Finite size scaling of the density of states in photonic band gap crystals

Abstract

Photonic crystals are tailored periodic dielectric media that allow for an unprecedented control in the manipulation of light-matter interactions. One of their outstanding features is the realization of a complete photonic band gap that drastically inhibits light propagation in all directions and for all polarizations. A band gap is associated with a complete vanishing of the density of optical states (DOS) in the crystal. As a necessary corollary, it implies a vanishing of the local DOS (LDOS) too, which leads to a complete inhibition of spontaneous emission everywhere inside such a crystal.In our paper, we will present our approach for the DOS in finite support crystals in both 2D and 3D spatial dimensions. We will show the surprising result that the DOS inside the bandgap decreases linearly with size irrespective of the crystal dimensionality as shown in Fig. 1(b) for the example of inverse woodpile crystals that are being pursued in our group [3]. Our work sets design rules for the sizes of photonic bandgap crystals for practical applications in cavity QED and quantum information processing (vacuum noise shielding). It also has the potential of establishing new methods for engineering finite crystals to enhance the suppression of DOS.