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In this work, we are concerned with the mathematical modeling of the electromagnetic (EM) scattering by arbitrarily shaped non-magnetic nanoparticles with high refractive indices. When illuminated by visible light, such particles can…
Accelerated charges emit both electromagnetic and gravitational radiation. Classically, it was found that the electromagnetic energy spectrum radiated by an electron in a monochromatic plane wave is proportional to the corresponding…
We present a numerical method for scalar conservation laws in one space dimension. The solution is approximated by local similarity solutions. While many commonly used approaches are based on shocks, the presented method uses rarefaction…
The dynamics of an electron driven by arbitrary plane wave laser radiation is formulated as a relativistically and mathematically exact refraction process based on an exact index of refraction. This reformulation leads to that index as an…
The interaction of an electron with a local static charge distribution (e.g., an atom or molecule) is dominated at large distances by the radial 1/r Coulomb potential. The second order effect comes from the non-central electric dipole…
We show that the known expressions for the force on a point-like dipole are incompatible with the relativistic transformation of force, and in this respect we apply the Lagrangian approach to the derivation of the correct equation for force…
Regardless of the unspecific notions of photons as light complexes, radiation bundles or wave packets, the radiation from a single state transition is at most a single continuous wave train that starts and ends with the transition. The…
Using geometric algebra and calculus to express the laws of electromagnetism we are able to present magnitudes and relations in a gradual way, escalating the number of dimensions. In the one-dimensional case, charge and current densities,…
The multiple colliding laser pulse concept formulated in Ref. [1] is beneficial for achieving an extremely high amplitude of coherent electromagnetic field. Since the topology of electric and magnetic fields oscillating in time of multiple…
4D mathematical models of structurally related (conjugated, entangled, dual) phenomena of dissipation and cumulation of electrical energy (an external source in continuous media) are discussed, accompanied by the formation of…
A coupled pair of waveguides with refractive indices of different signs is considered. It is shown that the gap in the linear wave spectrum closes if these waves are amplitude modulated. To look for solitons as envelopes of exponentially…
Invoking Maxwell's classical electrodynamics in conjunction with expressions for the electromagnetic (EM) energy, momentum, force, and torque, we use a few simple examples to demonstrate the nature of linear and angular momentum exchange…
Using different laser irradiation patterns to modify of silicon surface, it has been demonstrated that, at rather small overlapping between irradiation spots, highly regular laser-induced periodic surface structures (LIPSS) can be produced…
All the Doubly Special Relativity (DSR) models studied in literature so far involve a deformation of the energy conservation rule that forces us to release the hypothesis of the additivity of the energy for composite systems. In view of the…
In the current work we investigate the propagation of electromagnetic waves in the field of gravitational waves. Starting with simple case of an electromagnetic wave travelling in the field of a plane monochromatic gravitational wave we…
We study wave propagation through a one-dimensional array of subwavelength resonators with periodically time-modulated material parameters. Focusing on a high-contrast regime, we use a scattering framework based on Fourier expansions and…
It is shown in linear approximation that in the case of one-dimensional problem of transverse electron waves in a half-infinite slab of homogeneous Maxwellian collisionless plasma with the given boundary field frequency two wave branches of…
CS$_2$ molecules are spatially aligned upon irradiation by intense (1-100 TW cm$^{-2}$), 35 ps pulses of 512 nm or 355 nm light. When both colours are simultaneously present, spatial alignment disappears. We draw analogy with weak-field…
In this paper, a fractional generalization of the wave equation that describes propagation of damped waves is considered. In contrast to the fractional diffusion-wave equation, the fractional wave equation contains fractional derivatives of…
Aggregates immersed in a plasma or radiative environment will have charge distributed over their extended surface. Previous studies have modeled the aggregate charge using the monopole and dipole terms of a multipole expansion, with results…