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In the physical description of photonic lattices, leaky-mode resonance and bound states in the continuum are central concepts. Understanding of their existence conditions and dependence on lattice parameters is of fundamental interest. Primary leaky-wave effects are associated with the second stop band at the photonic lattice Γ point. The pertinent band gap is defined by the frequency difference between the leaky-mode band edge and the bound-state edge. This paper address the polarization properties of the band gaps resident in laterally periodic one-dimensional photonic lattices. We show that the band gaps pertinent to TM and TE leaky modes exhibit significantly differentiated evolution as the lattice parameters vary. This is because the TM band gap is governed by a surface effect due to the discontinuity of the dielectric constant at the interfaces of the photonic lattice as well as by a Bragg effect due to the periodic in-plane dielectric constant modulation. We find that when the lattice is thin (thick), the surface (Bragg) effect dominates the Bragg (surface) effect in the formation of the TM band. This leads to complex TM band dynamics with multiple band closures possible under parametric variation. In complete contrast, the TE band gap is governed only by the Bragg effect thus exhibiting simpler band dynamics. This research elucidates the important effect of polarization on resonant leaky-mode band dynamics whose explanation has heretofore not been available. 

The 1D canonical model is rich in properties and conceptually transparent, with all the main conclusions being applicable to 2D metasurfaces and periodic photonic slabs. We explain the operative physical mechanisms grounded in lateral leaky Bloch modes. We summarize the band dynamics of the leaky stopband. With several examples, we demonstrate that Mie scattering is not causative in resonant reflection. Illustrated applications include a wideband reflector at infrared bands as well as resonant reflectors with triangular profiles. We quantify the improved efficiency of a silicon reflector operating in the visible region relative to loss reduction as realizable with sample hydrogenation. A resonant polarizer with record performance is presented.