Applicability of the Rytov full effective-medium formalism to the physical description and design of resonant metasurfaces

Periodic photonic lattices constitute a fundamental pillar of physics supporting a plethora of scientific concepts and applications. The advent of metamaterials and metastructures is grounded in deep understanding of their properties. Based on the original 1956 formulation by Rytov, it is well known that a photonic lattice with deep subwavelength periodicity can be approximated with a homogeneous space having an effective refractive index. Whereas the attendant effective-medium theory (EMT) commonly used in the literature is based on the zeroth root, the closed-form transcendental equations possess an infinite number of roots. Thus far, these higher-order solutions have been totally ignored; even Rytov himself discarded them and proceeded to approximate solutions for the deep-subwavelength regime. In spite of the fact that the Rytov EMT models an infinite half-space lattice, it is highly relevant to modeling practical thin-film periodic structures with finite thickness as we show. Therefore, here, we establish a theoretical framework to systematically describe subwavelength resonance behavior and to predict the optical response of resonant photonic lattices using the full Rytov solutions. Expeditious results are obtained with direct, new physical insights available for resonant lattice properties. We show that the full Rytov formulation implicitly contains refractive-index solutions pertaining directly to evanescent waves that drive the laterally-propagating Bloch modes foundational to resonant lattice properties. In fact, the resonant reradiated Bloch modes experience wavelength-dependent refractive indices that are solutions of the Rytov expressions. This insight is useful in modeling guided-mode resonant devices including wideband reflectors, bandpass filters, and polarizers.