Modelos análogos para a propagação da luz em teorias não lineares do eletromagnetismo

Abstract

This work aims at studying analogous models for the propagation of light in nonlinear theories of electromagnetism. To do this, we first calculate the equations of motion and the momentum-energy tensor of an arbitrary theory dependent on the two electromagnetism invariants, 𝐹 and 𝐺, in both tensorial and vector formalisms. Then, we demonstrate, through two different methods, how to obtain the dispersion relation of electromagnetic waves for these theories.We also calculate the phase velocity, group velocity and refractive index for such theories. We apply the results to the Born-Infeld and Euler-Heisenberg theories. Additionally, we find the phase velocity of a wave in a material medium exhibiting Pockels and Kerr effects. We then propose a formal analogy between the effective metric of the nonlinear theory and the effective metric of the material medium. Furthermore, we show that we can obtain the same analogous result by relating the change in the value of the refractive index due to the presence of electromagnetic fields in both nonlinear theories with the change in the refractive index in the material medium due to the presence of electromagnetic fields. Finally, we apply the obtained results in the construction of analogous models based on Germanium and Silicon.