Optics in anisotropic inhomogeneous media and Lagrange geometry

Abstract

In this paper, the equations of motion associated with a Lagrangian inspired by relativistic optics in inhomogeneous moving medium are considered. The model describes optical effects in the inhomogeneous moving medium with special optical properties given by the self-consistent system. When using the metric restricted to the Minkowski manifold, we have established the Euler–Lagrange equations for corresponding geodesics. We have specified the general model to the special case when the metric coefficient [Formula: see text] linearly increases along the direction [Formula: see text]. The exact analytical solutions of the Euler–Lagrange equations have been constructed. The study of the obtained solutions shows that the light ray bends to the axis [Formula: see text] along which the effective refractive index increases.