Non-orthogonality and $\kappa$-dependence eccentricity of polarized electromagnetic waves in CPT-even Lorentz violation

We discuss the modified Maxwell action of a $K_{F}$-type Lorentz symmetry breaking theory and present a solution of Maxwell equations derived in the cases of linear and elliptically polarized electromagnetic waves in the vacuum of CPT-even Lorentz violation. We show in this case the Lorentz violation has the effect of changing the amplitude of one component of the magnetic field, while leaving the electric field unchanged, leading to non-orthogonal propagation of eletromagnetic fields and dependence of the eccentricity on $\kappa$-term. Further, we exhibit numerically the consequences of this effect in the cases of linear and elliptical polarization, in particular, the regimes of non-orthogonality of the electromagnetic wave fields and the eccentricity of the elliptical polarization of the magnetic field with dependence on the $\kappa$-term.