Light propagation in ( 2+1 )-dimensional electrodynamics: the case of nonlinear constitutive laws

Abstract

We scrutinize the geometrical properties of light propagation inside a hypothetical
nonlinear medium modeled by a fully covariant electromagnetic theory in (2+1)-dimensions.
After setting the local and nonlinear constitutive relations, the phase velocity and the
polarization of the waves are derived and three special cases are analyzed in detail. In
particular, we show that this version of electromagnetism in low dimensions may present
phenomena such as one-way propagation and controlled opacity, among others, for a large
class of dielectric and magneto-electric parameters.