Search Results (8)

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

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 complete understanding of the electromagnetic field characteristics in artificially created bulk or thin media is essential to the efficient harnessing of the multitude of linear and nonlinear effects resulting from it. Due to the fact that recently developed artificial metastructures exhibit controllable electric and magnetic properties that are completely different from natural ones, the spectrum of behavior resulting from subjecting such media to electromagnetic fields has to be revisited. In this paper, we introduce a k-surface framework that offers complete information on the dispersion properties of media with designer electric and magnetic responses with positive and negative values, as well as for the coupling between the two. The extension from the classic k-surface case resides in the consideration of magnetic and bianisotropic materials with positive and negative permittivity and permeability values, as well as the introduction of the chirality coefficient.To illustrate the applicability of our framework, we have investigated the conditions to obtain collinear second harmonic generation in the case of artificial media with positively and negatively valued electric and magnetic responses. As expected, the phase matching tuning curves, defined as the intersections between the k-surfaces at both frequencies, are significantly modified with respect to the classic ones. Full article

A recently developed theory is applied to deduce the well posedness and the finite element approximability of time-harmonic electromagnetic scattering problems involving bianisotropic media in free-space or inside waveguides. In particular, three example problems are considered of which one deals with scattering from plasmonic gratings that exhibit bianisotropy while the other two deal with bianisotropic obstacles inside waveguides. The hypotheses that guarantee the reliability of the numerical results are verified, and the ranges of the constitutive parameters of the media involved for which the finite element solutions are guaranteed to be reliable are deduced. It is shown that, within these ranges, there can be significant bianisotropic effects for the practical media considered as examples. The ensured reliability of the obtained results can make them useful as benchmarks for other numerical approaches. To the best of our knowledge, no other tool can guarantee reliable solutions. Full article

A set of sufficient conditions for the well posedness and the convergence of the finite element approximation of three-dimensional time-harmonic electromagnetic boundary value problems involving non-conducting rotating objects with stationary boundaries or bianisotropic media is provided for the first time to the best of authors’ knowledge. It is shown that it is not difficult to check the validity of these conditions and that they hold true for broad classes of practically important problems which involve rotating or bianisotropic materials. All details of the applications of the theory are provided for electromagnetic problems involving rotating axisymmetric objects. Full article

We describe novel topological phases of isofrequency k-space surfaces in bianisotropic optical materials—tri- and tetrahyperbolic materials—which are induced by the introduction of chirality. This completes the classification of isofrequency topologies for bianisotropic materials, as we showed that all optical materials belong to one of the following topological classes—tetra-, tri-, bi-, mono-, or nonhyperbolic. We showed that phase transitions between these classes occur in the k-space directions with zero group velocity at high k-vectors. This classification is based on the sets of high-k polaritons (HKPs), supported by materials. We obtained the equation describing these sets and characterized the longitudinal polarization-impedance of HKPs. Full article

We propose a new approach to calculate the complex photonic band structure, both purely dispersive and evanescent Bloch modes of a finite range, of arbitrary three-dimensional photonic crystals. Our method, based on a well-established plane wave expansion and the weak form solution of Maxwell’s equations, computes the Fourier components of periodic structures composed of distinct homogeneous material domains from a triangulated mesh representation of the inter-material interfaces; this allows substantially more accurate representations of the geometry of complex photonic crystals than the conventional representation by a cubic voxel grid. Our method works for general two-phase composite materials, consisting of bi-anisotropic materials with tensor-valued dielectric and magnetic permittivities ε and μ and coupling matrices ς. We demonstrate for the Bragg mirror and a simple cubic crystal closely related to the Kelvin foam that relatively small numbers of Fourier components are sufficient to yield good convergence of the eigenvalues, making this method viable, despite its computational complexity. As an application, we use the single gyroid crystal to demonstrate that the consideration of both conventional and evanescent Bloch modes is necessary to predict the key features of the reflectance spectrum by analysis of the band structure, in particular for light incident along the cubic [111] direction. Full article