Abstract

To gain important insights into the photonic band problem, we investigate an analytically exactly soluble model that consists of a two-dimensional periodic array of infinitely long rectangular dielectric cylinders. Our aims are (1) to have a model that exhibits a band gap that opens up in all directions in the Brillouin zone, (2) to identify some of the favorable conditions for creating sizable photonic band gaps, and (3) to set benchmarks to test numerical methods for calculating the band structures of more complicated analytically insoluble problems. We show that this model is capable of having a common gap simultaneously for the transverse-electric and transverse-magnetic waves irrespective of the direction of propagation within a two-dimensional plane. Because of the large number of free parameters in this model we have optimized only one of the parameters. We find that this gap can exist for a minimum refractive index ratio of about 3.4. We believe that by optimizing all the available parameters, a substantially lower value can be found.

© 1990 Optical Society of America