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.
