Monochromatic Electromagnetic Wave Research Articles

Special Relativity in Terms of Hyperbolic Functions with Coupled Parameters in 3+1 Dimensions

This paper presents a method for parameterizing new Lorentz spacetime coordinates based on coupled parameters. The role of symmetry in rapidity in special relativity is explored, and invariance is obtained for new spacetime intervals with respect to the Lorentz transformation. Using the Euler–Hamilton equations, an additional angular rapidity and perpendicular rapidity are obtained, and the Hamiltonian and Lagrangian of a relativistic particle are expanded into rapidity spectra. A so-called passage to the limit is introduced that makes it possible to decompose physical quantities into spectra in terms of elementary functions when explicit decomposition is difficult. New rapidity-dependent Lorentz spacetime coordinates are obtained. The descriptions of particle motion using the old and new Lorentz spacetime coordinates as applied to plane laser pulses are compared in terms of the particle kinetic energy. Based on a classical model of particle motion in the field of a plane monochromatic electromagnetic wave and that of a plane laser pulse, rapidity-dependent spectral decompositions into elementary functions are presented, and the Euler–Hamilton equations are derived as rapidity functions in 3+1 dimensions. The new and old Lorentz spacetime coordinates are compared with the Fermi spacetime coordinates. The proper Lorentz groups SO(1,3) with coupled parameters using the old and new Lorentz spacetime coordinates are also compared. As a special case, the application of Lorentz spacetime coordinates to a relativistic hydrodynamic system with coupled parameters in 1+1 dimensions is demonstrated.

Nonlinearized nonlinear electromagnetic guided waves in a circle cylindrical waveguide filled with nonlinear dielectric medium

We consider a problem of propagation of monochromatic electromagnetic waves in a circle cylindrical waveguide filled with nonlinear dielectric medium. The permittivity of the waveguide is described by the Kerr law, which is one of the most important nonlinear dependence in nonlinear optics. In order to find guided waves we develop an original mathematical approach that allows us to prove existence of infinitely many guided waves. In addition, we prove that only a finite number of the founded nonlinear guided waves have linear counterparts; the others are nonlinearizable solutions. Numerical results are also presented.

Scattering and conversion of electromagnetic and gravitational waves by Reissner-Nordström black holes: The Regge pole description

We investigate the problem of scattering and conversion of monochromatic planar gravitational and electromagnetic waves impinging upon a Reissner-Nordstr\"om black hole using a Regge pole description, i.e., a complex angular momentum approach. For this purpose, we first compute numerically the Regge pole spectrum for various charge-to-mass ratio configurations. We then derive an asymptotic expressions for the lowest Regge poles, and by considering Bohr-Sommerfeld-type quantization conditions, obtain the spectrum of weakly damped quasinormal frequencies from the Regge trajectories. Next, we construct the scattering and conversion amplitudes as well as the total differential cross sections for different processes using both a complex angular momentum representation and a partial wave expansion method. Finally, we provide an analytical approximation of the scattering and conversion cross sections of different processes from asymptotic expressions for the lowest Regge poles and the associated residues based on the correspondence Regge poles, ``surface waves'' propagating close to the photon (graviton) sphere. This allows us to extract the physical interpretation encoded in the partial wave expansions in the high-frequency regime (i.e., in the short-wavelength regime), and to describe semiclassically with very good agreement both black hole glory and a large part of the orbiting oscillations, thus unifying these two phenomena from a purely wave point of view.

Моделирование и расчет параметров процесса взаимодействия электромагнитной волны с единичной металлизированной частицей конденсированной фазы

At present, an important task is to determine the burning rate of energy condensed systems (ECS) with metal additives under non-stationary conditions. At the same time, a promising way to experimentally determine the law of the burning rate is the radio wave microwave method. However, the presence of a significant amount of condensed phase in the combustion products of metallized ECS complicates the tuning of the interference microwave diagnostic method. The article considers the interaction of an incident monochromatic electromagnetic wave with a single particle of the condensed phase in a closed volume without taking into account the influence of the result of the interaction of other particles with the incident wave. A mathematical model has been developed and scattering indicatrices have been obtained for various particle diameters in the range from 10 to 20 micrometers, generated radiation frequencies in the range of 9–15 GHz, and permittivities of condensed-phase particles in the range of 1.6–10. An analysis of the results of a numerical study demonstrates that an increase in the particle size leads to a sharp increase in the intensity of the scattered wave. Changing the frequency of the wave generated by the microwave generator is a priority method for amplifying the intensity of the scattered wave, which makes it possible to detect particles with smaller diameters up to several micrometers.

Modeling of narrow beams of electromagnetic waves with axial symmetry on a plane

A mathematical model of narrow beams of monochromatic electromagnetic waves propagating in vacuum is developed. Beams of electromagnetic waves are constructed with the order of axial symmetry m m( 0,1, 2, ), = K characterized by the beam localization radius Rпуч, the beam narrowness parameter n n( 2), ≥ and the beam attenuation coefficient N N( 2). ≥ The structure of the electric field for a TE-polarized wave beam is studied numerically.

Резонансное туннелирование фотонов в слоистых оптических наноструктурах (метаматериалах)

The conditions of resonant (almost complete) tunneling of photons (plane monochromatic electromagnetic waves) through layered dielectric and metal-dielectric structures are considered. Resonant tunneling occurs at frequencies at which the resonance conditions for the corresponding structures of open resonators are met. For metal-dielectric structures, the possibility of tunneling in the optical range with a strong barrier in the IR range is shown, which can be used to control the transmission of window panes.

Study of character of modulation instability in cyclotron resonance interaction of an electromagnetic wave with a counterpropagating rectilinear electron beam

In this paper, the interaction of a monochromatic electromagnetic wave with a counterpropagating electron beam moving in an axial magnetic field is considered. The purpose of this study is to investigate the conditions for occurrence of modulation instability (MI) in such a system and to determine at which parameters of the incident wave the MI is absolute or convective. Methods. Theoretical analysis of the MI character is carried out by studying the asymptotic form of unstable perturbations using the saddle-point analysis. The analytical results are verified by numerical simulations. Results. Theoretically, the boundary of change in the character of MI on the plane of input signal parameters (amplitude and detuning of the frequency from the cyclotron resonance) is determined. Numerical simulations confirm that as the signal frequency increases, the regime of self-modulation, which corresponds to the absolute MI, is replaced by the stationary single-frequency transmission corresponding to the convective MI. The numerical results coincide with the analytical ones for the system, which is matched at the end. The matching is implemented by smooth increasing of the guiding magnetic field in the region of electron beam injection. Conclusion. Determining the analytical conditions for the implementation of the absolute MI is of practical interest, since the emerging self-modulation can lead to the generation of trains of pulses with the spectrum in the form of frequency combs.

Resonant tunneling of photons in layered optical nanostructures (metamaterials)

The conditions of resonant (almost complete) tunneling of photons (plane monochromatic electromagnetic waves) through layered dielectric and metal-dielectric structures are considered. Resonant tunneling occurs at frequencies at which the resonance conditions for the corresponding structures of open resonators are met. For metal-dielectric structures, the possibility of tunneling in the optical range with a strong barrier in the IR range is shown, which can be used to control the transmission of window panes. Keywords: dielectric permittivity, homogenization, resonant tunneling, plasmons, metal nanoparticles, window panes.

Optical response of dielectric&metal-core/metal-shell nanoparticles: Near electromagnetic field and resonance frequencies

We study the diffraction of a monochromatic electromagnetic plane wave by a dielectric&metal-core/metal-shell nanoparticle surrounded by a dielectric medium. This problem was solved by using generalized Mie’s theory and both the scattering cross section and the square module of the electric field were calculated as a function of shell thickness. Numerically, the first particles studied were gold-core/silver-shell nanoparticles and their inverse configuration. The gold-core/silver-shell particle presented more variation of their optical properties. The second particles were vacuum-core/metal-shell surrounded by vacuum, symmetric configurations. In this case, the dispersive Drude dielectric function for the metal was used, and a comparative study between the positions of the resonance frequencies obtained from quasi-static limit and electrodynamic theory was performed. Thus, consequently the formula obtained from the quasi-static limit can be used to calculate the positions of the resonance frequencies instead of the electrodynamic theory, when the external radius is smaller than 20 nm.

Coupled Domain-Boundary Variational Formulations for Hodge\u2013Helmholtz Operators

We couple the mixed variational problem for the generalized Hodge–Helmholtz or Hodge–Laplace equation posed on a bounded 3D Lipschitz domain with the first-kind boundary integral equations arising from the latter when constant coefficients are assumed in the unbounded complement. Recently developed Calderón projectors for the relevant boundary integral operators are used to perform a symmetric coupling. We prove stability of the coupled problem away from resonant frequencies by establishing a generalized Gårding inequality (T-coercivity). The resulting system of equations describes the scattering of monochromatic electromagnetic waves at a bounded inhomogeneous isotropic body possibly having a “rough” surface. The low-frequency robustness of the potential formulation of Maxwell’s equations makes this model a promising starting point for Galerkin discretization.

Polarization adaptation when receiving a monochromatic electromagnetic wave

Polarization adaptation when receiving a monochromatic electromagnetic wave

Спектрально-угловые характеристики излучения заряженной частицы в поле Редмонда

Based on the solution of the equation of motion of a charge in an electromagnetic field, the classical theory of radiation of a relativistic charged particle linearly accelerated by a high-intensity laser pulse in the presence of a static component of the magnetic field is constructed. Solutions obtained by Kopytov G.F. and Pogorelov A.V., were used to study the spectral-angular characteristics of the radiation of a charged particle in a combination of the field of a plane monochromatic electromagnetic wave and a constant magnetic field, the so-called Redmond field. According to the calculated formulas for the radiation intensity of particles in the Redmond field, graphs of the dependence on the magnitude of the magnetic field, phase and phase-angular distributions are plotted. The Fourier transform of the intensity of the electric field of the radiation and the spectral density of the radiation of the particle in the case of linear polarization of the wave is obtained.

Spectral-angular characteristics of the radiation of a charged particle in the Redmond field

Based on the solution of the equation of motion of a charge in an electromagnetic field, the classical theory of radiation of a relativistic charged particle linearly accelerated by a high-intensity laser pulse in the presence of a static component of the magnetic field is constructed. Solutions obtained by Kopytov G.F. and Pogorelov A.V., were used to study the spectral-angular characteristics of the radiation of a charged particle in a combination of the field of a plane monochromatic electromagnetic wave and a constant magnetic field, the so-called Redmond field. According to the calculated formulas for the radiation intensity of particles in the Redmond field, graphs of the dependence on the magnitude of the magnetic field, phase and phase-angular distributions are plotted. The Fourier transform of the intensity of the electric field of the radiation and the spectral density of the radiation of the particle in the case of linear polarization of the wave is obtained. Keywords: Redmond field, spectral-angular characteristics, charged particle, Lawson-Woodward theorem, superpower laser radiation.

Optical properties of an extended gravitational lens

We continue to study the optical properties of the solar gravitational lens (SGL). The aim is prospective applications of the SGL for imaging purposes. We investigate the solution of Maxwell's equations for the electromagnetic (EM) field, obtained on the background of a static gravitational field of the Sun. We now treat the Sun as an extended body with a gravitational field that can be described using an infinite series of gravitational multipole moments. Studying the propagation of monochromatic EM waves in this extended solar gravitational field, we develop a wave-optical treatment of the SGL that allows us to study the caustics formed in an image plane in the SGL's strong interference region. We investigate the EM field in several important regions, namely i) the area in the inner part of the caustic and close to the optical axis, ii) the region outside the caustic, and iii) the region in the immediate vicinity of the caustic, especially around its cusps and folds. We show that in the first two regions the physical behavior of the EM field may be understood using the method of stationary phase. However, in the immediate vicinity of the caustic the method of stationary phase is inadequate and a wave-optical treatment is necessary. Relying on the angular eikonal method, we develop a new approach to describe the EM field accurately in all regions, including the immediate vicinity of the caustics and especially near the cusps and folds. The method allows us to investigate the EM field in this important region, which is characterized by rapidly oscillating behavior. Our results are new and can be used to describe gravitational lensing by realistic astrophysical objects, such as stars, spiral and elliptical galaxies.

The cylindrical column lenses and reflectors made of transverse an-isotropic plasma and dielectrics and their response to presence of plane electromagnetic waves

In this paper, a long column lens with circular cross section made of two transversely non-isotropic parts (dielectric and plasma ) covered by isotropic dielectric layer, is studied. The response of the mentioned object to presence of plane monochromatic electromagnetic waves will be investigated. The finite element method (FEM) have been used to calculate the field equations and the amplitudes of scattered wave in this research. This structure can be purposefully used as a device to focus electromagnetic wave energy in a specific area that its operation will be discussed by scattering theory. The electromagnetically responses of this structure have been simulated for two modes TE, TM of the incident wave, separately. Since in this lens a plasma region exist, therefore the plasma can be considered as transparent or non-transparent states, with variations of plasma frequency in a fixed incident wave frequency. Here we consider the mentioned states too.

Comparative analysis of exact and approximate solutions of the plane electromagnetic wave scattering from a discrete parabolic reflector made of parallel circular PEC wires

Numerical analysis of the scattering of a plane monochromatic electromagnetic wave from a discrete parabolic reflector made of parallel cylinders (wires) with perfect electric conductivity is carried out in the exact and approximate formulations, the latter neglecting all interactions between the wires. Both the TE and the TM polarizations of the incident field are considered. It is shown that the difference between the exact and approximate solutions strongly depends on the frequency of the incident wave and that the TM-polarized plane wave is focused better by the discrete reflector than the TE-polarized wave. The field in the vicinity of the geometrical focus is investigated. It is found that the focusing ability, oscillating, gradually decreases with frequency. This behavior is in stark contrast to a solid perfectly electrically conducting parabolic reflector.

High-frequency skin effect in a photoionized inert gas plasma

The penetration of a monochromatic electromagnetic wave into the weakly ionised plasma formed by multiphoton ionization of inert gas atoms has been studied. It is shown how the type of dependence of the photoelectron collision frequency on their velocity determines transverse permettivity in plasma. Explicit expressions for the absorption coefficient in inert gases at different probe radiation frequencies are obtained. In the high-frequency skin effect mode, the possibility of the absorption coefficient increasing due to the Ramsauer-Townsend effect has been demonstrated with argon as an example.

Plasma-covered long cylindrical non-isotropic dielectric lenses for targeted control of energy distribution

In this paper, a long column lens with a circular cross section made of two transversely non-isotropic dielectric parts covered by an isotropic plasma layer, is studied. The response of the mentioned object to the presence of plane monochromatic electromagnetic waves will be investigated. The finite element method has been used to calculate the field equations and the amplitudes of scattered waves in this research. This structure can be purposefully used as a device to focus electromagnetic wave energy in a specific area that its operation will be discussed by scattering theory. The electromagnetic responses of this structure have been simulated for two modes TE, TM of the incident wave, separately. Since in this lens a plasma region exists, the plasma can be considered as transparent or non-transparent states, with variations of plasma frequency in a fixed incident wave frequency. Here we consider the mentioned states too.

Method of Boundary Integral Equations in the Problem of Diffraction of a Monochromatic Electromagnetic Wave by a System of Perfectly Conducting and Piecewise Homogeneous Dielectric Objects

We consider the three-dimensional problem of diffraction of a monochromatic electromagnetic wave by a system of objects of various physical nature, including dielectric bodies (domains), perfectly conducting bodies, and perfectly conducting screens. The perfectly conducting bodies may be placed in an exterior medium or immersed into the dielectric domains. In addition, the perfectly conducting screens may reside at the interface of the dielectric domains, being part of each of those. We give a boundary value problem for the Maxwell equations that describes the electromagnetic field under consideration. Integral representations are derived for the electromagnetic field in terms of surface integrals, and the boundary value problem is reduced to a system of boundary integral equations containing weakly and strongly singular surface integrals. The integral equations are written on the dielectric and perfectly conducting parts of the interface between the dielectric domains, on the surfaces of the perfectly conducting bodies, and on the perfectly conducting screens.

Propagation of electromagnetic waves through very thin non-Hermitian slabs

A theoretical model is proposed to study the propagation of monochromatic electromagnetic plane waves through very thin slabs having gain or loss. The analysis is based on solving the differential equations directly and applying the appropriate boundary conditions. The optical response of the slabs is considered in the linear and nonlinear regimes with a Kerr-type nonlinearity. A number of relations between the real and imaginary parts of the dielectric function are derived in order that useful effects related to the non-Hermiticity of the system be presented. The transmission of plane waves through a system consisting of two thin slabs satisfying the condition of Parity-Time symmetry is also considered.