Light propagation in non-linear electrodynamics (original) (raw)

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

Cornell University - arXiv, 2022

We scrutinize the geometrical properties of light propagation inside a nonlinear medium modeled by a fully covariant electromagnetic theory in 2 + 1-dimensions. After setting the nonlinear constitutive relations, the phase velocity and the polarization of waves are derived and three special cases are analyzed in details. In spite of the dimensional reduction, our model still presents phenomena like one-way propagation, controlled opacity among others for a large class of dielectric and magneto-electric parameters. I.

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.

Effects of nonlinear vacuum electrodynamics on the polarization plane of light

Physical Review D

We consider the Plebański class of nonlinear theories of vacuum electrodynamics, i.e., Lagrangian theories that are Lorentz invariant and gauge invariant. Our main goal is to derive the transport law of the polarization plane in such a theory, on an unspecified general-relativistic spacetime and with an unspecified electromagnetic background field. To that end we start out from an approximateplane-harmonic-wave ansatz that takes the generation of higher harmonics into account. By this ansatz, the electromagnetic field is written as an asymptotic series with respect to a parameter α, where the limit α → 0 corresponds to sending the frequency to infinity. We demonstrate that by solving the generalized Maxwell equations to zeroth and first order with respect to α one gets a unique transport law for the polarization plane along each light ray. We exemplify the general results with the Born-Infeld theory.

Geometrical aspects of light propagation in nonlinear electrodynamics

Physical Review D, 2000

We analyze the propagation of light in the context of nonlinear electrodynamics, as it occurs in modified QED vacua. We show that the corresponding characteristic equation can be described in terms of a modification of the effective geometry of the underlying spacetime structure. We present the general form for this effective geometry and exhibit some new consequences that result from such approach.

Multirefringence phenomena in nonlinear electrodynamics

Physical Review D, 2013

Wave propagation in nonlinear theories of the electromagnetism described by Lagrangian densities dependent upon its two local invariants LðF; GÞ is revisited. On the light of the recent findings in metamaterials, it is here shown that trirefringence is also a possible phenomenon to occur in the realm of such nonlinear theories. A specific model exhibiting this effect is investigated in terms of both phase and group velocities. It is claimed that wave propagation in some well known nonlinear models for spin-one fields, like QED and QCD in certain regimes, may exhibit trirefringence.

Dispersion properties, nonlinear waves and birefringence in classical nonlinear electrodynamics

Journal of Physics Communications, 2020

Using the very basic physics principles, we have studied the implications of quantum corrections to classical electrodynamics and the propagation of electromagnetic waves and pulses. The initial nonlinear wave equation for the electromagnetic vector potential is solved perturbatively about the known exact plane wave solution in both the case of a polarized vacuum without external field, as well as when a constant magnetic field is applied. A nonlinear wave equation with nonzero convective part for the (relatively) slowly varying amplitude of the first-order perturbation has been derived. This equation governs the propagation of electromagnetic waves with a reduced speed of light, where the reduction is roughly proportional to the intensity of the initial pumping plane wave. A system of coupled nonlinear wave equations for the two slowly varying amplitudes of the first-order perturbation, which describe the two polarization states, has been obtained for the case of constant magnetic ...

Maxwell Optics: II. An Exact Formalism

2002

We present a formalism for light optics starting with the Maxwell equations and casting them into an exact matrix form taking into account the spatial and temporal variations of the permittivity and permeability. This 8times88 \times 88times8 matrix representation is used to construct the optical Hamiltonian. This has a close analogy with the algebraic structure of the Dirac equation, enabling the use of the rich machinery of the Dirac electron theory. We get interesting wavelength-dependent contributions which can not be obtained in any of the traditional approaches.

Classical electrodynamics and the quantum nature of light

Journal of Physics A: Mathematical and General, 1997

A review of old inconsistencies of Classical Electrodynamics (CED) and of some new ideas that solve them is presented. Problems with causality violating solutions of the wave equation and of the electron equation of motion, and problems with the non-integrable singularity of its self-field energy tensor are well known. The correct interpretation of the two (advanced and retarded) Lienard-Wiechert solutions are in terms of creation and annihilation of particles in classical physics. They are both retarded solutions. Previous work on the short distance limit of CED of a spinless point electron are based on a faulty assumption which causes the well known inconsistencies of the theory: a diverging self-energy (the non-integrable singularity of its self-field energy tensor) and a causalityviolating third order equation of motion (the Lorentz-Dirac equation). The correct assumption fixes these problems without any change in the Maxwell's equations and let exposed, in the zero-distance limit, the discrete nature of light: the flux of energy from a point charge is discrete in time. CED cannot have a true equation of motion but only an effective one, as a consequence of the intrinsic meaning of the Faraday-Maxwell concept of field that does not correspond to the classical description of photon exchange, but only to the smearing of its effects in the space around the charge. This, in varied degrees, is transferred to QED and to other field theories that are based on the same concept of fields as space-smeared interactions.

Causal structure and birefringence in nonlinear electrodynamics

Modern Physics Letters A, 2015

We investigate the causal structure of general nonlinear electrodynamics and determine which Lagrangians generate an effective metric conformal to Minkowski. We also prove that there is only one analytic nonlinear electrodynamics not presenting birefringence.