Gaussian beam propagation in a Lorentz-violating vacuum in the presence of a semi-transparent mirror

Abstract In this paper we study the propagation of structured optical scalar beams in a Lorentz-violating (LV) vacuum parametrized by constant 4-vector $u^{\mu}$ and presence semi-transparent mirror. The two bosonic degrees freedom electromagnetic field can be described LV extension massless theory, whose part is characterized term $(u \cdot \partial \phi ) ^{2}$. mirror at surface $\Sigma$ modelled delta-type potential Lagrange density for field, i.e. $\lambda \delta (\Sigma ^{2}$, where parameter $\lambda$ controls degree transparency Using Green's function techniques, investigate Gaussian beam which perpendicular to direction particular choices background 4-vector: parallel direction. To quantify effects introduce fidelity as measurement closeness propagated distribution with respect that conventional vacuum. absence ($\lambda = 0$) found close one, hence are quite small. However mirror, there regions drops zero, thus implying could clearly differentiated from Within paraxial approximation determine analytically upon Rayleigh range, radius beam, Gouy phase curvature wavefronts. We discuss possible scenarios our results apply, using optically transparent multiferroic materials, offer unprecedented opportunities tailor propagation, well simulate an