Relative Effects of Fabry-Perot, Mie, and Guided-Mode Resonance in Periodic Photonic Lattice Physics.

We investigate the physical origins of resonance effects in one-dimensional periodic photonic lattices (PhL), focusing on the relative roles of Fabry-Perot (FP), Mie, and guided-mode resonance (GMR) mechanisms. Using rigorous numerical simulations and modal analysis, we demonstrate that the localized field patterns commonly attributed to FP or Mie resonances arise instead from the coherent superposition of guided slab modes. By analyzing both edge-excited and free-space-illuminated configurations, we show that counterpropagating guided modes form Bloch-like standing-wave fields consistent with observed GMR behavior. Lattices composed of Mie-resonant particles reveal that spectral responses are governed primarily by lattice periodicity rather than intrinsic particle resonances, with perfect reflection or transmission emerging independent of the isolated-particle resonance condition. Furthermore, designs incorporating antireflection layers and index-matched substructures suppress FP and Mie contributions while preserving the principal resonance spectra. These results establish that resonant photonic lattice behavior is fundamentally governed by lateral leaky Bloch modes and their coupling to external radiation via GMR, providing a unified framework for understanding and designing metamaterial-based photonic devices.