High-order bandgaps in one-dimensional photonic crystals

Bandgaps, including high-order ones, of one-dimensional photonic crystals are analysed. Accurate analytical expressions for band edges for both s and p polarized light are derived. As a consequence, the conditions for bandgap closing are obtained in a simple analytical form. The derivation is based on a perturbative expansion of the dispersion equation using a new parameter which remains small around the band edges of all physically feasible one-dimensional photonic crystals.