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Closed-form expressions were recently derived for depolarization dyadics for truncated spheres and truncated spheroids, and the formalism was extended to truncated ellipsoids. These results were exploited to develop an implementation of the Maxwell Garnett homogenization formalism for the relative permittivity parameters of homogenized composite mediums (HCMs) arising from an isotropic host medium impregnated with isotropic inclusions that are truncated spheres, spheroids, and ellipsoids. In so doing, the anisotropy of the HCM was related to the geometry of the inclusions: in general, the more the shape of the inclusions deviated from spherical, the greater was the degree of anisotropy exhibited by the HCM.

Depolarization dyadics play a central role in theoretical studies involving scattering from small particles and homogenization of particulate composite materials. Closed-form expressions for depolarization dyadics have been developed for truncated spheres and truncated spheroids, and the formalism has been extended to truncated ellipsoids; the evaluation of depolarization dyadics for this latter case requires numerical integration. The H\"{o}lder continuity condition has been exploited to fix the origin of the coordinate system for the evaluation of depolarization dyadics.These results will enable theoretical studies involving scattering from small particles and homogenization of particulate composite materials to accommodate particles with a much wider range of shapes than was the case hitherto.

The propagation of surface-plasmon-polariton (SPP) waves at the planar interface of a metal and a dielectric material was investigated for a dielectric material with strongly temperature-dependent constitutive properties. The metal was silver and the dielectric material was vanadium multioxide impregnated with a combination of active dyes. Depending upon the volume fraction of vanadium multioxide, either attenuation or amplification of the SPP waves may be achieved; the degree of attenuation or amplification is strongly dependent on both the temperature and whether the temperature is increasing or decreasing. At intermediate volume fractions of vanadium multioxide, for a fixed temperature, a SPP wave may experience attenuation if the temperature is increasing but experience amplification if the temperature is decreasing.

The Bruggeman homogenization formalism was used to numerically investigate the dielectric properties of a columnar thin film (CTF) made from vanadium dioxide. For visible and near-infrared wavelengths, the CTF is electromagnetically equivalent to a homogeneous orthorhombic material. Over the 58 deg C -- 72 deg C temperature range, the eigenvalues of the CTF's relative permittivity dyadic are highly sensitive to temperature, and vary according to whether the CTF is being heated or cooled. The anisotropy revealed through the eigenvalues, and the anisotropy of the associated hysteresis, were investigated in relation to temperature for CTFs of different porosities and columnar cross sections. When the free-space wavelength is 800 nm, the CTF is a dissipative dielectric material that exhibits temperature-dependent anisotropy and anisotropic hysteresis. In contrast, when the free-space wavelength is 1550 nm, the CTF can be either a dissipative dielectric material, a hyperbolic material or a metal-like material, depending on the temperature and the porosity of the CTF. As the porosity of the CTF decreases from 0.55 to 0.3, the anisotropy of the CTF becomes more pronounced, as does the anisotropy of the hysteresis. Only relatively modest variations in anisotropy and hysteresis arise in response to varying the columnar cross-sectional shape, as compared to the variations induced by varying the porosity.

Vanadium dioxide (VO2) transforms from purely monoclinic to purely tetragonal on being heated from 58 deg C to 72 deg C, the transformation being reversible but hysteretic. Electromagnetically, VO2 transforms from a dissipative dielectric to another dissipative dielectric if the free-space wavelength is less than 1100 nm, but from a dissipative dielectric to a plasmonic metal (or vice versa) if the free-space wavelength exceeds 1100 nm. Calculating the extinction, total scattering, absorption, radiation-pressure, back-scattering, and forward-scattering efficiencies of a VO2 sphere, we found clear signatures of thermal hysteresis in (i) the forward-scattering, back-scattering, and absorption efficiencies for free-space wavelength less than 1100 nm, and (ii) the forward-scattering, back-scattering, total scattering, and absorption efficiencies for free-space wavelength more than 1100 nm. Vacuum and null-permittivity quasistates occur between 58 deg C and 72 deg C, when tetragonal VO2 is a plasmonic metal, once each on the heating branch and once each on the cooling branch of thermal hysteresis. But none of the six efficiencies show significant differences between the two quasistates., Comment: 11 pages, 4 figures

The homogenization of vaterite impregnated with gold nanoparticles was accomplished using the extended Maxwell Garnett formalism. The extended formalism takes into account the intrinsic anisotropy of vaterite as well as the size, shape, and orientation of the nanoparticles. Size-dependent permittivity was used for the gold nanoparticles. Numerical studies revealed that the homogenized composite material's permittivity parameters are acutely sensitive to the size, shape, orientation, and volume fraction of the gold nanoparticles.

Ordinarily, a trimaterial structure comprising a sufficiently thin metal film interposed between two homogeneous dielectric materials guides compound plasmon-polariton (CPP) waves, for which the fields on both sides of the metal film decay exponentially with distance from the nearest metal/dielectric interface. However, if one of the dielectric materials is anisotropic then the trimaterial structure can guide an exceptional CPP wave for a particular propagation direction. On the side of the metal film occupied by the anisotropic dielectric material, the fields of the exceptional CPP wave decay as the product of a linear function and an exponential function of the distance from the nearest metal/dielectric interface. The canonical boundary-value problem for CPP-wave propagation has been analyzed and solved numerically; thereby, the spatial field profiles for exceptional CPP waves for a uniaxial-dielectric/metal/isotropic-dielectric structure have been established.

An exceptional surface wave can propagate in an isolated direction, when guided by the planar interface of two homogeneous dielectric partnering mediums of which at least one is anisotropic, provided that the constitutive parameters of the partnering mediums satisfy certain constraints. Exceptional surface waves are distinguished from unexceptional surface waves by their localization characteristics: the fields of an exceptional surface wave in the anisotropic partnering medium decay as a combined linear-exponential function of distance from the interface, whereas the decay is purely exponential for an unexceptional surface wave. If both partnering mediums are anisotropic then a doubly exceptional surface wave can exist for an isolated propagation direction. The decay of this wave in both partnering mediums is governed by a combined linear-exponential function of distance from the interface.

Guided by the planar interface of two dissimilar linear, homogeneous mediums, a Voigt surface wave arises due to an exceptional point of either of the two matrixes necessary to describe the spatial characteristics in the direction normal to the planar interface. There is no requirement for either or both partnering mediums to be dissipative, unlike a Voigt plane wave which can propagate only in a dissipative medium.

The Lorenz--Mie formulation of electromagnetic scattering by a homogeneous, isotropic, dielectric-magnetic sphere was extended to incorporate topologically insulating surface states characterized by a surface admittance $\gamma$. Closed-form expressions were derived for the expansion coefficients of the scattered field phasors in terms of those of the incident field phasors. These expansion coefficients were used to obtain analytical expressions for the total scattering, extinction, forward scattering, and backscattering efficiencies of the sphere. Resonances exist for relatively low values of $\gamma$, when the sphere is either nondissipative or weakly dissipative. For large values of $\gamma$, the scattering characteristics are close to that of a perfect electrically conducting sphere, regardless of whether the sphere is composed of a dissipative or nondissipative material, and regardless of whether that material supports planewave propagation with positive or negative phase velocity.

The propagation of Dyakonov-Tamm (DT) surface waves guided by the planar interface of two nondissipative materials $A$ and $B$ was investigated theoretically and numerically, via the corresponding canonical boundary-value problem. Material $A$ is a homogeneous uniaxial dielectric material whose optic axis lies at an angle $\chi$ relative to the interface plane. Material $B$ is an isotropic dielectric material that is periodically nonhomogeneous in the direction normal to the interface. The special case was considered in which the propagation matrix for material $A$ is non-diagonalizable because the corresponding surface wave-named the Dyakonov-Tamm-Voigt (DTV) surface wave-has unusual localization characteristics. The decay of the DTV surface wave is given by the product of a linear function and an exponential function of distance from the interface in material $A$; in contrast, the fields of conventional DT surface waves decay only exponentially with distance from the interface. Numerical studies revealed that multiple DT surface waves can exist for a fixed propagation direction in the interface plane, depending upon the constitutive parameters of materials $A$ and $B$. When regarded as functions of the angle of propagation in the interface plane, the multiple DT surface-wave solutions can be organized as continuous branches. A larger number of DT solution branches exist when the degree of anisotropy of material $A$ is greater. If $\chi = 0^\circ$ then a solitary DTV solution exists for a unique propagation direction on each DT branch solution. If $\chi > 0^\circ$, then no DTV solutions exist. As the degree of nonhomogeneity of material $B$ decreases, the number of DT solution branches decreases., Comment: arXiv admin note: text overlap with arXiv:1910.10972

Dyakonov-Voigt (DV) surface waves guided by the planar interface of (i) material $A$ which is a uniaxial dielectric material specified by a relative permittivity dyadic with eigenvalues $\epsilon^s_A$ and $\epsilon^t_A$, and (ii) material $B$ which is an isotropic dielectric material with relative permittivity $\epsilon_B$, were numerically investigated by solving the corresponding canonical boundary-value problem. The two partnering materials are generally dissipative, with the optic axis of material $A$ being inclined at the angle $\chi \in [ 0^\circ, 90^\circ ]$ relative to the interface plane. No solutions of the dispersion equation for DV surface waves exist when $\chi=90^\circ$. Also, no solutions exist for $\chi \in ( 0^\circ, 90^\circ )$, when both partnering materials are nondissipative. For $\chi \in [ 0 ^\circ, 90^\circ )$, the degree of dissipation of material $A$ has a profound effect on the phase speeds, propagation lengths, and penetration depths of the DV surface waves. For mid-range values of $\chi$, DV surface waves with negative phase velocities were found. For fixed values of $\epsilon^s_A$ and $\epsilon^t_A$ in the upper-half-complex plane, DV surface-wave propagation is only possible for large values of $\chi$ when $| \epsilon_B|$ is very small.

The canonical boundary-value problem for surface-plasmon-polariton (SPP) waves guided by the planar interface of a dielectric material and a plasmonic material was solved for cases wherein either partnering material could be a uniaxial material with optic axis lying in the interface plane.Numerical studies revealed that two different SPP waves, with different phase speeds, propagation lengths, and penetration depths, can propagate in a given direction in the interface plane; in contrast, the planar interface of isotropic partnering materials supports only one SPP wave for each propagation direction. Also, for a unique propagation direction in each quadrant of the interface plane, it was demonstrated that a new type of SPP wave--called a surface-plasmon-polariton-Voigt (SPP-V) wave--can exist. The fields of these SPP-V waves decay as the product of a linear and an exponential function of the distance from the interface in the anisotropic partnering material; in contrast, the fields of conventional SPP waves decay only exponentially with distance from the interface. Explicit analytic solutions of the dispersion relation for SPP-V waves exist and help establish constraints on the constitutive-parameter regimes for the partnering materials that support SPP-V-wave propagation.

A numerical investigation was undertaken to elucidate the propagation of electromagnetic surface waves guided by the planar interface of two temperature-sensitive materials. One partnering material was chosen to be isotropic and the other to be anisotropic. Both partnering materials were engineered composite materials, based on the temperature-sensitive semiconductor InSb. At low temperatures the anisotropic partnering material is a non-hyperbolic uniaxial material; as the temperature is raised this material becomes a hyperbolic uniaxial material. At low temperatures, a solitary Dyakonov wave propagates along any specific direction in a range of directions parallel to the planar interface. At high temperatures, up to three different surface waves can propagate in certain directions parallel to the planar interface; one of these surface waves propagates with negative phase velocity (NPV). At a fixed temperature, the range of directions for NPV propagation decreases uniformly in extent as the volume fraction of InSb in the isotropic partnering material decreases. At a fixed volume fraction of InSb in the isotropic partnering material, the angular range for NPV propagation varies substantially as the temperature varies.

The so-called electromagnetic ghost waves are simply electromagnetic nonuniform plane waves, whose association with both propagating and evanescent fields has long been known, even for isotropic dielectric materials that are non-dissipative.

The propagation of electromagnetic surface waves guided by the planar interface of two isotropic chiral materials, namely materials $\calA$ and $\calB$, was investigated by numerically solving the associated canonical boundary-value problem. Isotropic chiral material $\calB$ was modeled as a homogenized composite material, arising from the homogenization of an isotropic chiral component material and an isotropic achiral, nonmagnetic, component material characterized by the relative permittivity $\eps_a^\calB$. Changes in the nature of the surface waves were explored as the volume fraction $f_a^\calB$ of the achiral component material varied. Surface waves are supported only for certain ranges of $f_a^\calB$; within these ranges only one surface wave, characterized by its relative wavenumber $q$, is supported at each value of $f_a^\calB$. For $\mbox{Re} \lec \eps_a^\calB \ric > 0 $, as $\left| \mbox{Im} \lec \eps_a^\calB \ric \right|$ increases surface waves are supported for larger ranges of $f_a^\calB$ and $\left| \mbox{Im} \lec q \ric \right|$ for these surface waves increases. For $\mbox{Re} \lec \eps_a^\calB \ric < 0 $, as $ \mbox{Im} \lec \eps_a^\calB \ric $ increases the ranges of $f_a^\calB$ that support surface-wave propagation are almost unchanged but $ \mbox{Im} \lec q \ric $ for these surface waves decreases. The surface waves supported when $\mbox{Re} \lec \eps_a^\calB \ric < 0 $ may be regarded as akin to surface-plasmon-polariton waves, but those supported for when $\mbox{Re} \lec \eps_a^\calB \ric > 0 $ may not.

Electromagnetic surface waves supported by an isotropic chiral material were investigated via the associated canonical boundary-value problem. Specifically, two scenarios were considered: surface waves guided by the planar interface of an isotropic chiral material and (a) an isotropic dielectric material and (b) a uniaxial dielectric (or plasmonic) material. Both plasmonic and non-plasmonic achiral partnering materials were investigated. In scenario (a) surface waves akin to surface-plasmon-polariton (SPP) waves were excited, while in scenario (b) surface waves akin to Dyakonov waves and akin to SPP waves were excited. For numerical studies, an isotropic chiral material capable of simultaneously supporting attenuation and amplification of plane waves, depending upon circular polarization state, was used. The amplitude of the SPP-like waves could be either amplified or attenuated, depending upon the relative permittivity of the isotropic dielectric partnering material for scenario (a), or depending upon the direction of propagation relative to the optic axis of the uniaxial dielectric partnering material for scenario (b).

The propagation of Dyakonov surface waves guided by the planar interface of (i) an isotropic dielectric material and (ii) a homogenized uniaxial dielectric composite material comprising both passive and active component materials was theoretically investigated, under the assumption that the optic axis of the uniaxial partnering material lies wholly in the interface plane. For a certain range of the volume fraction of the active component material, the uniaxial partnering material is neither wholly dissipative nor wholly active and the Dyakonov surface waves propagating in certain directions amplify but the Dyakonov surface waves propagating in other directions attenuate.

We numerically investigated the plane-wave reflection-transmission characteristics of a columnar thin film (CTF) whose columns are made from a dissipative material but whose void regions are filled with an active material. By computing the reflectances and transmittances, we found that the CTF can simultaneously amplify $s$-polarized incident light and attenuate $p$-polarized incident light, or vice versa. This polarization-state-dependent attenuation and amplification phenomenon depends upon the angle of incidence and the thickness of the CTF.

Two numerical studies, one based on a canonical boundary-value problem and the other based on a reflection-transmission problem, revealed that the propagation of high-phase-speed Dyakonov-Tamm (HPSDT) surface waves may be supported by the planar interface of a chiral sculptured thin film and a dissipative isotropic dielectric material. Furthermore, many distinct HPSDT surface waves may propagate in a specific direction, each with a phase speed exceeding the phase speed of plane waves that can propagate in the isotropic partnering material. Indeed, for the particular numerical example considered, the phase speed of an HPSDT surface wave could exceed the phase speed in bulk isotropic dielectric material by a factor of as much as 10.

We numerically solved the boundary-value problem for Tamm waves (which may also be classified as Uller-Zenneck waves here) guided by the planar interface of a homogeneous isotropic dissipative dielectric (HIDD) material and a periodically multilayered isotropic dielectric material. The HIDD material was chosen to be VO${}_2$ which, at optical wavelengths, has a temperature-dependent refractive index with a hysteresis feature, i.e., the temperature-dependence of its refractive index varies depending upon whether the temperature is increasing or decreasing. A numerical code was implemented to extract solutions of the dispersion equation at a fixed wavelength for both $p$- and $s$-polarization states over the temperature range [50,80] degrees. A multitude of Tamm waves of both linear polarization states were found, demonstrating a clear demarcation of the heating and cooling phases in terms of wavenumbers and propagation distances. Thereby, the signatures of thermal hysteresis in Tamm-wave propagation were revealed.

The effect of changing the temperature on the propagation of electromagnetic surface waves (ESWs), guided by the planar interface of a homogeneous isotropic temperature-sensitive material (namely, InSb) and a temperature-insensitive structurally chiral material (SCM) was numerically investigated in the terahertz frequency regime. As the temperature rises, InSb transforms from a dissipative dielectric material to a dissipative plasmonic material. Correspondingly, the ESWs transmute from Dyakonov-Tamm surface waves into surface-plasmon-polariton waves. The effects of the temperature change are clearly observed in the phase speeds, propagation distances, angular existence domains, multiplicity, and spatial profiles of energy flow of the ESWs. Remarkably large propagation distances can be achieved; in such instances the energy of an ESW is confined almost entirely within the SCM. For certain propagation directions, simultaneous excitation of two ESWs with (i) the same phase speeds but different propagation distances or (ii) the same propagation distances but different phase speeds are also indicated by our results.

A topological insulator is classically modeled as an isotropic dielectric-magnetic with a magnetoelectric pseudoscalar $\Psi$ existing in its bulk while its surface is charge-free and current-free. An alternative model is obtained by setting $\Psi\equiv0$ and incorporating surface charge and current densities characterized by an admittance $\gamma$. Analysis of plane-wave reflection and refraction due to a topological-insulator half space reveals that the parameters $\Psi$ and $\gamma$ arise identically in the reflection and transmission coefficients, implying that the two classical models cannot be distinguished on the basis of any scattering scenario. However, as $\Psi$ disappears from the Maxwell equations applicable to any region occupied by the topological insulator, and because surface states exist on topological insulators as protected conducting states, the alternative model must be chosen., Comment: 6 pages

The electromagnetic field phasors in an isotropic chiral material (ICM) are superpositions of two Beltrami fields of different handedness. Application of the Bruggeman homogenization formalism to two-component composite materials delivers ICMs wherein Beltrami fields of one handedness attenuate whereas Beltrami waves of the other handedness amplify. One component material is a dissipative ICM, the other an active dielectric material.

Two active dielectric materials may be blended together to realize a homogenized composite material (HCM) which exhibits more gain than either component material. Likewise, two dissipative dielectric materials may be blended together to realize an HCM which exhibits more loss than either component material. Sufficient conditions for such gain/loss enhancement were established using the Bruggeman homogenization formalism. Gain/loss enhancement arises when (i) the imaginary parts of the relative permittivities of both component materials are similar in magnitude and (ii) the real parts of the relative permittivities of both component materials are dissimilar in magnitude.

Anisotropic homogeneous metamaterials that are neither wholly dissipative nor wholly active at a specific frequency are permitted by classical electromagnetic theory. Well-established homogenization formalisms indicate that such a metamaterial may be realized quite simply as a random mixture of electrically small (possibly nanoscale) spheroidal particles of at least two different isotropic dielectric materials, one of which must be dissipative but the other active. The dielectric properties of this metamaterial are influenced by the volume fraction, spatial distribution, particle shape and size, and the relative permittivities of the component materials. Similar metamaterials with more complicated linear as well as nonlinear constitutive properties are possible. Dynamic control of the active component material, for example via stimulated Raman scattering, affords dynamic control of the metamaterial.

After formulating the frequency-domain Maxwell equations for a homogeneous, linear, bianisotropic material occupying a bounded region, we found that the axionic piece vanishes from both the differential equations valid in the region and the boundary conditions, thereby vindicating the Post constraint. Our analysis indicates that characteristic effects that may be observed experimentally with magnetoelectric materials are not the consequences of the axionic piece but of an admittance that describes surface states., Comment: Comments are welcome

A possible means of optical sensing, based on a porous hyperbolic material which is infiltrated by a fluid containing an analyte to be sensed, was investigated theoretically. The sensing mechanism relies on the observation that extraordinary plane waves propagate in the infiltrated hyperbolic material only in directions enclosed by a cone aligned with the optic axis of the infiltrated hyperbolic material. The angle this cone subtends to the plane perpendicular to the optic axis is $\theta_c$. The sensitivity of $\theta_c$ to changes in refractive index of the infiltrating fluid, namely $n_b$, was explored; also considered were the permittivity parameters and porosity of the hyperbolic material, as well as the shape and size of its pores. Sensitivity was gauged by the derivative $d \theta_c / d n_b$. In parametric numerical studies, values of $d \theta_c / d n_b$ in excess of 500 degrees per refractive index unit were computed, depending upon the constitutive parameters of the porous hyperbolic material and infiltrating fluid, and the nature of the porosity. In particular, it was observed that exceeding large values of $d \theta_c / d n_b$ could be attained as the negative--valued eigenvalue of the infiltrated hyperbolic material approached zero.

If a dissipative anisotropic dielectric material, characterized by the permittivity matrix $\underline{\underline{\epsilon}}$, supports Voigt-wave propagation, then so too does the analogous active material characterized by the permittivity matrix $\underline{\underline{{\tilde{\epsilon}}}}$, where $\underline{\underline{{\tilde{\epsilon}}}}$ is the hermitian conjugate of $\underline{\underline{\epsilon}}$. Consequently, a dissipative material that supports Voigt-wave propagation can give rise to a material that supports the propagation of Voigt waves with attendant linear gain in amplitude with propagation distance, by infiltration with an active dye.

The homogenization of a composite material comprising three isotropic dielectric materials was investigated. The component materials were randomly distributed as spherical particles, with the particles of two of the component materials being coupled to form dimers. The Bruggeman and Maxwell Garnett formalisms were developed to estimate the permittivity dyadic of the homogenized composite material (HCM), under the quasi-electrostatic approximation. Both randomly oriented and identically oriented dimers were accommodated; in the former case the HCM is isotropic, whereas in the latter case the HCM is uniaxial. Representative numerical results for composite materials containing dielectric--dielectric dimers demonstrate close agreement between the estimates delivered by the Bruggeman and Maxwell Garnett formalisms. For composite materials containing metal--dielectric dimers with moderate degrees of dissipation, the estimates of the two formalisms are in broad agreement, provided that the dimer volume fractions are relatively low. In general, the effects of intradimer coupling on the estimates of the HCM permittivity are relatively modest but not insignificant, these effects being exacerbated by anisotropy when all dimers are identically oriented.

Voigt wave propagation was investigated in a homogenized composite material (HCM) arising from a porous electro--optic host material infiltrated by a fluid of refractive index $n_a$. The constitutive parameters of the HCM were estimated using the extended Bruggeman homogenization formalism. Numerical studies revealed that the directions which support Voigt wave propagation in the HCM could be substantially controlled by means of an applied dc electric field. Furthermore, the extent to which this control could be achieved was found to be sensitive to the porosity of the host material, the shapes, sizes and orientations of the pores, as well as the refractive index $n_a$. These findings may be particularly significant for potential technological applications of Voigt waves, such as in optical sensing.

We considered the experimental realization of a Tamm medium that is optically equivalent to the collision of two linearly polarized gravitational plane waves as a piecewise homogeneous metamaterial. Our formulation was based on the homogenization of remarkably simple arrangements of oriented ellipsoidal nanoparticles of isotropic dielectric-magnetic mediums. The inverse Bruggeman homogenization was used to estimate the constitutive parameters, volume fractions, and shape parameters for the component mediums. The presented formulation is appropriate for the regions of spacetime where the two gravitational plane waves interact, excluding the immediate vicinity of the nonsingular Killing-Cauchy horizon at the focusing point of the two plane waves.