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Periodic photonic lattices constitute a fundamental pillar of physicssupporting a plethora of scientific concepts and applications. The advent ofmetamaterials and metastructures is grounded in deep understanding of theirproperties. Based on the original 1956 formulation by Rytov, it is well knownthat a photonic lattice with deep subwavelength periodicity can be approximatedwith a homogeneous space having an effective refractive index. Whereas theattendant effective-medium theory (EMT) commonly used in the literature isbased on the zeroth root, the closed-form transcendental equations possess aninfinite number of roots. Thus far, these higher-order solutions have beentotally ignored; even Rytov himself discarded them and proceeded to approximatesolutions for the deep-subwavelength regime. In spite of the fact that theRytov EMT models an infinite half-space lattice, it is highly relevant tomodeling practical thin-film periodic structures with finite thickness as weshow. Therefore, here, we establish a theoretical framework to systematicallydescribe subwavelength resonance behavior and to predict the optical responseof resonant photonic lattices using the full Rytov solutions. Expeditiousresults are obtained with direct, new physical insights available for resonantlattice properties. We show that the full Rytov formulation implicitly containsrefractive-index solutions pertaining directly to evanescent waves that drivethe laterally-propagating Bloch modes foundational to resonant latticeproperties. In fact, the resonant reradiated Bloch modes experiencewavelength-dependent refractive indices that are solutions of the Rytovexpressions. This insight is useful in modeling guided-mode resonant devicesincluding wideband reflectors, bandpass filters, and polarizers.

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