Related papers: Nonradiating sources of Maxwell's equations
This paper offers an extensive exploration of nonradiating sources for the two- and three-dimensional biharmonic wave equations. Various equivalent characterizations are derived to reveal the nature of a nonradiating source. Additionally,…
In this work, we discuss theoretical findings on the common feature describing nonradiating sources, based on equivalent sources from which it is possible to derive cloaking devices and anapole mode conditions. Starting from the…
Nonradiating sources are nontrivial charge-current distributions that do not generate fields outside the source domain. The pursuit of their possible existence has fascinated several generations of physicists and triggered developments in…
The goal of this paper is to sketch a broader outline of the mathematical structures present in the Nonlinear Maxwell Theory in continuation of work presented in my previous articles. In particular, I display new types of both dynamic and…
The complete dynamic multipole expansion of electromagnetic sources contains more types of multipole terms than it is conventionally perceived. The toroidal multipoles are one of the examples of such contributions that have been widely…
A new relativistic invariant version of nonlinear Maxwell equations is offerred. Some properties of these equations are considered.
A connection between classical non-radiating sources and free-particle wave equations in quantum mechanics is rigorously made. It is proven that free-particle wave equations for all spins have currents which can be defined which are…
Single- and multi-valued solutions of homogeneous Maxwell equations in vacuum are considered, with ''sources'' formed by the (point- or string-like) singularities of the field strengths and, generally, irreducible to any delta-functions'…
The Maxwell theory on non-commutative spaces has been considered. The non-linear equations of electromagnetic fields on non-commutative spaces were obtained in the compact spin-tensor (quaternion) form. It was shown that the plane…
This paper is concerned with non-radiating elastic sources in inhomogeneous elastic media. We demonstrate that the value of non-radiating elastic sources must vanish at convex corners of their support, provided the sources exhibit H\"older…
The notion of ``radiating'' and ``non-radiating'' current sources in classical electrodynamics plays an important role in calculations of direct and inverse electromagnetic scattering problems. Such a decomposition of the current is central…
This paper provides a view of Maxwell's equations from the perspective of complex variables. The study is made through complex differential forms and the Hodge star operator in $\mathbb{C}^2$ with respect to the Euclidean and the Minkowski…
In this paper, we study the inverse source problem for the biharmonic wave equation. Mathematically, we characterize the radiating sources and non-radiating sources at a fixed wavenumber. We show that a general source can be decomposed into…
This paper presents a brief review of the newly developed \emph{Extended Electrodynamics}. The relativistic and non-relativistic approaches to the extension of Maxwell equations are considered briefly, and the further study is carried out…
Radiation field and channel of energy method have become important tools in the study of nonlinear wave equations in recent years. In this work we give basic theory of radiation fields of free waves in the energy sub-critical case. We also…
This paper presents a fast and robust numerical method for reconstructing point-like sources in the time-harmonic Maxwell's equations given Cauchy data at a fixed frequency. This is an electromagnetic inverse source problem with broad…
In this work, we study the inverse source problem of a fixed frequency for the Navier's equation. We investigate that nonradiating external forces. If the support of such a force has a convex or non-convex corner or edge on their boundary,…
In this work we give a few explicit formulas regarding the radiation fields of linear free waves. We then apply these formulas on the channel of energy theory. We characterize all the radial weakly non-radiative solutions in all dimensions…
A full characterization of nonclassical space-time dependent correlations of radiation is formulated in terms of normally and time-ordered field correlation functions. It describes not only the properties of initially prepared multimode…
We begin by reviewing the derivation of generalized Maxwell equations from an operational definition of the electromagnetic field and the most basic notions of what constitutes a dynamical field theory. These equations encompass the…