Search Results (5)

We have developed the paraxial approximation for electromagnetic fields in arbitrary isotropy-broken media in terms of the ray–wave tilt and the curvature of materials’ Fresnel wave surfaces. We have obtained solutions of the paraxial equation in the form of biaxial Gaussian beams, which is a novel class of electromagnetic field distributions in generic isotropy-broken materials. Such beams have been previously observed experimentally and numerically in hyperbolic metamaterials but have evaded theoretical analysis in the literature up to now. Biaxial Gaussian beams have two axes: one in the direction of the Abraham momentum, corresponding to the ray propagation, and another in the direction of the Minkowski momentum, corresponding to the wave propagation, in agreement with the recent theory of refraction, ray–wave tilt, and hidden momentum [Durach, 2024]. We show that the curvature of the wavefronts in the biaxial Gaussian beams correspond to the curvature of the Fresnel wave surface at the central wave vector of the beam. We obtain the higher-order modes of the biaxial beams, including the biaxial Hermite–Gaussian and Laguerre–Gaussian vortex beams, which opens avenues toward studies of the optical angular momentum (OAM) in isotropy-broken media, including generic anisotropic and bianisotropic materials. Full article

The mysterious nature of electromagnetic momentum in materials is considered one of the most significant challenges in physics, surpassing even Hilbert’s mathematical problems. In this paper, we demonstrate that the difference between the Minkowski and Abraham momenta, which consists of Roentgen and Shockley hidden momenta, is directly related to the phenomenon of refraction and the tilt of rays from the wavefront propagation direction. We show that individual electromagnetic waves with non-unit indices of refraction (n) appear as quasistatic high-k waves to an observer in the proper frames of the waves. When Lorentz transformed into the material rest frames, these high-k waves are Fresnel–Fizeau dragged from rest to their phase velocities, acquiring longitudinal hidden momentum and related refractive properties. On a material level, all electromagnetic waves belong to Fresnel wave surfaces, which are topologically classified according to hyperbolic phases by Durach and determined by the electromagnetic material parameters. For moving observers, material parameters appear modified, leading to alterations in Fresnel wave surfaces and even the topological classes of the materials may appear differently in moving frames. We discuss the phenomenon of electromagnetic momentum tilt, defined as the non-zero angle between Abraham and Minkowski momenta or, equivalently, between the rays and the wavefront propagation direction. This momentum tilt is only possible in isotropy-broken media, where the E and H fields can be longitudinally polarized in the presence of electric and magnetic bound charge waves. The momentum tilt can be understood as a differential aberration of rays and waves when observed in the material rest frame. Full article

This study focuses on microscale anisotropy in rock structure and texture, exploring its influence on the macro anisotropic electromagnetic parameters of the geological media, specifically electric conductivity (σ), relative permittivity (ε), and magnetic permeability (μ). The novelty of this research lies in the advancement of geophysical monitoring methods for calculating cross properties through the estimation of effective parameters—a kind of integral macroscopic characteristic of media mostly used for composite materials with inclusions. To achieve this, we approximate real geological media with layered bianisotropic media, employing the effective media approximation (EMA) averaging technique to simplify the retrieval of the effective electromagnetic parameters (e.g., apparent resistivity–inversely proportional to electrical conductivity). Additionally, we investigate the correlation between effective electromagnetic parameters and geodynamic processes, which is supported by the experimental data obtained during monitoring studies in the Tien Shan region. The observed decrease and increase in apparent electrical resistivity values of ρ_k over time in orthogonal azimuths leads to further ρ_k deviations of up to 80%. We demonstrate that transitioning to another coordinate system is equivalent to considering gradient anisotropic media. Building upon the developed method, we derive the effective electric conductivity tensor for gradient anisotropic media by modeling the process of fracturing in a rock mass. Research findings validate the concept that continuous electromagnetic monitoring can aid in identifying natural geodynamic disasters based on variations in integral macroscopic parameters such as electrical conductivity. The geodynamic processes are closely related to seismicity and stress regimes with provided constraints. Therefore, disasters such as earthquakes are damaging and seismically hazardous. Full article

Electromagnetic fields in bulk bianisotropic media contain plane waves whose k-vectors can be found using the method of the index of refraction’s operator and belong to the Fresnel wave surfaces that fall into one of the five hyperbolic classes of the Durach et al. taxonomy of bianisotropic media. Linear combinations of vector spherical harmonics can be used as a set of solutions of vector Helmholtz equations in gyrotropic media to develop Mie’s theory of scattering by anisotropic spheres as accomplished by Lin et al. and Li et al. In this study, we introduced electromagnetic orbitals for bianisotropic media as linear combinations of vector spherical harmonics, which represent solutions of Maxwell’s equations in bianisotropic media. Using these bianisotropic orbitals, we developed a theory of the scattering of electromagnetic radiation by bianisotropic spheres with arbitrary effective material parameters and sizes. As a by-product, we obtained a simple expression for the expansion of a vector plane wave over vector spherical harmonics in a more compact form than the frequently used by Sarkar et al. We obtained the polarizability expressions in the Rayleigh limit in agreement with the results of the electrostatic approximation of Lakhtahia and Sihvola. Full article

The present work considers the investigation of the effects of both electrical and magnetic uniaxial anisotropies on the input impedance, resonant length, and fields distribution of a dipole printed on an anisotropic grounded substrate. In this study, the associated integral equation, based on the derivation of the Green’s functions in the spectral domain, is numerically solved employing the method of moments. In order to validate the computing method and the evaluated calculation code, numerical results are compared with available data in the literature treating particular cases of electrical uniaxial anisotropy; reasonable agreements are reported. Novel results of the magnetic uniaxial anisotropy effects on the input impedance and the evaluated electromagnetic field are presented and discussed. This work will serve as a stepping stone for further works for a better understanding of the electromagnetic field behavior in complex anisotropic and bi-anisotropic media. Full article