Photonic band structure and defects in one and two dimensions

Abstract

We present an experimental and numerical study of electromagnetic wave propagation in one-dimensional (1D) and two-dimensional (2D) systems composed of periodic arrays of dielectric scatterers. We demonstrate that there are regions of frequency for which the waves are exponentially attenuated for all propagation directions. These regions correspond to band gaps in the calculated band structure, and such systems are termed photonic band-gap (PBG) structures. Removal of a single scatterer from a PBG structure produces a highly localized defect mode, for which the energy density decays exponentially away from the defect origin. Energy-density measurements of defect modes are presented. The experiments were conducted at 6–20 GHz, but we suggest that they may be scaled to infrared frequencies. Analytic and numerical solutions for the band structure and the defect states in 1D structures are derived. Applications of 2D PBG structures are briefly discussed.