Electromagnetic wave propagation inside a material medium: an effective geometry interpretation

We present a method developed to deal with electromagnetic wave propagation inside a material medium that reacts, in general, nonlinearly to the field strength. We work in the context of Maxwellʹs representation of light paths for each case presented. The isotropic case and artificial birefringence caused by an external electric field are analyzed as an application of the formalism and the effective geometry associated to the wave propagation is exhibited.