Uniaxial Anisotropic Media Research Articles

Eigen Waves of a Plane Symmetric Anisotropic Waveguide

Precise dispersion equations for a plane symmetric dielectric anisotropic waveguide are obtained, in which the waveguide layer is isotropic, and the framing media are assumed to be anisotropic uniaxial media. The tensors of the dielectric permittivity of the framing media are not assumed to be diagonal, namely, in one of them this tensor is formed by rotating the diagonal tensor by some angle between the optical axis of the anisotropic medium and the direction of propagation of the electromagnetic wave. The tensor of dielectric permittivity of another anisotropic medium is rotated by the same angle, but in the opposite direction, with the optical axes of both framing media lying in a plane parallel to the boundaries of the waveguiding structure. Thus, in framing media, the existence of six-component electromagnetic waves is maintained. In the dispersion properties of such a waveguide, certain features are observed in comparison with the case when the framing media are assumed to be isotropic. It is found that the first symmetric mode of such a waveguide has a finite deceleration with zero thickness of the isotropic layer, which indicates the possibility of the appearance of surface electromagnetic waves (the so-called Dyakonov waves) at the boundaries of this isotropic layer. It is noted that the transition of the antisymmetric mode to the Dyakonov wave occurs with a finite thickness of the waveguiding layer. Dependencies of the deceleration of the elementary (symmetric) mode on the angle of rotation of the optical axis of anisotropic media relative to the direction of propagation of the guided wave of the waveguide structure are given.

Paraxial light beams in structured anisotropic media.

We discuss the paraxial approximation for optical waves propagating in a uniaxial anisotropic medium inhomogeneously twisted on the plane normal to the wave vector, with the latter being parallel to one of the two principal axes normal to the optic axis. Such geometry implies a continuous power transfer between the ordinary and extraordinary components, regardless of the input beam polarization. We pinpoint that this peculiar feature, generalizable to any inhomogeneous linear birefringent material, strongly affects the application of the paraxial approximation due to the simultaneous presence of two different phase velocities. We eventually show that a local coordinate transformation permits a correct application of the paraxial approximation.

Scattering response of featured uniaxial anisotropic chiral medium-coated twisted PEC cylinder

Scattering of electromagnetic waves from a perfectly electrical conducting (PEC) cylinder of circular cross-section, coated with uniaxial non-magnetic chiral anisotropic medium, was discussed. A conducting sheath helix structure with adjustable pitch angle exists over the outer surface of coated cylinder, which is interfaced with the free-space. Under the uniform parallel polarized plane wave with fixed oblique incidence angle, the echo widths were determined emphasizing the other relevant scattering-related parameters (e.g. scattering/extinction efficiency etc.), taking into account different pitch angle values (of the sheath helix) and the kinds of coating mediums. The results revealed that the coating of negative uniaxial chiral medium causes enhancement in scattering efficiency (of the scatterer). Also, the scattering efficiency was found to be the same as the extinction efficiency, thereby yielding vanishing absorption of the medium. The obtained results were also compared with the situation of vanishing chirality of coating medium over the PEC cylinder; the echo width and scattering efficiency both decrease in this case.

Prevailing-frequency approximation of the coupling ray theory along the SH and SV reference rays in a heterogeneous generally anisotropic medium which is approximately uniaxial

The behaviour of the actual polarization of an electromagnetic wave or elastic S–wave is described by the coupling ray theory, which represents the generalization of both the zero–order isotropic and anisotropic ray theories and provides continuous transition between them. The coupling ray theory is usually applied to anisotropic common reference rays, but it is more accurate if it is applied to reference rays which are closer to the actual wave paths. In a generally anisotropic or bianisotropic medium, the actual wave paths may be approximated by the anisotropic–ray–theory rays if these rays behave reasonably. In an approximately uniaxial (approximately transversely isotropic) anisotropic medium, we can define and trace the SH (ordinary) and SV (extraordinary) reference rays, and use them as reference rays for the prevailing–frequency approximation of the coupling ray theory. In both cases, i.e. for the anisotropic–ray–theory rays or the SH and SV reference rays, we have two sets of reference rays. We thus obtain two arrivals along each reference ray of the first set and have to select the correct one. Analogously, we obtain two arrivals along each reference ray of the second set and have to select the correct one. In this paper, we suggest the way of selecting the correct arrivals. We then demonstrate the accuracy of the resulting prevailing–frequency approximation of the coupling ray theory using elastic S waves along the SH and SV reference rays in four different approximately uniaxial (approximately transversely isotropic) velocity models.

Penetration Effect: Exotic Behavior of a Wave in Anisotropic Media

Plane harmonic wave propagation along an interface between vacuum and a semi-infinite uniaxial anisotropic medium is considered. It is shown that there is a bulk wave within an anisotropic medium in this case. It is also proved for the first time that a reflected wave must propagate perpendicularly to an interface. Moreover, a reflected wave is absent in the case of ordinary wave propagation.

LIGHT ABERRATION IN OPTICAL ANISOTROPIC SINGLE-AXIS MEDIUM

The entrainment of the light flux by a uniaxial anisotropic medium and its influence on the measurement of stellar aberration are analyzed. The influence of the entrainment of the light flux by an isotropic medium on the measurement of stellar aberration was considered by Fresnel early. The absence of such influence was confirmed by Erie's experience when filling the telescope tube with water. The formula itself was perfectly confirmed by Fizeau's experiments with moving water and the repetition of this experiment with an increase in the accuracy of measurements by Michelson, Zeeman, and others. G.A. Lorentz already on the basis of the electromagnetic theory specified the formula with allowance for the frequency dispersion of the light flux. A. Einstein made an analysis of the schemes of experiments for determining the drag coefficient, covering all possible variants of similar experiments. As a result, he obtained Fresnel and Lorentz formulas, taking into account the frequency dispersion of light, starting from the theory of relativity. The entrainment of light and its influence on the measurement of stellar aberration by a uniaxial anisotropic medium have not been considered anywhere. An analysis of such influence is carried out. The results of the analysis indicate the possibility of measuring the current value of stellar aberration using a uniaxial anisotropic medium. The concept of active light aberration is introduced. The proposed schemes of experiments of using the entrainment of a light flux by an anisotropic substance for measuring the current value of stellar aberration are investigated. It is concluded that it is possible to study the determination of the current velocity of an inertial system relative to the light flux.

Effect of Chirality on Dispersion Characteristics of Uniaxial Anisotropic Chiral Elliptical Waveguide

AbstractIn this paper, the dispersion characteristic of elliptical waveguide consisting of uniaxial anisotropic chiral medium is investigated. The eigenvalue equation for the waveguide that is to be studied is deduced by solving the Mathieu and modified Mathieu functions. The cutoff frequencies for several lower order even modes have been calculated and their dispersion characteristics are correspondingly plotted. The effects of elliptical eccentricity and chirality on the mode cutoff frequencies and mode transmission are examined numerically.

The Double Jones Birefringence in Magneto-electric Medium

In this paper, the Maxwell’s equations for a tensorial magneto-electric (ME) medium are solved, which is an extension to the work on the uniaxial anisotropic nonmagnetic medium. The coefficients of the dielectric permittivity, magnetic permeability, and of the magneto-electric effect are considered as tensors. The polarization is shown lying in the plane of two perpendicular independent vectors, and the relationship for the transverse polarization is given. The propagation of an electromagnetic wave through a ME medium gives rise to double Jones birefringence. Besides, the condition for an independent phenomenon of D’yakonov surface wave in a magneto-isotropic but with magneto-electric medium is given, which is measurable experimentally when the incident angle is . Lastly, it is shown that the parameter for the magneto-electric effect plays a role in the damping of the wave.

Investigation of uniaxial anisotropic chiral metamaterial waveguide with perfect electromagnetic conductor loading

The paper presents investigations of the electromagnetic characteristics of circular waveguides made of uniaxial anisotropic chiral medium; the outer surface of the guide being coated with a PEMC (perfect electromagnetic conductor) medium. The emphasis is given on the energy flux density patterns of such guides with varieties of anisotropic chiral materials. Dispersion relation of the guide is developed, and followed by the evaluation of sustained modes, which determine the energy flux density patterns corresponding to different low-order hybrid modes. The flux density characteristics provide the evidence of existing backward waves in uniaxial anisotropic mediums, contributing more to the phenomenon of slow light in chiral metamaterials.

Second harmonic generation of flat-topped Gaussian beams in single and twin BBO crystals

The coupled wave equations for second harmonic generation of flat-topped beam propagating in birefringent uniaxial anisotropic medium are presented. Based on them, specific physical models of single and twin BBO crystals have been established and numerically computations have been carried out. The influences of beam waist, medium structure on second harmonic generation are analyzed. The calculation results indicate that a wider beam waist can make a better phase matching, therefore the second harmonic beam will maintain the flat-topped property better but with a lower intensity and twin crystals can eliminate beam walk-off in some way.

T-matrix method for electromagnetic scattering by a general anisotropic particle

A general T-matrix solution for electromagnetic or light scattering by an anisotropic particle with an arbitrary permittivity tensor is constructed based on the extended boundary condition method (EBCM). By using the inverse Fourier transform, a system of quasi-spherical vector wave functions (qSVWFs) are obtained for an expansion representation of electromagnetic fields inside a general anisotropic medium. Special cases for gyroelectric anisotropic medium, biaxial anisotropic medium as well as uniaxial anisotropic medium are discussed. By virtue of the obtained series of qSVWFs, T-matrix formula are constructed to find solutions for characterizing electromagnetic or light scattering from an arbitrary shaped homogeneous anisotropic particle, and a home-made FORTRAN program is written. To validate the presented theoretical treatments as well as the home-made program, numerical results concerning radar cross section (RCS) or differential scattering cross sections (DSCSs) for various parameters are calculated by using the present method and are compared with those computed using other methods. Very good agreements are achieved, which partially confirms the correctness of the theoretical derivations and home-made program. Some new numerical results are also presented to analyze the influences of anisotropy components in permittivity tensor upon the scattering properties, which also provide a reference data for other methods.

Comparative analysis of Dyakonov hybrid surface waves at dielectric–elliptic and dielectric–hyperbolic media interfaces

We comparatively investigate Dyakonov surface waves (DSWs) traveling along the plane interface between a dielectric isotropic medium and a lossless anisotropic uniaxial medium with the optic axis (OA) parallel to the interface, when the principal permittivities of the uniaxial medium are both positive (elliptic medium) and of opposite signs (hyperbolic medium). New insights concerning the DSWs are given by analyzing the behavior of the Poynting vector (PV) components. Thus, singularity points at which the PV of the DSW vanishes can exist at the dielectric–elliptic media interface. The range of angles with respect to the OA, which is determined both for the wave vector and the respective PV, can be larger for the DSWs at the dielectric–hyperbolic media interface. Extremely high values of the wave vector and the PV components of the DSWs can be attained at the dielectric–hyperbolic media interface.

Energy streamlines in near-field radiative heat transfer between hyperbolic metamaterials.

Metallodielectric photonic crystals having hyperbolic dispersions are called indefinite materials because of their ability to guide modes with extremely large lateral wavevectors. While this is useful for enhancing near-field radiative heat transfer, it could also give rise to large lateral displacements of the energy pathways. The energy streamlines can be used to depict the flow of electromagnetic energy through a structure when wave propagation does not follow ray optics. We obtain the energy streamlines through two semi-infinite uniaxial anisotropic effective medium structures, separated by a small vacuum gap, using the Green functions and fluctuation-dissipation theorem. The lateral shifts are determined from the streamlines within two penetration depths. For hyperbolic modes, the predicted lateral shift can be several thousand times of the vacuum gap width.

Evaluation of Scattering From Electrically Large and Complex PEC Target Coated With Uniaxial Electric Anisotropic Medium Layer Based on Asymptotic Solution in Spectral Domain

This paper presents a novel and original approach for the evaluation of electromagnetic (EM) scattering from electrically large and complex target coated with uniaxial electric anisotropic medium (UEAM) layer. The evaluation includes two indispensable aspects, the geometry modeling of the target and the determination of the surface currents. Once the equivalent surface currents (ESCs) induced on the outer surface of the coated target are determined, the scattered field could be calculated by the corresponding radiation integrals. First, the outer surface of the arbitrarily shaped target is discretized using flat triangle facets. Second, the ESCs on any facet are deduced from the surface fields, which involve a complicated coupling of type I and type II waves existing in the UEAM. Thus, the determination of the surface fields and the ESCs on the surface of the target with large radius of curvature is the crux of the whole evaluation. By making the tangent plane approximation, used in the physical optics (PO) method, any discretized flat facet could be approximated as an infinite PEC plate coated with a homogenous UEAM layer. Thereafter, the scattering from the infinite coated plate is asymptotically calculated by using the proposed spectral domain method combined with saddle point evaluation (SDM-SPE). Ultimately, comparisons of the proposed asymptotic solution with the reference solutions calculated numerically confirm the validity and efficiency of the proposed SDM-SPE. Numerical results of several canonical and complex targets coated with UEAM layer are given by the proposed approach for the first time.

Reflection and Transmission at the Interface With an Electric–Magnetic Uniaxial Medium With Applications to Boundary Conditions

The interface between an isotropic medium and a general uniaxial anisotropic medium is considered and the reflection coefficients are obtained. Their behavior in some particular cases is presented. A new boundary condition for the electromagnetic field is introduced. It requires the cancellation of both the electric and the magnetic fields along a generic direction. The realization of this boundary condition is proposed by means of a uniaxial medium: the properties of such medium are investigated. An interesting property of the reflection matrix is demonstrated, i.e., when the uniaxial medium is affinely isotropic and has the same impedance of the isotropic medium, the reflection matrix is proportional to a unitary matrix.

Guided Modes in Uniaxial Chiral Waveguide of Circular Cross-Section under PEC Boundary

Propagation of electromagnetic waves through a circular waveguide of uniaxial anisotropic chiral medium is studied with the emphasis on the energy flux patterns. The outer surface of the guide is assumed to be bounded by a perfect electric conductor (PEC) medium. The dispersion relation of guide is derived by applying suitable boundary conditions, and the allowed values of propagation constants are computed. Energy flux patterns corresponding to three different types of uniaxial anisotropic chiral metamaterials are taken into account. The propagation of negative energy flux is observed, and attributed to the presence of backward waves in the waveguide structure.

Propagation through uniaxial anisotropic chiral waveguide under DB-boundary conditions

The paper describes the propagation of electromagnetic waves through a cylindrical waveguide composed of uniaxial anisotropic chiral medium that is treated under the DB-boundary. The emphasis is given on the energy flux density in the guide considering varieties of chiral mediums and the waveguide dimensions. For this purpose, the eigenvalue equation is obtained using the appropriate boundary conditions, and the modal propagation constants of the guide are deduced. It has been investigated that the flux density mostly remains confined in the central regions of guide which, however, strongly depends on the type of waveguide medium as well as the dimensional measures. Both forward and backward wave propagations are observed in such guides – the feature essentially governed by the characteristics of the guiding medium.

Modal method based on subsectional Gegenbauer polynomial expansion for nonperiodic structures: complex coordinates implementation

In this paper we present an extension of the modal method by Gegenbauer expansion (MMGE) [J. Opt. Soc. Am. A28, 2006 (2011)], [Progress Electromagn. Res.133, 17 (2013)] to the study of nonperiodic problems. The nonperiodicity is introduced through the perfectly matched layers (PMLs) concept, which can be introduced in an equivalent way either by a change of coordinates or by the use of a uniaxial anisotropic medium. These PMLs can generate strong irregularities of the electromagnetic fields that can significantly alter the convergence and stability of the numerical scheme. This is the case, e.g., for the famous Fourier modal method, especially when using complex stretching coordinates. In this work, it will be shown that the MMGE equipped with PMLs is a robust approach because of its natural immunity against spurious modes.

SCALAR POTENTIAL DEPOLARIZING DYAD ARTIFACT FOR A UNIAXIAL MEDIUM

A scalar potential formulation for a uniaxial anisotropic medium is succinctly derived through the exclusive use of Helmholtz's theorem and subsequent identiflcation of operator orthogonality. The resulting formulation is shown to be identical to prior published research, with the notable exception that certain scalar potential flelds not considered in previous work are rigorously demonstrated to be unimportant in the fleld recovery process, thus ensuring uniqueness. In addition, it is revealed that both a physically expected and unexpected depolarizing dyad contribution appears in the development. Using a Green's function spectral domain analysis and subsequent careful application of Leibnitz's rule it is shown that, for an unbounded homogeneous uniaxial medium, the unexpected depolarizing dyad term is canceled, leading to a mathematically and physically consistent and correct theory.

Van der Waals interaction in uniaxial anisotropic media

Van der Waals interactions between flat surfaces in uniaxial anisotropic media are investigated in the nonretarded limit. The main focus is the effect of nonzero tilt between the optical axis and the surface normal on the strength of the van der Waals attraction. General expressions for the van der Waals free energy are derived using the surface mode method and the transfer-matrix formalism. To facilitate numerical calculations a temperature-dependent three-band parameterization of the dielectric tensor of the liquid crystal 5CB is developed. A solid slab immersed in a liquid crystal experiences a van der Waals torque that aligns the surface normal relative to the optical axis of the medium. The preferred orientation is different for different materials. Two solid slabs in close proximity experience a van der Waals attraction that is strongest for homeotropic alignment of the intervening liquid crystal for all the materials studied. The results have implications for the stability of plate-like colloids in liquid crystal hosts.