Geometrical Approach to Light in Inhomogeneous Media (original) (raw)

Effective electromagnetic geometry

Physical Review D, 2001

We show that the propagation of photons in a nonlinear dielectric medium can be described in terms of a modification of the metric structure of space-time. We solve completely the case in which the dielectric constant ⑀ is an arbitrary function of the electric field ⑀(E). The particular case of no dependence on the field reduces to the Gordon metric.

ELECTROMAGNETIC LIGHT RAYS IN LOCAL DIELECTRICS

The Eleventh Marcel Grossmann Meeting - On Recent Developments in Theoretical and Experimental General Relativity, Gravitation and Relativistic Field Theories - Proceedings of the MG11 Meeting on General Relativity, 2008

An approach to deal with the limit of geometrical optics of electromagnetic waves which propagate in moving nonlinear local dielectric media in the context of Maxwellian electrodynamics is here developed in order to apply to quite general material media. Fresnel equations for the light rays are generically found, and its solutions are intrinsically obtained. The multi-refringence problem is addressed, and no more than four monochromatic polarization modes are found to propagate there.

Differential geometry approach to asymmetric transmission of light

Optics Express

In the last ten years, the technology of differential geometry, ubiquitous in gravitational physics, has found its place in the field of optics. It has been successfully used in the design of optical metamaterials, through a technique now known as "transformation optics". This method, however, only applies for the particular class of metamaterials known as impedance matched, that is, materials whose electric permittivity is equal to their magnetic permeability. In that case, the material may be described by a spacetime metric. In the present work we will introduce a generalization of the geometric methods of transformation optics to situations in which the material is not impedance matched. In such situation, the material-or more precisely, its constitutive tensor-will not be described by a metric only. We bring in a second tensor, with the local symmetries of the Weyl tensor, the "W-tensor". In the geometric optics approximation we show how the properties of the W-tensor are related to the asymmetric transmission of the material. We apply this feature into the design of a particularly interesting set of asymmetric materials. These materials are birefringent when light rays approach the material in a given direction, but behave just like vacuum when the rays have the opposite direction with the appropriate polarization (or, in some cases, independently of the polarization).

On the Electromagnetic Propagation Paths and Wavefronts in the Vicinity of a Refractive Object

Radio Science, 2020

Maxwell's equations are transformed from a Cartesian geometry to a Riemannian geometry. A geodetic path in the Riemannian geometry is defined as the raypath on which the electromagnetic energy efficiently travels through the medium. Consistent with the spatial behavior of the Poynting vector, the metric tensor is required to be functionally dependent on the refractive index of the medium. A symmetric nonorthogonal transformation is introduced, in which the metric is a function of an electromagnetic tension. This so-called refractional tension determines the curvature of the geodetic line. To verify the geodetic propagation paths and wavefronts, a spherical object with a refractive index not equal to one is considered. A full 3-D numerical simulation based on a contrast-source integral equation for the electric field vector is used. These experiments corroborate that the geodesics support the actual wavefronts. This result has consequences for the explanation of the light bending around the Sun. Next to Einstein's gravitational tension there is room for an additional refractional tension. In fact, the total potential interaction energy controls the bending of the light. It is shown that this extended model is in excellent agreement with historical electromagnetic deflection measurements. This result has consequences we will discuss at the end of the paper, namely, the bending of electromagnetic waves around the Sun. The accepted conclusion is that the bending of light passing a massive star, the Sun,

The geometry of induced electromagnetic fields in moving media

arXiv: Classical Physics, 2020

In this manuscript we provide a fully geometric formulation for the induced electromagnetic fields and their corresponding constitutive relations in moving media. To this end, we present the reader with a brief geometric summary to show how vector calculus electromagnetic theory is embedded in the more general language of differential forms. Then, we consider the class of \emph{metric} constitutive relations describing the medium in which electromagnetic fields propagate. We explicitly obtain the components of the induced fields in a moving medium, as seen in the the lab \emph{rest} frame. This allows us to read the expressions for the permitivity, permeability and magnetoelectric matrices for the moving medium which, in turn, can be interpreted as a different physical material from the lab point of view

The Theory of Electrodynamics in a Linear Dielectric

We adopt the continuum limit of a linear, isotropic, homogeneous, transparent, dispersionnegligible dielectric of refractive index n and examine the consequences of the effective speed of light in a stationary dielectric, c/n, for D'Alembert's principle and the Lagrange equations. The principles of dynamics in the dielectric-filled space are then applied to the electromagnetic Lagrangian and we derive equations of motion for the macroscopic fields. A direct derivation of the total energymomentum tensor from the field strength tensor for the electromagnetic field in a dielectric is used to demonstrate the utility of the new theory by resolving the century-old Abraham-Minkowski electromagnetic momentum controversy in a way that preserves the principles of conservation of energy, conservation of linear momentum, and conservation of angular momentum.

Influence of Space-Time Curvature on the Light Propagation

This article is devoted to the problem of light propagation in a space-time which curvature is due not to massive sources but to the electromagnetic field of the wave itself. Some methodological questions are discussed, such as an isotropy of metric, implementation of the Kalutza-Klein model, topology of space-time, etc.

Light propagation in (2+1)-dimensional electrodynamics: the case of linear constitutive laws

Cornell University - arXiv, 2022

In this paper, we turn our attention to light propagation in three-dimensional electrodynamics. More specifically, we investigate the behavior of light rays in a continuous bi-dimensional hypothetical medium living in a three-dimensional ambient spacetime. Relying on a fully covariant approach, we assume that the medium is endowed with a local and linear response tensor which maps field strengths into excitations. In the geometric optics limit, we then obtain the corresponding Fresnel equation and, using well known results from algebraic geometry, we derive the effective optical metric. I.

Dispersion surfaces and light propagation in homogeneous dielectric-magnetic uniaxial medium

Journal of Physics: Conference Series, 2012

We investigated light propagation in a homogeneous medium having double anisotropy (i.e. with anisotropy of both dielectric and magnetic permittivities) and an arbitrary orientation of its optical axis in the plane of incidence. We investigated wave surfaces for the considered medium. We showed that only some groups of surfaces can arise. We investigated the conditions for total independent of polarization reflection and the conditions for total transmission, as well as possibilities of the subject system of serving as: an omnidirectional reflector, a beam splitter and a phase retarder.