Optics in anisotropic inhomogeneous media and Lagrange geometry

Abstract

n 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 γ linearly increases along the direction Z. 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 Z along which the effective refractive index increases.