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

Abstract

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.