We reveal extraordinary electromagnetic properties for a general class of uniaxially polarizable media. Depending on parameters, such metamaterials may have a wide range of nontrivial shapes of isofrequency contours including lemniscate, diamond, and multiply connected curves with connectivity number reaching 5. The possibility of the dispersion engineering paves a way to more flexible manipulation of electromagnetic waves. Employing first-principles 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 of capturing all of the second-order spatial dispersion effects.

• Received 27 March 2015
• Revised 6 May 2015

DOI:https://doi.org/10.1103/PhysRevB.92.085107