Minkowski-Space Modeling of Hyperbolic Lenses
Abstract
The extreme anisotropy of hyperbolic materials enables extreme wave confinement, but it is also associated with an inherent misalignment between phase and energy flow, which complicates device modeling and design. Here we introduce a Minkowski-space approach to describe hyperbolic wave propagation, showing that this complexity is geometric rather than physical. By embedding anisotropy into an effective Lorentzian metric, we establish a rational design framework for hyperbolic interfaces and lenses, and analytically derive their transfer function and resolution limits, enabling ultra-large numerical apertures and deep sub-diffraction focusing. We validate our theory with the design and full-wave modeling of a planar van der Waals polaritonic lens operating in the mid-infrared frequency range.
Cite
@article{arxiv.2603.14166,
title = {Minkowski-Space Modeling of Hyperbolic Lenses},
author = {Enrico Maria Renzi and Simon Yves and Sveinung Erland and Diana Strickland and Eitan Bachmat and Andrea Alù},
journal= {arXiv preprint arXiv:2603.14166},
year = {2026}
}