Counterintuitive properties of two-dimensional photonic crystal structures

This study presents a numerical study of square and hexagonal lattices of cylindrical solid rods and air holes over a large range of air-filling fractions. This work demonstrates quantitatively how the fundamental band gaps of these structures depend on the air-filling fraction for different dielectrics, and shows that changing the index contrast or air-filling factor (AFF) of a given structure often has unexpected effects on the band gap. These findings indicate that the widespread belief that increasing the index contrast always widens the primary band gap and decreases its exponential attenuation length is incorrect. Surprisingly, for some AFFs, the primary band gap may shrink or even virtually disappear as the index of refraction contrast is increased. In particular, a change in dielectric strength can cause a complete change in the shape or inflection of the band gap width and exponential attenuation length vs. AFF curves.