Related papers: Potential-based formalism for electrodynamics of m…
The potential concept that is successful in classical electrodynamics should also be applicable to the nonlinear electromagnetic forces acting on matter. The obvious method of determining these potentials should be provided by Helmholtz's…
We set up the Maxwell's equations and the corresponding classical wave equations for the electromagnetic waves which together with the generating source, a traveling oscillatory charge of zero rest mass, comprise a particle traveling in the…
An approximate solution of the Dyson equation related to a stochastic Helmholtz equation, which describes the acoustic dynamics of a three-dimensional isotropic random medium with elastic tensor fluctuating in space, is obtained in the…
The classical theory of electromagnetism is based on Maxwell's macroscopic equations, an energy postulate, a momentum postulate, and a generalized form of the Lorentz law of force. These seven postulates constitute the foundation of a…
Spatially dispersive (also known as non-local) electromagnetic media are considered where the parameters defining the permittivity relation vary periodically. Maxwell's equations give rise to a difference equation corresponding to the…
We analyze the stability of Maxwell equations in bounded domains taking into account electric and magnetization effects. Well-posedness of the model is obtained by means of semigroup theory. A passitivity assumption guarantees the…
The multipole expansion is a key tool in the study of light-matter interactions. All the information about the radiation of and coupling to electromagnetic fields of a given charge-density distribution is condensed into few numbers: The…
We give the Lagrangian formulation of a generic non-minimally extended Einstein-Maxwell theory with an action that is linear in the curvature and quadratic in the electromagnetic field. We derive the coupled field equations by a first order…
It is proved that the space of differential forms with weak exterior and co-derivative, is compactly embedded into the space of square integrable differential forms. Mixed boundary conditions on weak Lipschitz domains are considered.…
A boundary integral equation formulation is presented for the electromagnetic transmission problem where an incident electromagnetic wave is scattered from a bounded dielectric object. The formulation provides unique solutions for all…
We introduce a new notion of "matrix potential" to nonlinear optical systems. In terms of a matrix potential $g$, we present a gauge field theoretic formulation of the Maxwell-Bloch equation that provides a semiclassical description of the…
Complex formalism of Riemann - Silberstein - Majorana - Oppenheimer in Maxwell electrodynamics is extended to the case of arbitrary pseudo-Riemannian space - time in accordance with the tetrad recipe of Tetrode - Weyl - Fock - Ivanenko. In…
These notes contain a rapid overview of the methods and results obtained in the field of propagation of waves in disordered media. The case of Schr\"odinger and Helmholtz equations are considered that describe respectively electrons in…
We study one of the interesting properties of the electromagnetic wave propagation in the curved Schwarzschild background spacetime in the framework of general relativity (GR). The electromagnetic wave equation has been derived from vacuum…
A self-consistent theory for the classical description of the interaction of light and matter at the nano-scale is presented, which takes into account spatial dispersion. Up to now, the Maxwell equations in nanostructured materials with…
We present an extension of the canonical coupled mode theory of electromagnetic waves to the case of pulses and spatio-temporal perturbations in complex media. Unlike previous attempts to derive such a model, our approach involves no…
The electromagnetic theory is considered in the framework of the generally covariant approach, that is applied to the analysis of electromagnetism in noninertial coordinate and frame systems. The special-relat\-ivistic formulation of…
We propose some modification of Maxwell's equations describing mediums which electric and magnetic properties are changed essentially after interaction with outer electromagnetic field. We show for such mediums that electromagnetic waves…
We explore the propagation and transformation of electromagnetic waves through spatially homogeneous yet smoothly time-dependent media within the framework of classical electrodynamics. By modelling the smooth transition, occurring during a…
This paper deals with the Klein-Gordon-Maxwell system in a bounded spatial domain. We study the existence of solutions having a specific form, namely standing waves in equilibrium with a purely electrostatic field. We prescribe Dirichlet…