-invariant, motivating, for instance, definitions based on the best directly fitted zeroth-order model.
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BibTeX
@misc{hougne2026möbius,
title = {{Möbius Reparametrization of Multiport-Network Models of PIN-Diode-Programmable Metasurfaces for Accurate Low-Order Neumann Approximations}},
author = {Philipp del Hougne},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.37557},
eprint = {2609.37557},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37557},
}
RIS
TY - UNPB
TI - Möbius Reparametrization of Multiport-Network Models of PIN-Diode-Programmable Metasurfaces for Accurate Low-Order Neumann Approximations
AU - Philipp del Hougne
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.37557
UR - https://arxiv.org/abs/2609.37557
AB - Accurate models of programmable metasurfaces based on multiport-network theory (MNT) account for mutual coupling (MC) through a configuration-dependent matrix inversion. The latter's high computational cost during gradient-based optimization (GBO) can be alleviated via a finite-order Neumann approximation. We show that the accuracy of this approximation depends strongly on the (tacitly) chosen MNT parametrization. For 1-bit-programmable meta-elements (e.g., meta-elements based on PIN diodes), we identify a closed-form Möbius reparametrization that depends only on the meta-element's two load states and requires neither training data nor numerical optimization. For an experimentally estimated proxy MNT model of a fabricated 96-element 19-GHz dynamic metasurface antenna with strong MC, a second-order Neumann approximation with our reparametrization achieves forward and control-gradient accuracies of 21.68 and 21.70 dB, respectively. Relative to the full proxy MNT, it reduces the runtime of a combined forward and control-gradient evaluation by a third and the saved-tensor memory by a factor of ten. In a prototypical GBO problem of end-to-end optimization for DMA-based scene classification, it achieves 94.97% test accuracy vs. 95.57% with the full model. We further note that MC-strength metrics and MC-unaware benchmarks should be parametrization-invariant, motivating, for instance, definitions based on the best directly fitted zeroth-order model.
ER -