Effective medium theory for photonic pseudospin-1/2 system

TL;DR

This paper develops an effective medium theory for photonic pseudospin-1/2 systems with Dirac points at the Brillouin zone center, revealing unique electromagnetic properties and enabling prediction of edge states and exotic phenomena.

Contribution

It introduces a novel effective medium approach for photonic pseudospin-1/2 systems with Dirac points at the zone center, including the design of magneto-optical complex conjugate metamaterials.

Findings

Effective permittivity approaches zero at the Dirac point.

Determinant of effective permeability vanishes at the Dirac point.

Edge state dispersion can be predicted using effective parameters.

Abstract

Photonic pseudospin-1/2 systems, which exhibit Dirac cone dispersion at Brillouin zone corners in analogy to graphene, have been extensively studied in recent years. However, it is known that a linear band crossing of two bands cannot emerge at the center of Brillouin zone in a two-dimensional photonic system respecting time reversal symmetry. Using a square lattice of elliptical magneto-optical cylinders, we constructed an unpaired Dirac point at the Brillouin zone center as the intersection of the second and third bands corresponding to the monopole and dipole excitations. Effective medium theory can be applied to the two linearly crossed bands with the effective constitutive parameters numerically calculated using the boundary effective medium approach. It is shown that only the effective permittivity approaches zero while the determinant of the nonzero effective permeability vanishes at the Dirac point frequency, showing a different behavior from the double-zero index metamaterials obtained from the pseudospin-1 triply degenerate points for time reversal symmetric systems. Exotic phenomena, such as the Klein tunneling and Zitterbewegung, in the pseudospin-1/2 system can be well understood from the effective medium description. When the Dirac point is lifted, the edge state dispersion near the $\Gamma$ point can be accurately predicted by the effective constitutive parameters. We also further realized magneto-optical complex conjugate metamaterials for a wide frequency range by introducing a particular type of non-Hermittian perturbations which make the two linear bands coalescence to form exceptional points at the real frequency.