second-order Bragg condition was satisfied. Later, in 1979, Vincent and Neviere numerically demonstrated the existence of a nonleaky edge pertinent to symmetric grating designs while introducing asymmetry to the grating profile resulted in leaky radiating modes at both band edges. [4] Ding and Magnusson manipulated the separation of the nondegenerate leaky resonances associated with asymmetric profiles to engineer the resonant spectral response of periodic films. [5] Experimentally, the nonleaky edge, and thus BIC, was revealed in 1998 by imposing asymmetry on an otherwise symmetric periodic structure by variation in the angle of incidence. [6] Thus, optical BICs are grounded in confined (nonleaky) modes with an infinite lifetime above the light line in the dispersion diagram of periodic structures. Well established symmetry-protected BICs with exact zero resonance bandwidth (true BIC) reside at the Γ point of the band diagram based on the symmetry incompatibility between the asymmetric standing waves inside the structure and symmetric outgoing waves. [7][8][9][10][11][12] In addition, it has been shown both theoretically and experimentally that off-Γ BIC, with nearzero resonance linewidth (quasi-BIC or asymptotic BIC) can be obtained at specific incident angles in periodic structures. [13][14][15] Moreover, quasi-BICs at the Γ point were reported for specific physical parameters of nanostructures. [16] These nearly zero resonance linewidths possess quasiembedded eigenvalues which cause coupling to the radiated waves.Whereas there have been extensive studies conducted on metamaterial devices with a single spatial periodicity, [17][18][19][20][21][22][23] there is less research on resonance elements containing multiple spatial periodic layers. Unquestionably, there are additional design dimensions to be exploited with such architectures as any multiperiodic construct will operate on available bound modes differently than a single periodicity. Thus, there are scientific and practical reasons to explore attendant device designs and corresponding spectral response. Past related work includes demonstration that properly designed dually corrugated waveguides support unidirectional output radiation. [24] Similar elements were advanced as solutions to improve the efficiency and stability of second-order surface emitting laser diodes via substrate radiation suppression. [24,25] In 2014, a unidirectional coupler for surface plasmon polaritons was proposed and Properties of photonic devices fashioned with dual-grating metamaterials are reported. Enclosed by dual periodic regions, laterally propagating Bloch modes undergo radiative scattering and leaky-mode resonance whose properties differ markedly from those with single periodicity. The resonance signatures are sensitively controlled by the relative parameters of the periodic regions. In particular, if they are physically identical and separated by a half-wavelength, there ensues a bound state in the continuum (BIC) with extremely narrow resonance linewidth. On varying the...

No abstract

No abstract

Resonant periodic nanostructures provide perfect reflection across small or large spectral bandwidths depending on the choice of materials and design parameters. This effect has been known for decades, observed theoretically and experimentally via onedimensional and two-dimensional structures commonly known as resonant gratings, metamaterials, and metasurfaces. The physical cause of this extraordinary phenomenon is guided-mode resonance mediated by lateral Bloch modes excited by evanescent diffraction orders in the subwavelength regime. In recent years, hundreds of papers have declared Fabry-Perot or Mie resonance to be basis of the perfect reflection possessed by periodic metasurfaces. Treating a simple one-dimensional cylindrical-rod lattice, here we show clearly and unambiguously that Mie resonance does not cause perfect reflection. In fact, the spectral placement of the Bloch-mode-mediated zero-order reflectance is primarily controlled by the lattice period by way of its direct effect on the homogenized effective-medium refractive index of the lattice. In general, perfect reflection appears away from Mie resonance. However, when the lateral leaky-mode field profiles approach the isolated-particle Mie field profiles, the resonance locus tends towards the Mie resonance wavelength. The fact that the lattice fields "remember" the isolated particle fields is referred here as "Mie modal memory." On erasure of the Mie memory by an index-matched sublayer, we show that perfect reflection survives with the resonance locus approaching the homogenized effective-medium waveguide locus. The results presented here will aid in clarifying the physical basis of general resonant photonic lattices.

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.