Related papers: Optics in nonuniform media and Lagrange geometry
The geodesic equations for optical media whose refractive indices have a non-vanishing gradient are developed. It is shown that when those media are optically isotropic, the light paths will be mull geodesics of a spatial metric that is…
The trajectory of light rays propagating through a nonuniformly moving anisotropic medium is determined by considering the Fresnel drag experienced by the wave at each point along the ray. By showing that symmetries in the velocity field…
In this paper we present the distinguished (d-) Riemannian geometry (in the sense of nonlinear connection, Cartan canonical linear connection, together with its d-torsions and d-curvatures) for a possible Lagrangian inspired by optics in…
It is shown that the geometrical optics limit of the Maxwell equations for certain nonlinear media with slow variation along one axis and particular dependence of dielectric constant on the frequency and fields gives rise to the…
A moving dielectric appears to light as an effective gravitational field. At low flow velocities the dielectric acts on light in the same way as a magnetic field acts on a charged matter wave. We develop in detail the geometrical optics of…
We develop a relativistic variational model for a nematic liquid crystal interacting with an electro- magnetic field. The constitutive relation for a general anisotropic uniaxial diamagnetic and dielectric medium is analyzed. We discuss…
Electromagnetism in an inhomogeneous dielectric medium at rest is described using the methods of differential geometry. In contrast to a general relativistic approach the electromagnetic fields are discussed in three-dimensional space only.…
Geometrical optics provides an instructive insight into Brownian motion, ``pushed" into a large-deviations regime by imposed constraints. Here we extend geometrical optics of Brownian motion by accounting for diffusion inhomogeneity in…
Light propagating in a moving medium with refractive index other than unity is subject to light drag. While the light drag effect due to the linear refractive index is often negligibly small, it can be enhanced in materials with a large…
The influence of the relativistic motion of the reference frame on the light reflection law is investigated. The method is based on applying the relativistic aberration affect for three light signals: incident, normal and reflected rays.…
It is known that a relative translational motion between the deflector and the observer affects gravitational lensing. In this paper, a lens equation is obtained to describe such effects on actual lensing observables. Results can be easily…
The deflection of light rays near gravitating objects can be influenced not only by gravity itself but also by the surrounding medium. Analytical studies of such effects are possible within the geometrical optics approximation, where the…
For a Lagrangian system with nonholonomic constraints, we construct extensions of the equations of motion to sets of second-order ordinary differential equations. In the case of a purely kinetic Lagrangian, we investigate the conditions…
Fully describing light propagation in a rotating, anisotropic medium with thermal nonlinearity requires modeling the interplay between nonlinear refraction, birefringence, and the nonlinear group index. Incorporating these factors into a…
Geometrical optics limit of the Maxwell equations for nonlinear media with the Cole-Cole dependence of dielectric function and magnetic permeability on the frequency is considered. It is shown that for media with slow variation along one…
The optical refractive index of a moving regular medium is calculated by using the Lorentz transformation in this note. It is shown that in some velocity region of medium moving relative to the initial frame K, the moving medium may possess…
Light is the richest information retriever for most physical systems, particularly so for astronomy and cosmology, in which gravitation is of paramount importance, and also for solid state defects and metamaterials, in which some effects…
Invariant Lagrangians yield invariant Euler-Lagrange equations, and it was discussed in the literature how to compute those using various local methods. The focus of this paper is on global algebraic differential invariants. In this case…
A novel statistical approach based on the Wigner transform is proposed for the description of partially incoherent optical wave dynamics in nonlinear media. An evolution equation for the Wigner transform is derived from a nonlinear…
The Fermat principle is used to define trajectories in nonhomogenous optical media. The Poincare model of the Lobachevskii geometry is derived. The index of refraction is determined for the light confined in the circular trajectory in the…