Band flips and bound-state transitions in leaky-mode photonic lattices

Leaky-mode photonic lattices exhibit intricate resonance effects originating in quasi-guided lateral Bloch modes. Key spectral properties are associated with phase-matched modes at the second (leaky) stop band. One band edge mode suffers radiation loss generating leaky-mode resonance whereas the other band edge mode becomes a bound state in the continuum (BIC). Here, we present analytical and numerical results on the formation and properties of the leaky stop band. We show that the frequency of the leaky-mode resonance band edge, and correspondingly the BIC edge, is determined by superposition of Bragg processes chiefly generated by the first two Fourier harmonics of the spatial modulation. We derive conditions for the band closure and band flip wherein the leaky edge and the bound-state edge transit across the band gap. Our work elucidates fundamental aspects of periodic photonic films and has high relevance to the burgeoning field of metamaterials.