  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.
