Linear Electromagnetic Waves Research Articles

Self-consistent interaction of linear gravitational and electromagnetic waves in non-magnetized plasma

This paper explores the hybridization of linear metric perturbations with linear electromagnetic (EM) perturbations in non-magnetized plasma for a general background metric. The local wave properties are derived from first principles for inhomogeneous plasma, without assuming any symmetries of the background metric. First, we derive the effective (“oscillation-center”) Hamiltonian that governs the average dynamics of plasma particles in a prescribed quasimonochromatic wave that involves metric perturbations and EM fields simultaneously. Then, using this Hamiltonian, we derive the backreaction of plasma particles on the wave itself and obtain gauge-invariant equations that describe the resulting self-consistent gravito-electromagnetic (GEM) waves in a plasma. The transverse tensor modes of gravitational waves are found to have no interaction with the plasma and the EM modes in the geometrical-optics limit. However, for longitudinal GEM modes with large values of the refraction index, the interplay between gravitational and EM interactions in plasma can have a strong effect. In particular, the dispersion relation of the Jeans mode is significantly affected by electrostatic interactions. As a spin-off, our calculation also provides an alternative resolution of the so-called Jeans swindle.

Application of a Virtual Magnetic Dipoles in Antenna Array to Increase the Direction Finding Accuracy

The article discusses the method of forming a virtual antenna array based on magnetic dipoles. To test the effectiveness of the formation of a virtual antenna array, a simulation of an unmanned aerial vehicle with a directionfinding complex of four vector antenna elements was carried out. To perform direction finding, two methods are considered ‒ based on the electric field and magnetic. On the basis of the study, it was found that the use of direction finding based on magnetic dipoles can significantly improve the stability and accuracy of the bearing for both linear and elliptical electromagnetic waves. The article presents the main mathematical expressions that are used to determine the characteristics of the direction finding, as well as the dependence of the bearings in the studied frequency range.

Theory of reflectionless scattering modes

We develop the theory of a special type of scattering state in which a set of asymptotic channels are chosen as inputs and the complementary set as outputs, and there is zero reflection back into the input channels. In general an infinite number of such solutions exist at discrete complex frequencies. Our results apply to linear electromagnetic and acoustic wave scattering and also to quantum scattering, in all dimensions, for arbitrary geometries including scatterers in free space, and for any choice of the input/output sets. We refer to such a state as reflection-zero (R-zero) when it occurs off the real-frequency axis and as an Reflectionless Scattering Mode (RSM) when it is tuned to a real frequency as a steady-state solution. Such reflectionless behavior requires a specific monochromatic input wavefront, given by the eigenvector of a filtered scattering matrix with eigenvalue zero. Steady-state RSMs may be realized by index tuning which do not break flux conservation or by gain-loss tuning. RSMs of flux-conserving cavities are bidirectional while those of non-flux-conserving cavities are generically unidirectional. Cavities with ${\cal PT}$-symmetry have unidirectional R-zeros in complex-conjugate pairs, implying that reflectionless states naturally arise at real frequencies for small gain-loss parameter but move into the complex-frequency plane after a spontaneous ${\cal PT}$-breaking transition. Numerical examples of RSMs are given for one-dimensional cavities with and without gain/loss, a ${\cal PT}$ cavity, a two-dimensional multiwaveguide junction, and a two-dimensional deformed dielectric cavity in free space. We outline and implement a general technique for solving such problems, which shows promise for designing photonic structures which are perfectly impedance-matched for specific inputs, or can perfectly convert inputs from one set of modes to a complementary set.

Linear and nonlinear electromagnetic waves in modulated honeycomb media

AbstractWave dynamics in topological materials has been widely studied recently. A striking feature is the existence of robust and chiral wave propagations that have potential applications in many fields. A common way to realize such wave patterns is to utilize Dirac points, which carry topological indices and is supported by the symmetries of the media. In this work, we investigate these phenomena in photonic media. Starting with Maxwell's equations with a honeycomb material weight as well as the nonlinear Kerr effect, we first prove the existence of Dirac points in the dispersion surfaces of transverse electric and magnetic Maxwell operators under very general assumptions of the material weight. Our assumptions on the material weight are almost the minimal requirements to ensure the existence of Dirac points in a general hexagonal photonic crystal. We then derive the associated wave packet dynamics in the scenario where the honeycomb structure is weakly modulated. It turns out the reduced envelope equation is generally a two‐dimensional nonlinear Dirac equation with a spatially varying mass. By studying the reduced envelope equation with a domain‐wall‐like mass term, we realize the subtle wave motions, which are chiral and immune to local defects. The underlying mechanism is the existence of topologically protected linear line modes, also referred to as edge states. However, we show that these robust linear modes do not survive with nonlinearity. We demonstrate the existence of nonlinear line modes, which can propagate in the nonlinear media based on high‐accuracy numerical computations. Moreover, we also report a new type of nonlinear modes, which are localized in both directions.

A nonlinear least squares framework for periodic grating identification with a high–order perturbation of surfaces implementation

The scattering of linear electromagnetic waves by a layered structure is a central model in many problems of engineering interest. In this contribution, we focus on the interaction of visible and near–visible radiation with periodic structures on the micron or nanometer scales which are relevant for many applications in nanoplasmonics. The fabrication of such structures is extremely difficult and costly, and even the most sophisticated laboratories have difficulty measuring the dimensions of gratings they have constructed. We present a new, extremely rapid and robust, identification algorithm for providing precisely this information. It is built upon a Nonlinear Least Squares framework, and implemented with a High–Order Perturbation of Surfaces methodology which is orders of magnitude faster than volumetric solvers, while outperforming surface methods (such as Boundary Integral Methods) for the geometries we consider here. In addition to a full derivation and specification of the algorithm, we also support our claims with a number of illustrative simulations.

Modification of transfer-matrix method for electromagnetic waves in layered superconductor in presence of dc magnetic field

In the present paper, we modify the transfer-matrix method to study the dissipation-free transition of electromagnetic waves of terahertz range through a plate of layered superconductor embedded in the dielectric environment in the presence of external direct current (dc) magnetic field. In this work, we сonsider TM-polarized electromagnetic waves. The setup is arranged in such a way that the dielectric and superconducting layers in the plate are perpendicular to its interface, and the external magnetic field is directed along the plate and parallel to the layers. We consider the case of a weak external dc field at which magnetic vortices do not penetrate the plate. Due to the nonlinearity of the Josephson plasma formed in the layered superconductor, the dc magnetic field penetrates non-uniformly into the plate and affects the electromagnetic wave. Hence, the magnitude of the external dc magnetic field can be used as a variable parameter to tune various phenomena associated with the propagation of an electromagnetic waves in layered superconductors. In the presence of the external homogeneous dc magnetic field, linear electromagnetic waves in the layered superconductor turn out to be non-exponential. Therefore we cannot directly apply the transfer matrix method, in which the amplitudes of the corresponding exponents are compared. However, in the present paper, it is shown that for a sufficiently thick plate, the matrices describing the wave transfer through the plate can be introduced. The analytical expressions for these matrices are derived explicitly in terms of special Legendre functions. The obtained transfer-matrices can be used for the further study of the wave transfer through the layered superconductor in the presence of an external dc magnetic field.

Tunneling ionization of atoms and ions in a linear electromagnetic wave and a constant magnetic field and the “imaginary time” method

The tunneling ionization of atoms and negative ions in an intense linearly polarized laser field and a constant uniform magnetic field is discussed in the quasiclassical theory framework. We use the “imaginary time” method, where tunneling is described by the classical equations of motion but with purely imaginary “time” to derive the extremal subbarrier trajectory of the photoelectron. This allows to obtain simple analytical expressions for ionization rates in the tunneling regime for an arbitrary angle between a laser beam and a constant magnetic field accounting for the Coulomb interaction of the photoelectron with the atomic core. The resonance case, when the frequency of a monochromatic electromagnetic wave and the cyclotron frequency are equal, is also considered. The limits of weak and strong magnetic fields and the expressions for the barrier width and the emission angle of photoelectrons are discussed. It is shown that a magnetic field in the presence of a linear electromagnetic wave increases the barrier width and thus decreases the ionization probability, i.e., stabilizes the bound level.

Linear Analyses of Langmuir and EM Waves in Relativistic Hot Plasmas**Supported by the National Natural Science Foundation of China under Grant Nos. 11064005 and 51460020, and the financial support provided by the Key Subject of Atomic and Molecular Physics in Jiangxi Province (2011-1015).

The linear Langmuir and electromagnetic (EM) waves in relativistic hot plasmas are discussed, and the dispersion relations are obtained based on the covariant Maxwell’s and fluid equations. When kBT/mc2 ˃ 1, the effective mass of electrons will be increased obviously. As the results, many other influences are induced, such as the decrease of the plasmas frequency and the critical frequency, the reduction of the electron sound velocity and the electrons’ oscillation velocity, and so on. Numerical results show that these influences can affect the dispersion relations of Langmuir and EM waves seriously even in linear regime.

Quick calculation of Luneberg lens scattering signature

The paper focuses on solving the problem of diffraction of a linear polarization electromagnetic wave on multilayer bodies of a spherical shape, i.e. a metal sphere with a dielectric cover and Luneberg lens. For this purpose tensor Green function method was used. Within the research we described the electrodynamic system verifying the expressions obtained for the calculation of electromagnetic fields. Furthermore, we compared the obtained results of calculations with the results of simulation of a similar problem in the software package ANSYS HFSS . Finally, we estimated the computational burden and computing time for solving the problem in two ways

Linear electromagnetic wave equations in materials

After a short review of microscopic electrodynamics in materials, we investigate the relation of the microscopic dielectric tensor to the current response tensor and to the full electromagnetic Green function. Subsequently, we give a systematic overview of microscopic electromagnetic wave equations in materials, which can be formulated in terms of the microscopic dielectric tensor.

Electromagnetic surface waves in liquid metacrystals

We study linear electromagnetic waves guided by an interface between a dielectric medium and liquid metacrystal (LMC) as well as by a slab of LMC. We derive the dispersion equation for such waves and find their transverse structure for the arbitrarily oriented anisotropy axis of LMC controlled by an external constant electric field. A high degree of anisotropy can be reached in LMC near the resonance of the inclusions (meta-atoms), and it allows propagation of known Dyakonov surface waves below the resonance frequency and also specific surface modes above the resonance frequency (in the hyperbolic dispersion regime) along the LMC–dielectric interface. Both types of surface waves are characterized by sensitivity to the parameters (radiation frequency, orientation of the optical axis, etc.) and have hybrid (mixed ordinary and extraordinary) polarization. In the LMC slab there can exist two families of eigenmodes: low-k and high-k modes, with the latter arising only in the hyperbolic dispersion regime. In the case when the normal to the slab interface is along the resonance cone generatrix in the LMC, a very high density of eigenmodes can take place that results from the inherent property of the hyperbolic medium—infinite density of photonic states.

Linear and nonlinear electromagnetic waves in a magnetized quantum electron-positron plasma

The linear and nonlinear properties of the electromagnetic waves are investigated in a magnetized quantum electron–positron (e–p) plasma by employing the quantum hydrodynamic (QHD) model. It is found that the quantum dispersion relation in comparison with the classical version is modified by the quantum corrections through quantum diffraction and statistics. The standard reductive perturbation technique is used to derive the Korteweg–de Vries (KdV) equation. The exact soliton solutions and the existence regions of the solitary waves are also defined precisely. It is also shown that the results are affected by the quantum corrections.

Minimum variational principles for time-harmonic waves in a dissipative medium and associated variational principles of Hashin–Shtrikman type

Minimization variational principles for linear elastodynamic, acoustic or electromagnetic time-harmonic waves in dissipative media were obtained by Milton et al. (Milton et al. 2009 Proc. R. Soc. A 465 , 367–396 ( doi:10.1098/rspa.2008.0195 )), generalizing the quasistatic variational principles of Cherkaev and Gibiansky (Cherkaev & Gibiansky 1994 J. Math. Phys. 35 , 127–145 ( doi:10.1063/1.530782 )). Here, a further generalization is made to allow for a much wider variety of boundary conditions, and in particular Dirichlet and Neumann boundary conditions. In addition minimization or maximization principles of the Hashin–Shtrikman type, incorporating ‘polarization fields’, are developed. The corresponding principles for static problems have found substantial use in bounding the effective static properties of composite materials. The new dynamical principles offer the prospect of developing bounds on the effective dynamic properties of such materials.

Short pulse equations and localized structures in frequency band gaps of nonlinear metamaterials

We consider short pulse propagation in nonlinear metamaterials characterized by a weak Kerr-type nonlinearity in their dielectric response. Two short-pulse equations (SPEs) are derived for the high- and low-frequency “band gaps” (where linear electromagnetic waves are evanescent) with linear effective permittivity ϵ < 0 and permeability μ > 0 . The structure of the solutions of the SPEs is also briefly discussed, and connections with the soliton solutions of the nonlinear Schrödinger equation are made.

Erratum: “Nonlinear electromagnetic wave equations for superdense magnetized plasmas” [Phys. Plasmas 16, 072114 (2009)

By using the quantum hydrodynamic and Maxwell equations, we derive nonlinear electron-magnetohydrodynamic (MHD), Hall-MHD, and dust Hall-MHD equations for dense quantum magnetoplasmas. The nonlinear equations include the electromagnetic, the electron pressure gradient, as well as the quantum electron tunneling and electron spin forces. They are useful for investigating a number of wave phenomena including linear and nonlinear electromagnetic waves, as well as three-dimensional electromagnetic wave turbulence spectra arising from the mode coupling processes in dense magnetoplasmas.

Nonlinear electromagnetic wave equations for superdense magnetized plasmas

By using the quantum hydrodynamic and Maxwell equations, we derive the generalized nonlinear electron magnetohydrodynamic, the generalized nonlinear Hall-MHD (HMHD), and the generalized nonlinear dust HMHD equations in a self-gravitating dense magnetoplasma. Our nonlinear equations include the self-gravitating, the electromagnetic, the quantum statistical electron pressure, as well as the quantum electron tunneling and electron spin forces. They are useful for investigating a number of wave phenomena including linear and nonlinear electromagnetic waves, as well as three-dimensional electromagnetic wave turbulence spectra and structures arising from mode coupling processes at nanoscales in dense quantum magnetoplasmas.

Nonlinear dust drift Alfvén waves in rotating planetary magnetospheres

Linear and nonlinear electromagnetic waves are investigated in the dusty magnetospheres of rotating planets. In the presence of heavy dust, the plasma may support very low frequency waves that can be affected by the plasma rotation. It is also shown that Alfvén waves can couple with the electrostatic dust drift waves induced by the planetary rotation. A comparison of the results with a previous work has also been made in the electrostatic limit. The electromagnetic vortex structures can be formed in rotating planetary dusty plasmas in the nonlinear regime. An application of this theory to dusty plasmas of the magnetospheres of Saturn and Jupiter is pointed out.

Polarization Plane Rotation of Electromagnetic Waves by the Artificial Periodic Structure with One-Turn Helical Elements

The rotation of polarization plane of electromagnetic waves by the metallic helices is experimentally investigated. The object of investigation is electromagnetic waves scattered by the copper wire one-turn helices. Flat periodic structure consists of 1-turn helices placed on the radio transparent material that is manufactured. The helices are excited by a linear electromagnetic wave. The experimental method is based on the registration of polarization plane rotation of wave reflected by a two-dimensional (2D) lattice. The optimal pitch angle of the helix which is necessary for maximal rotation of polarization plane of waves was calculated previously. The optimal parameters of the helix were taken into account when the 2D lattice was manufactured. As a result even the flat lattice was enough for observation of considerable rotation of the polarization plane of transmitted and reflected waves. For transmitted wave, the resonance behavior of rotation of the polarization plane with sign change of angle of rotation as a function of frequency is observed.

Calculation of pitch angle and energy diffusion coefficients with the PADIE code

We present a new computer code (PADIE) that calculates fully relativistic quasi‐linear pitch angle and energy diffusion coefficients for resonant wave‐particle interactions in a magnetized plasma. Unlike previous codes, the full electromagnetic dispersion relation is used so that interactions involving any linear electromagnetic wave mode in a predominantly cold plasma can be addressed for any ratio of the plasma‐frequency to the cyclotron frequency ωpe/∣Ωe∣. The code can be applied to problems in astrophysical, magnetospheric, and laboratory plasmas. The code is applied here to the Earth's radiation belts to calculate electron diffusion by whistler mode chorus, electromagnetic ion cyclotron (EMIC), and Z mode waves. The high‐density approximation is remarkably good for electron diffusion by whistler mode chorus for energies E ≥ 100 keV, even for ωpe/∣Ωe∣ ≈ 2 but underestimates diffusion by orders of magnitude at low energies (∼10 keV). When a realistic angular spread of propagating waves is introduced for EMIC waves, electron diffusion at ∼0.5 MeV is only slightly reduced compared with the assumption of field‐aligned propagation, but at ∼5 MeV, electron diffusion at pitch angles near 90° is reduced by a factor of 5 and increased by several orders of magnitude at pitch angles 30°–80°. Scattering by EMIC waves should contribute to flattening of the distribution function. The first results for electron diffusion by Z mode waves are presented. They show that unlike the whistler and EMIC waves, energy diffusion exceeds pitch angle diffusion over a broad range of pitch angles less than 45°. The results suggest that Z mode waves could provide a significant contribution to electron acceleration in the radiation belts during storm times.

Propagation of electromagnetic waves in spatially modulated Josephson junctions

The propagation of small amplitude (linear) electromagnetic waves in periodically spatiallymodulated finite Josephson junctions is studied using the transfer matrix approach. Thetransmittance of a finite length Josephson junction with thick, identical, periodic defects ispresented. The linear wave spectrum consists of pass- and stop-bands, whose width mayvary with the geometrical and/or the physical parameters of the junction. Theband boundaries as a function of several junction parameters are also presented,and the possibility of creating mid-gap states of finite transmittance within thegaps by slightly disturbing the periodicity is demonstrated. The dependence ofthe plasma frequency on the parameters of the junction is also calculatedusing several simple approaches. The possibility of applying this approach toϕ-junctions is briefly discussed. The knowledge of the mode spectrum may be useful inconstructing elements of nonlinear systems for development of tunable superconductingresonators. It can also be useful in calculating the resonance voltages appearing in thecurrent–voltage characteristics of a long periodically defected Josephson junction in amagnetic field, as proposed by Fistul et al.