Related papers: Unified matrix-vector wave equation, reciprocity a…
Exact space-time propagator for the wave (second-order in time) equation in a layered system, made up of a layer sandwiched between two other different semi-infinite layers, is obtained by means of the multiple scattering theory (MST)…
We analyze a homogenization limit for the linear wave equation of second order. The spatial operator is assumed to be of divergence form with an oscillatory coefficient matrix $a^\varepsilon$ that is periodic with characteristic length…
In this article, we discard the bra-ket notation and its correlative definitions, given by Paul Dirac. The quantum states are only described by the wave functions. The fundamental concepts and definitions in quantum mechanics is simplified.…
In this paper, we consider the problem of the scattering of in-plane waves at an interface between a homogeneous medium and a metamaterial. The relevant eigenmodes in the two regions are calculated by solving a recently described non…
Modes generally provide an economical description of waves, reducing complicated wave functions to finite numbers of mode amplitudes, as in propagating fiber modes and ideal laser beams. But finding a corresponding mode description for…
Accurate and efficient prediction of three-dimensional (3D) fields in wave interactions with large, complex-shaped objects is essential for applications in electromagnetic computation, computer graphics, optical metrology, and freeform…
We study wave propagation phenomena modelled in the frequency domain by the Helmholtz equation in heterogeneous media with focus on media with discontinuous, highly oscillating wave speed. We restrict to problems with spherical symmetry and…
In general, the relativistic wave equation considered to mathematically describe the so-called Majorana particle is the Dirac equation with a real Lorentz scalar potential plus the so-called Majorana condition. Certainly, depending on the…
Long-distance transmission of energy by waves is a key mechanism for many natural processes. It becomes possible when the inhomogeneous medium is arranged in such a manner that it enables a specific type of waves to propagate with virtually…
In this paper we review the results of the author on the theory of scalar and vector wave scattering by small bodies of an arbitrary shape with the emphasis on practical applicability of the formulas obtained and on the mathematical rigor…
The scattering of electromagnetic waves by three--dimensional periodic structures is important for many problems of crucial scientific and engineering interest. Due to the complexity and three-dimensional nature of these waves, the fast,…
Stationary potential scattering admits a formulation in terms of the quantum dynamics generated by a non-Hermitian effective Hamiltonian. We use this formulation to give a proof of the reciprocity theorem in two and three dimensions that…
We develop a model for the reflection and transmission of plane waves by an isotropic layer sandwiched between two uniaxial crystals of arbitrary orientation. In the laboratory frame, reflection and transmission coefficients corresponding…
We describe a generalized formalism, addressing the fundamental problem of reflection and transmission of complex optical waves at a plane dielectric interface. Our formalism involves the application of generalized operator matrices to the…
We describe traveling waves in a basic model for three-dimensional water-wave dynamics in the weakly nonlinear long-wave regime. Small solutions that are periodic in the direction of translation (or orthogonal to it) form an…
Properties of six-component electromagnetic field solutions of a matrix form of the Maxwell equations, analogous to the four-component solutions of the Dirac equation, are described. It is shown that the six-component equation, including…
The one dimensional wave equation serves as a basic model for imaging modalities such as seismic which utilize acoustic data reflected back from a layered medium. In 1955 Peterson et al. described a single scattering approximation for the…
Backflow, or retropropagation, is a counterintuitive phenomenon whereby for a forward-propagating wave the energy locally propagates backward. In the context of backflow, physically most interesting are the so-called unidirectional waves,…
A new idea for iterative solution of the Helmholtz equation is presented. We show that the iteration which we denote WaveHoltz and which filters the solution to the wave equation with harmonic data evolved over one period, corresponds to a…
Wave transport in a media with slow spatial gradient of its characteristics is found to exhibit a universal wave pattern ("gradient marker") in a vicinity of the maxima/minima of the gradient. The pattern is common for optics, quantum…