Three-dimensional crystal of cavities in a 3D photonic band gap crystal

Abstract

We investigate theoretically and numerically the transport of light in a three-dimensional (3D) crystal of cavities inside a 3D inverse woodpile photonic crystal. This class of crystals consists of two perpendicular arrays of pores and has a very broad 3D photonic band gap. An individual point defect is formed by reducing the radius of two intersecting pores. An earlier study revealed that an isolated point defect supports up to five cavity resonances within the band gap of the infinite crystal [1]. We explore light transport in a three-dimensional crystal of such cavities. Our question is what physics we can expect and whether there is an analogy to condensed matter physics. Indeed, inside the band gap light hops from cavity to cavity by evanescent mode coupling. Our freedom in choosing the cavity locations gives us a high level of control over light transport. This makes a crystal of cavities a promising framework for studying Anderson localization [2]. Two-dimensional arrays of coupled cavities [3] are used as lasers [4] and have an application in discrete solitons [5,6]. Hopping transport can be described by an expansion in eigenstates. In this work we have made a quantitative study of the eigenfunctions and resonance frequencies in a finite crystal of cavities.