Related papers: Electromagnetic Wavelets as Hertzian Pulsed Beams …
The representation of solutions of Maxwell's equations as superpositions of scalar wavelets with vector coefficients developed earlier is generalized to wavelets with polarization, which are matrix-valued. The construction proceeds in four…
We study a class of localized solutions of the wave equation, called eigenwavelets, obtained by extending its fundamental solutions to complex spacetime in the sense of hyperfunctions. The imaginary spacetime variables y, which form a…
Point sources in complex spacetime, which generate acoustic and electromagnetic pulsed-beam wavelets, are rigorously defined and computed with a view toward their realization.
A new representation for solutions of Maxwell's equations is derived. Instead of being expanded in plane waves, the solutions are given as linear superpositions of spherical wavelets dynamically adapted to the Maxwell field and…
We present a unified framework that fully represents electromagnetic potentials, fields, and sources in vacuum, based on a reinterpretation of the classical Hertz-potential formalism. In this construction, $\phi$, $A$, $E$, $B$, $\rho$, and…
One set of the Ziolkowski family of exact solutions of the wave equation are shown to represent pulses propagating with momentum smaller than energy/c. This is explicitly demonstrated for special cases by calculating the total…
We study the harmonic analysis of the quadrature mirror filters coming from multiresolution wavelet analysis of compactly supported wavelets. It is known that those of these wavelets that come from third order polynomials are parametrized…
For the first time, complete source distributions for the emission and absorption of acoustic and electromagnetic wavelets are defined and computed, both in spacetime and Fourier space. The biggest surprise is the great simplicity of the…
In this paper, we study electron wavepacket dynamics in electric and magnetic fields. We rigorously derive the semiclassical equations of electron dynamics in electric and magnetic fields. We do it both for free electron and electron in a…
Electromagnetic waves are described by not only polarization ellipses but also cyclically rotating vectors tracing out them. The corresponding fields are respectively directionless steady line fields and directional instantaneous vector…
We investigate the transient electromagnetic field radiated by a pulsed vertical electric dipole above a lossy half-space and identify its time-domain signatures associated with the Zenneck wave. Starting from the classical Sommerfeld…
We present a Parseval tight wavelet frame for the representation and analysis of velocity vector fields of incompressible fluids. Our wavelets have closed form expressions in the frequency and spatial domains, are divergence free in the…
We provide a space domain oriented separation of magnetic fields into parts generated by sources in the exterior and sources in the interior of a given sphere. The separation itself is well-known in geomagnetic modeling, usually in terms of…
In this paper, we study the interactions of electromagnetic waves with a non-dispersive dynamic medium that is temporally dependent. Electromagnetic fields under material time-modulation conserve their momentum but not their energy. We…
Despite the intrinsic coupling between electric and magnetic fields in random stationary light, their polarization properties are not mutually determined. A complete second-order description thus necessitates a joint electromagnetic…
Motivated by previous investigations on the radiative effects of the electric dipoles embedded in structured cavities, localization of electromagnetic waves in two dimensions is studied {\it ab initio} for a system consisting of many…
We construct an electromagnetic field whose scalar potential is a pulsed-beam wavelet Psi (an analytic continuation of a classical Huygens wavelet). The vector potential A is determined up to three complex parameters by requiring that (a)…
Singularities, i.e. places of discontinuities of parameters are extremely general objects appearing in electromagnetic waves and thus are the key to understanding fundamental wave processes. These structures commonly occur in purely…
An exact solution of the homogeneous wave equation, which was found previously, is treated from the point of view of continuous wavelet analysis (CWA). If time is a fixed parameter, the solution represents a new multidimensional mother…
Electric and magnetic Hertz potentials are a formalism for obtaining solutions of Maxwell's equations from solutions of the inhomogeneous wave equation, with polarisation and magnetisation as the sources. We provide an overview of their…