Resumo:
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.
