Applicability of Rytov’s Full Effective-Medium Formalism to the Physical Description and Design of Resonant Metasurfaces

Abstract

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 Rytov's original 1956 formulation, 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, Rytov's closed-form transcendental equations possess, in principle, 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 Rytov's 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 because of the semi-analytical formulation 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 wavelengthdependent refractive indices that are solutions of Rytov's expressions. This insight is useful in modeling guided-mode resonant devices including wideband reflectors, bandpass filters, and polarizers. For example, the Rytov indices define directly the bandwidth of the resonant reflector and the extent of the bandpass filter sidebands as verified with rigorous simulations. As an additional result, we define a clear transition point between the resonance subwavelength region and the deep-subwavelength region with an analytic formula provided in a special case.

Perfectly-reflecting guided-mode-resonant photonic lattices possessing Mie modal memory

“…The mode loci pertinent to the homogenized lattice are computed with effective medium theory (EMT) and waveguide theory. We apply the full Rytov formalism 24,25 to extract the zero-order EMT (…”

Meta‐Structured Silicon Nanophotonic Polarization Beam Splitter with an Optical Bandwidth of 415 nm

“…The corresponding index tensors can be expressed as: [ 52 ] $$$$\begin{equation} {\tilde{\bm\varepsilon }}_{{\rm{SWG}}}^{ < 100 > } = \left[ { \def\eqcellsep{&}\begin{array}{lll} {n_{\rm{e}}^2}&0&0\\ 0&{n_{\rm{o}}^2}&0\\ 0&0&{n_{\rm{o}}^2} \end{array} } \right] \end{equation}$$$$ $$$$\begin{equation} {\tilde{\bm\varepsilon }}_{{\rm{SWG}}}^{ < 010 > } = \left[ { \def\eqcellsep{&}\begin{array}{lll} {n_{\rm{o}}^2}&0&0\\ 0&{n_{\rm{e}}^2}&0\\ 0&0&{n_{\rm{o}}^2} \end{array} } \right]\end{equation}$$$$where n o denotes the ordinary medium index, and n e denotes the extraordinary medium index. Here, n o and n e can be formulated by applying Rytov's theory: [ 53 ] $$$$\begin{equation}n_{\rm{o}}^2 = {f_{{\rm{SWG}}}}n_{{\rm{Si}}}^2 + \left( {1 - {f_{{\rm{SWG}}}}} \right)n_{{\rm{Si}}{{\rm{O}}_2}}^2\end{equation}$$$$ …”

Physics of resonant optical lattices: experimental leaky bands and symmetry-blocked radiant channels modeled by Rytov’s formalism

“…For subwavelength periodic systems, EMT defines an "equivalent" homogeneous system as experienced by incident electromagnetic radiation. Originated in 1956 by Rytov [43], various approximations to his full formalism have been applied over time in simple analytical form with a strict assumption of "deep-subwavelength" operation [6,17,32]. It comes as a surprise to many that the full Rytov solutions hold in regions where the wavelength and period are not so different; this is the case here.…”

“…As pertinent to the system in Fig. 4(a), we recall that Rytov's solutions with symmetric field distributions in the lattice are expressed by [43,32]…”