Band dynamics of leaky-mode photonic lattices

External waves incident on a periodic metamaterial lattice couple to it at frequencies corresponding to the leaky, or second, stop band. The resulting leaky-mode or guided-mode resonance effects are useful in device design and spectral manipulation. Indeed, some of the most important properties of metamaterials are associated with the leaky stopband. Thus motivated, we treat the band dynamics of leaky-mode resonant photonic lattices. In particular, properties of the band gap and conditions for band closure and band flips under multimode conditions are quantified. For a symmetric lattice, the nonleaky band edge hosts a bound state in the continuum whose band transition reverses the modal symmetry of the band edge modes. The leaky edge supports a guided-mode resonant radiative peak that also undergoes band flip upon band closure. We analyze a canonical one-dimensional lattice with exact numerical methods and a semianalytical formulation modified to handle the multimodal case. We show that the band dynamics of the various leaky modes present differ appreciably with, for example, the band associated with the fundamental TE₀ and the first higher order TE₁ modes closing at differing values of dielectric-constant modulation. We compare the thin-film lattice with an infinite lattice and find an approximate analytical condition for band closure that we verify with rigorous computations.