Multirefringence phenomena in 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 ...

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.

Physics Letters B, 2000

Working on the approximation of low frequency, we present the light cone conditions for a class of theories constructed with the two gauge invariants of the Maxwell field without making use of average over polarization states. Different polarization states are thus identified describing birefringence phenomena. We make an application of the formalism to the case of Euler-Heisenberg effective Lagrangian and well know results are obtained.

The relativistic transform of electromagnetic fields an inductions in a nonlinear medium is studied theoretically, within the framework of classical electrodynamics. A covariant formulation of the electrodynamics of nonlinear media is presented. The Oerenkov radiation process is treated as an example in the rest frame of the interacting electron ; it is found that in that case the linear refractive index of the dielectric medium becomes anisotropic and exhibits a singularity at the usual Oerenkov radiation angle. This theoretical formulation is particularly relevant to relativistic nonlinear media such as free-electron lasers and astrophysical plasmas, and to the such experiments as the probing of magnetic materials with spin-polarized beams. In particular, the spatial symmetries of a given medium, which determine most of its linear and nonlinear electromagnetic properties through group theory, are not conserved by the Lorentz transform (space-time symmetry), therefore giving rise to phenomena such as relativistic magnetic phase-transitions.

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.

2003

The limits of linear electrodynamics are reviewed, and possible directions of nonlinear extension are explored. The central theme is that the qualitative character of the empirical successes of quantum electrodynamics must be used as a guide for understanding the nature of the nonlinearity of electrodynamics at the subatomic level. Some established theories of nonlinear electrodynamics, namely, those of Mie, Born and Infeld are presented in the language of the modern geometrical and topological methods of mathematical physics. The manner by which spacetime curvature and topology can affect electromagnetism is also reviewed. Finally, the phenomena of nonlinear optics are reviewed as a possible guide to building one's intuition regarding the process of extending electrodynamics into nonlinearity in a manner that is consistent with the qualitative and empirical results of quantum electrodynamics.

We consider a sub-wavelength periodic layered medium whose slabs are filled by arbitrary linear metamaterials and standard nonlinear Kerr media and we show that the homogenized medium behaves as a Kerr medium whose parameters can assume values not available in standard materials. Exploiting such a parameter availability, we focus on the situation where the linear relative dielectric permittivity is very small thus allowing the observation of the extreme nonlinear regime where the nonlinear polarization is comparable with or even greater than the linear part of the overall dielectric response. The behavior of the electromagnetic field in the extreme nonlinear regime is very peculiar and characterized by novel features as, for example, the transverse power flow reversing. In order to probe the novel regime, we consider a class of fields (transverse magnetic nonlinear guided waves) admitting full analytical description and we show that these waves are allowed to propagate even in media with ǫ < 0 and µ > 0 since the nonlinear polarization produces a positive overall effective permittivity. The considered nonlinear waves exhibit, in addition to the mentioned features, a number of interesting properties like hyper-focusing induced by the phase difference between the field components.

2006

Some of the basic notions of nonlinear optics are summarized and then applied to the case of the Dirac vacuum, as described by the Heisenberg-Euler effective one-loop Lagrangian. The theoretical and experimental basis for the appearance of nonlinear optical phenomena, such as the Kerr effect, Cotton-Mouton effect, and four-wave mixing are discussed. Further effects due to more exotic assumptions on

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.

In this paper, we outline a novel class of materials, called metamaterials, with negative refractive index and a high degree of nonlinearity. A brief summary is given on the basic theory of optics to show how this condition arrives for metamaterials to be designed into an antenna with split-ring-resonator (SRR). An example is given on the modeling of such SRR-based metamaterials. On a continuum Hamiltonian, a Klein-Gordon equation was derived which gave rise to both dark and bright solitons that showed interesting behavior against nondimensional time, even to the extent of revealing bi-and tri-breathers.