Uniaxial Dielectric Material Research Articles

Homogenization of a random mixture of identically oriented superspheroidal particles

Depolarization dyadics were computed for superspheroidal particles made of an isotropic dielectric material and immersed in a uniaxial dielectric material. Superspheroidal shapes of two kinds were considered: one intermediate between spheroidal and cylindrical, and the other intermediate between spheroidal and cuboidal. These depolarization dyadics were employed in the Maxwell Garnett and Bruggeman homogenization formalisms to estimate the relative permittivity dyadics of homogenized composite materials (HCMs) that are random mixtures of identically oriented superspheroidal particles. The anisotropy of the HCMs was exposed through numerical investigations which revealed the dependencies of the HCM's anisotropy upon the shapes of the constituent particles and their volume fractions. The largest degrees of HCM anisotropy arose when the shape of the constituent particles deviated most from spherical, especially at mid-range volume fractions. Estimates of HCM anisotropy from the Maxwell Garnett and Bruggeman formalisms were broadly similar over the volume-fraction range appropriate for the Maxwell Garnett formalism, with modest differences being most apparent for particle shapes that deviated most from spherical.

Analysis of the far-field radiation pattern by a current loop in hyperbolic material

In this article, we investigate the radiations from a current loop in hyperbolic materials. To encounter the arbitrary orientation of the loop, the results are presented when the loop axis is aligned parallel and perpendicular to the optic axis. Closed-form expressions as well as numerical results are presented for both ordinary and extraordinary waves. The results indicate a strong dependence on the size of the loop, in contrast to the case of uniaxial dielectric materials. When the loop axis is parallel to the optic axis, the pattern is quite similar to that of uniaxial dielectric materials; however, a significant change in the pattern is observed when the optic axis turns perpendicular to the loop axis. The results show a significant role of the size of the loop in the hyperbolic material as compared to the uniaxial dielectric material.

Magnetothermally-controllable coating for scattering and absorption in the terahertz spectral regime

Plane-wave scattering and absorption characteristics of a spherical core composed of an isotropic material, and covered by InSb spherical coating are investigated in the terahertz spectral regime. The InSb coating is subjected to a magnetostatic field; hence it is a gyrotropic, uniaxial dielectric material comprised of two parameters: temperature and magnetostatic field. It is seen that the interplay of these two parameters can modify the various scattering efficiencies, depending on (i) the frequency of the incident plane wave, (ii) the incident plane-wave orientation with respect to the magnetostatic field's direction, and (iii) the identity of the core material. In particular, for a fixed orientation of the incident plane wave, the impact of the temperature and the magnetostatic field on the total scattering and the backscattering efficiencies becomes more pronounced at higher frequencies, compared to lower frequencies. The absorption efficiency, on the other hand, is strongly dependent upon these two parameters, regardless of the frequency. On fixing the two parameters of InSb, the role of the orientation of the incident plane wave with respect of the magnetostatic field' direction emerges in some spectral regimes for the total scattering and absorption efficiencies, and in high-frequency spectral regimes for the backscattering efficiency. These hold true for dielectric core, as well as for conductive core.

Grating-coupled excitation of high-phase-speed Dyakonov surface waves

Excitation of high-phase-speed Dyakonov surface waves guided by a surface-relief grating made of a uniaxial dielectric material was theoretically studied using the rigorous coupled-wave approach for illumination by p - and/or s -polarized plane waves. The absorptance at a fixed value of the free-space wavelength was plotted against the polar angle of incidence, and absorptance peaks were correlated with the solution of the dispersion equation of the underlying canonical boundary-value problem for Dyakonov-surface-wave propagation. Both p - and s -polarized plane waves can excite the high-phase-speed Dyakonov surface waves. No, one, or multiple excitations of high-phase-speed Dyakonov surface waves are possible, depending upon the structural parameters of the grating. Excitation of a high-phase-speed Dyakonov surface wave as a specular Floquet harmonic also appears possible.

A multiplicity of exceptional compound plasmon-polariton waves

The propagation of compound plasmon-polariton (CPP) waves was investigated for the canonical boundary-value problem involving a metal film sandwiched between a homogeneous uniaxial dielectric material and a periodically nonhomogeneous isotropic dielectric material. Attention was focused upon exceptional CPP waves whose decay in the uniaxial dielectric material is governed by the product of a linear and an exponential function of distance from the uniaxial dielectric/metal interface. For physically realistic constitutive-parameter values, up to three exceptional CPP waves were found to exist, each with different propagation directions and with different wavenumbers, in each quadrant of the interface plane. The number of exceptional CPP waves, and their natures, were found to be sensitive to the period of the nonhomogeneous material, the thickness of the metal, as well as the constitutive properties of all three materials involved.

High-phase-speed Dyakonov surface waves

The canonical boundary-value problem for Dyakonov-surface-wave propagation in a fixed direction guided by the planar interface of a uniaxial dielectric material and an isotropic nondissipative dielectric material was solved. Both partnering materials were taken to be homogeneous and the constitutive parameters for both to lie within the ranges of available materials. Solutions were found for which the phase speed of the Dyakonov surface wave is greater than the phase speed of a plane wave in the bulk isotropic partnering material.

Exceptional compound plasmon–polariton waves guided by a metal film embedded in a uniaxial dielectric material

The canonical boundary-value problem for the propagation of compound plasmon–polariton (CPP) waves, guided by a symmetric structure comprising a metal film embedded in a uniaxial dielectric material, was formulated and solved. In addition to unexceptional CPP waves whose field strength, in the dielectric material, decays exponentially with distance from the nearest dielectric/metal interface, this structure can also guide exceptional CPP waves whose fields, in the dielectric material, decay as the product of a linear function and an exponential function of distance from the nearest dielectric/metal interface. An explicit solution for exceptional CPP-wave propagation was derived and spatial field profiles for exceptional CPP waves were computed. At most, two exceptional CPP waves were found to propagate in two different directions within each quadrant of the interfacial plane.

Two Dyakonov\u2013Voigt surface waves guided by a biaxial\u2013isotropic dielectric interface

Electromagnetic surface waves guided by the planar interface of an orthorhombic dielectric material and an isotropic dielectric material were analyzed theoretically and numerically. Both naturally occurring minerals (crocoite, tellurite, and cerussite) and engineered materials were considered as the orthorhombic partnering material. In addition to conventional Dyakonov surface waves, the analysis revealed that as many as two Dyakonov–Voigt surface waves can propagate in each quadrant of the interface plane, depending upon the birefringence of the orthorhombic partnering material. The coexistence of two Dyakonov–Voigt surface waves marks a fundamental departure from the corresponding case involving the planar interface of a uniaxial dielectric material and an isotropic dielectric material for which only one Dyakonov–Voigt surface wave is possible. The two Dyakonov–Voigt surface waves propagate in different directions in each quadrant of the interface plane, with different relative phase speeds and different penetration depths. Furthermore, the localization characteristics of the two Dyakonov–Voigt surface waves at the planar interface are quite different: the Dyakonov–Voigt surface wave with the higher relative phase speed is much less tightly localized at the interface in the isotropic dielectric partnering material.

Theory of Dyakonov–Tamm surface waves featuring Dyakonov–Tamm–Voigt surface waves

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 χ 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 χ=0°, a solitary DTV solution exists for a unique propagation direction on a DT solution branch and should be regarded as the manifestation of an exceptional point. No DTV solutions exist if χ>0°. As the degree of nonhomogeneity of material B decreases, the number of DT solution branches decreases. For most propagation directions in the interface plane, no solutions exist in the limiting case wherein the degree of nonhomogeneity approaches zero; but one solution persists provided that the direction of propagation falls within the angular existence domain of the corresponding Dyakonov surface wave.

On Dyakonov–Voigt surface waves guided by the planar interface of dissipative materials

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.

Closed-form expressions for electromagnetic waves generated by a current loop in a uniaxial dielectric medium in the far zone

The radiations by a current loop in an unbounded uniaxial dielectric material with uniform current distribution are studied. The closed-form expressions for the radiation in the far zone are found using the dyadic Green functions in the frequency domain. Analytical results are obtained when the axis of the loop is parallel to the optic axis and when it is perpendicular to the optic axis. Only ordinary waves are emitted when the axis of the loop is parallel to the optic axis. When the axis of the loop is perpendicular to the optic axis, both the ordinary and the extraordinary waves are emitted. The results for different radii of the loop show that the radiation pattern strongly depends upon the size of the loop.

Simultaneous existence of amplified and attenuated surface-plasmon-polariton waves

The propagation of surface-plasmon-polariton (SPP) waves guided by the planar interface of (1) an isotropic metal and (2) an active uniaxial dielectric material was theoretically investigated, under the assumption that the optic axis of the uniaxial partnering material lies wholly in the interface plane. The uniaxial partnering material was conceptualized as a homogenized composite material (HCM) arising from both non-dissipative and active component materials. For a certain range of the volume fraction of the active component material, the SPP waves propagating in certain directions in the interface plane are amplified, but the SPP waves propagating in other directions are attenuated. In a critical propagation direction, the SPP wave is neither amplified nor attenuated. This critical propagation direction was found to be acutely sensitive to the composition of the HCM.

Equivalence principle algorithm using characteristic basis functions with application to finite periodic arrays including uniaxial dielectrics and conducting objects

In this paper, an equivalence principle algorithm combined with the characteristic basis function (CBF) method has been developed to efficiently analyze the finite periodic arrays composed of uniaxial dielectric materials and conducting objects. Three kinds of the CBFs for each equivalent surface and its surrounding object are simultaneously constructed using multiple plane wave illuminations and singular value decomposition technique, and thus memories related to the scattering and translation operators are significantly saved, while retaining good computational accuracy. Numerical results of a frequency selective conducting array, a uniaxial dielectric cube array, and a periodic array of the composite object including a uniaxial rod and a split ring resonator are given to illustrate good performance of proposed method.

Photorealistic ray tracing of free-space invisibility cloaks made of uniaxial dielectrics

The design rules of transformation optics generally lead to spatially inhomogeneous and anisotropic impedance-matched magneto-dielectric material distributions for, e.g., free-space invisibility cloaks. Recently, simplified anisotropic non-magnetic free-space cloaks made of a locally uniaxial dielectric material (calcite) have been realized experimentally. In a two-dimensional setting and for in-plane polarized light propagating in this plane, the cloaking performance can still be perfect for light rays. However, for general views in three dimensions, various imperfections are expected. In this paper, we study two different purely dielectric uniaxial cylindrical free-space cloaks. For one, the optic axis is along the radial direction, for the other one it is along the azimuthal direction. The azimuthal uniaxial cloak has not been suggested previously to the best of our knowledge. We visualize the cloaking performance of both by calculating photorealistic images rendered by ray tracing. Following and complementing our previous ray-tracing work, we use an equation of motion directly derived from Fermat's principle. The rendered images generally exhibit significant imperfections. This includes the obvious fact that cloaking does not work at all for horizontal or for ordinary linear polarization of light. Moreover, more subtle effects occur such as viewing-angle-dependent aberrations. However, we still find amazingly good cloaking performance for the purely dielectric azimuthal uniaxial cloak.

Surface Integral Equation Solutions for Modeling 3-D Uniaxial Media Using Closed-Form Dyadic Green's Functions

In this paper, a method of moments (MoM) implementation of surface integral equations (SIEs) is presented for uniaxial dielectric materials using closed-form dyadic Green's functions. The standard Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) SIE is adapted for homogeneous uniaxial materials. A challenge in the implementation was the evaluation of the self impedance matrix elements and singularities due to the distinguished axis of the uniaxial media. For validation, bistatic scattering patterns of uniaxial targets are computed and compared with the well-known finite-element boundary integral (FE-BI) method solutions. A parametric study of the radiation by dipoles placed within high-contrast uniaxial layers is also presented for various distinguished axis orientations.

A Measurement Process to Characterize Natural and Engineered Low-Loss Uniaxial Dielectric Materials at Microwave Frequencies

We present a measurement method to characterize low-loss engineered materials and natural uniaxial dielectrics. Our approach employs a rectangular cavity coupled with tailored finite-element simulations to accurately determine the permittivity tensors and loss tangents of material assemblies. Although similar approaches for natural crystals have been reported, this is the first time this method is adapted to engineered metamaterials. Loss-tangent measurements with an accuracy of 4-5 significant digits can be achieved by this simple and effective measurement approach. To demonstrate the method, we characterize a layered barium titanate-alumina stack and show that low-loss engineered crystals can be achieved via a proper choice of a bonding agent.

Mie scattering by a uniaxial anisotropic sphere

The field solution to the electromagnetic scattering of a plane wave by a uniaxial anisotropic sphere is obtained in terms of a spherical vector wave function expansion form. Using the source-free Maxwell's equations for uniaxial anisotropic media and making the Fourier transform of the field quantities, the electromagnetic fields in the spectral domain in uniaxial anisotropic media are assumed to have a form similar to the plane wave expanded also in terms of the spherical vector wave functions. Applying the continuous boundary conditions of electromagnetic fields on the surface between the air region and uniaxial anisotropic sphere, the coefficients of transmitted fields and the scattered fields in uniaxial anisotropic media can be obtained analytically in the expansion form of vector wave eigenfunctions. Numerical results for some special cases are obtained and compared with those of the classical Lorenz-Mie theory and the method of moments accelerated with the conjugate-gradient fast-Fourier-transform approach. We also present some new numerical results for the more general uniaxial dielectric material media.

T-matrix Approach for Calculating the Electromagnetic Fields Diffracted by a Corrugated, Anisotropic Grating

Abstract The diffraction of electromagnetic plane waves incident on a corrugated grating made of a uniaxial dielectric material is studied using a fully vectorial treatment based on a T-matrix approach and the Rayleigh hypothesis. The optic axis is considered parallel to the mean surface of the periodic interface. The theory is exemplified numerically for the case of sinusoidal gratings made of sodium nitrate.