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

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.