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Periodic arrays of resonant dielectric nano- or microstructures provide perfect reflection across spectral bands whose extent is controllable by design. At resonance, the array yields this result even in a single subwavelength layer fashioned as a membrane or residing on a substrate. The resonance effect, known as guided-mode resonance, is basic to modulated films that are periodic in one dimension (1D) or in two dimensions (2D). It has been known for 40 years that these remarkable effects arise as incident light couples to leaky Bloch-type waveguide modes that propagate laterally while radiating energy. Perfect reflection by periodic lattices derives from the particle assembly and not from constituent particle resonance. We show that perfect reflection is independent of lattice particle shape in the sense that it arises for all particle shapes. The resonance wavelength of the Bloch-mode-mediated zero-order reflectance is primarily controlled by the period for a given lattice. This is because the period has direct, dominant impact on the homogenized effective-medium refractive index of the lattice that controls the effective mode index experienced by the mode generating the resonance. In recent years, the field of metamaterials has blossomed with a flood of attendant publications. A significant fraction of this output is focused on reflectors with claims that local Fabry-Perot or Mie resonance causes perfect reflection with the leaky Bloch-mode viewpoint ignored. In this paper, we advance key points showing the essentiality of lateral leaky Bloch modes while laying bare the shortcomings of the local mode explanations. The state of attendant technology with related applications is summarized. The take-home message is that it is the assembly of particles that delivers all the important effects including perfect reflection. 

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 one-dimensional 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. 

Polarizers serve many application fields such as imaging, display technology, and telecommunications. Focusing on the visible spectral region, we provide the design and fabrication of compact high-efficiency resonant polarizers in the crystalline silicon-on-quartz material system. We experimentally verify the improved efficiency attained by a cascaded dual-module polarizer assembled with building blocks of elemental subwavelength grating structures. We obtain a measured extinction ratio (ER) of $\sim <\#comment/>3000$in a 2 mm thick stacked prototype device across a bandwidth of $\sim <\#comment/>110\mathrm{n}\mathrm{m}$in the 570–680 nm spectral domain. The ridge width of the constituent nanograting is $\sim <\#comment/>84\mathrm{n}\mathrm{m}$. Computed results show a high ER in spite of the lossy nature of crystalline silicon in the visible region, enabling cascaded metasurfaces while preserving high transmission. 

The 1D canonical model is rich in properties and conceptually transparent, with all the main conclusions being applicable to 2D metasurfaces and periodic photonic slabs. We explain the operative physical mechanisms grounded in lateral leaky Bloch modes. We summarize the band dynamics of the leaky stopband. With several examples, we demonstrate that Mie scattering is not causative in resonant reflection. Illustrated applications include a wideband reflector at infrared bands as well as resonant reflectors with triangular profiles. We quantify the improved efficiency of a silicon reflector operating in the visible region relative to loss reduction as realizable with sample hydrogenation. A resonant polarizer with record performance is presented. 

Key principles and applications of guided-mode resonant photonic lattices were presented in one-hour-long plenary lecture in Reykjavik, Iceland.