Three dimensional Dirac point at k=0 in photonic and phononic systems

TL;DR

This paper demonstrates the existence of three-dimensional Dirac points at the Brillouin zone center in photonic and phononic crystals, revealing their properties and effective medium descriptions.

Contribution

It introduces 3D Dirac points in simple cubic photonic and phononic crystals, showing their formation through accidental degeneracy and effective medium theory mapping.

Findings

3D Dirac point at k=0 in photonic crystal with sixfold degeneracy

4-fold Dirac point in acoustic wave crystal from degeneracy of dipole and monopole modes

Linear dispersion near Dirac points leading to spherical equi-frequency surfaces

Abstract

While "Dirac cone" dispersions can only be meaningfully defined in two dimensional (2D) systems, the notion of a Dirac point can be extended to three dimensional (3D) classical wave systems. We show that a simple cubic photonic crystal composing of core-shell spheres exhibits a 3D Dirac point at the center of the Brillouin zone at a finite frequency. Using effective medium theory, we can map our structure to a zero refractive index material in which the effective permittivity and permeability are simultaneously zero at the Dirac point frequency. The Dirac point is six-fold degenerate and is formed by the accidental degeneracy of electric dipole and magnetic dipole excitations, each with three degrees of freedom. We found that 3D Dirac points at k=0 can also be found in simple cubic acoustic wave crystals, but different from the case in the photonic system, the 3D Dirac point in acoustic wave system is fourfold degenerate, and is formed by the accidental degeneracy of dipole and monopole excitations. Using effective medium theory, we can also describe this acoustic wave system as a material which has both effective mass density and reciprocal of bulk modulus equal to zero at the Dirac point frequency. For both the photonic and phononic systems, a subset of the bands has linear dispersions near the zone center, and they give rise to equi-frequency surfaces that are spheres with radii proportional to (omega-omega_dirac).