Nonlocality in uniaxially polarizable media

TL;DR

This paper explores the unique electromagnetic properties of uniaxially polarizable media, revealing complex isofrequency contours and emphasizing the importance of nonlocal permittivity tensors for accurate wave manipulation.

Contribution

It demonstrates that uniaxially polarizable media exhibit nonlocal electromagnetic behavior that cannot be simplified to local parameters, introducing a new set of local parameters to describe these effects.

Findings

Isofrequency contours can have complex shapes like lemniscate and diamond.

Nonlocal permittivity tensors are essential for accurate description.

Introduces quadrupole susceptibility as a local parameter.

Abstract

We reveal extraordinary electromagnetic properties for a general class of uniaxially polarizable media. Depending on parameters, such metamaterials may have wide range of nontrivial shapes of isofrequency contours including lemniscate, diamond and multiply connected curves with connectivity number reaching five. The possibility of the dispersion engineering paves a way to more flexible manipulation of electromagnetic waves. Employing first-principle considerations we prove that uniaxially polarizable media should be described in terms of the nonlocal permittivity tensor which by no means can be reduced to local permittivity and permeability even in the long-wavelength limit. We introduce an alternative set of local material parameters including quadrupole susceptibility capable to capture all of the second-order spatial dispersion effects.