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We treat operational principles and resulting properties of periodic photonic lattices. These lattices can be fashioned in the lab as 2D or 1D patterned films on substrates or modeled as membrane particle arrays for simplest geometry. Even though the basic periodic element, namely the diffraction grating, has been known for 100+ years, new solutions and applications based on periodic spatial modulations continue to appear. In recent literature, corresponding assemblies and devices are called metamaterials or metasurfaces. Current lithographic technology enables fabrication of spatial modulations on subwavelength scales in one, two, or three dimensions. The resulting diffractive optical elements or metasurfaces may support waveguide modes when designed with proper refractive indices and dimensions. Waveguide modes that are guided or quasi-guided in waveguide gratings experience stopbands and passbands as the light frequency is varied. Associated with these leaky bands, there appear resonant bright channels and non-resonant dark channels in the spectra. The bright state corresponds to a high reflectivity guided-mode resonance (GMR) whereas the dark channel represents a bound state in the continuum (BIC). We review past results placing these physical observations in historical context. The BIC states correspond to symmetry-blocked resonance channels. In earlier work, the BIC was often referenced as the non-leaky band edge. We show theoretical dispersion charts and experimental sampling of those revealing GMR and BIC channels. Along similar lines, recent results show experimental lattice band dynamics of simple resonance systems. Finally, the connection of the classic Rytov effective medium formalism to the GMR/BIC states is presented. We show that all key resonancelattice properties are embodied in Rytov-equivalent homogeneous waveguides. This interesting fact overwhelmingly proves the waveguide character of the lattice systems.
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