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

Abstract

We scrutinize the geometrical properties of light propagation inside a nonlinear medium modeled by a fully covariant electromagnetic theory in 2 + 1-dimensions. After setting the nonlinear constitutive relations, the phase velocity and the polarization of waves are derived and three special cases are analyzed in details. In spite of the dimensional reduction, our model still presents phenomena like one-way propagation, controlled opacity among others for a large class of dielectric and magneto-electric parameters.I.

Dimensional reduction of the Dirac theory

“…and the resulting (2 + 1)-dimensional equations coincide with equations ( 31) and (32). The algebraic background of this discussion as well as its generalization to arbitrary dimensions will be the topic of future research.…”

“…its eigenspaces corresponding to 1 or −1 are exactly the subspaces spanned by the ↑ and ↓ spinor components, respectively. Accordingly, equations ( 31) and (32) and equations ( 19) and ( 20) are just different expressions (in terms of algebraic objects of different orders, 2 and 4, respectively) of the same couple of (2 + 1)-dimensional Dirac equations.…”

“…There are two possible approaches to dimensional reduction. The first and most common one consists in formulating a lower dimensional version of the theory in 3 + 1 dimensions, characterized by the same ab initio properties of the starting point, as long as they are allowed by the new dimensionality [26][27][28][29][30][31][32]. An alternative approach is represented by the method of descent.…”