arXiv subjects
Publications and source records attributed to Tom G. Mackay.
Establishing the constitutive parameters of a nonhomogeneous bianisotropic medium that is equivalent to the spacetime metric of a spinning cosmic string, in a noncovariant formalism, we found a metamaterial route to investigate the existence of closed timelike curves.
Via exploitation of surface plasmon polaritons (SPPs), columnar thin films (CTFs) are attractive potential platforms for optical sensing as their relative permittivity dyadic and porosity can be tailored to order. Nanoscale model parameters of a CTF were determined from its measured relative permittivity dyadic, after inverting the Bruggeman homogenization formalism. These model parameters were then used to determine the relative permittivity dyadic of a fluid-infiltrated CTF. Two boundary-value problems were next solved: the first relating to SPP-wave propagation guided by the planar interface of a semi-infinitely thick metal and a semi-infinitely thick CTF, and the second to the plane-wave response of the planar interface of a finitely thick metallic layer and a CTF in a modified Kretschmann configuration. Numerical studies revealed that SPP waves propagate at a lower phase speed and with a shorter propagation length, if the fluid has a larger refractive index. Furthermore, the angle of incidence required to excite an SPP wave in a modified Kretschmann configuration increases as the refractive index of the fluid increases.
A dielectric columnar thin film (CTF), characterized macroscopically by a relative permittivity dyadic, was investigated theoretically with the assumption that, on the nanoscale, it is an assembly of parallel, identical, elongated ellipsoidal inclusions made of an isotropic dielectric material that has a different refractive index from the bulk material that was evaporated to fabricate the CTF. The inverse Bruggeman homogenization formalism was developed in order to estimate the refractive index of the deposited material, one of the two shape factors of the ellipsoidal inclusions, and the volume fraction occupied by the deposited material, from a knowledge of relative permittivity dyadic of the CTF. A modified Newton--Raphson technique was implemented to solve the inverse Bruggeman equations. Numerical studies revealed how the three nanoscale parameters of CTFs vary as functions of the vapour incidence angle.
The refraction of linearly polarized plane waves into a half-space occupied by a material moving at constant velocity was studied by directly implementing the Lorentz transformations of electric and magnetic fields. From the perspective of a co-moving observer, the moving material was a spatially local, pseudochiral omega material. Numerical studies revealed that whether or not negative refraction occurrs in the moving material depends upon the speed of movement as well as the angle of incidence and the polarization state of the incident plane wave. Furthermore, the phenomenons of negative phase velocity and counterposition in the moving material were similarly found not to be Lorentz covariant; both phenomenons were also found to be sensitive to the angle of incidence and the polarization state of the incident plane wave.
The planewave response of a linear passive material generally cannot be characterized by a single scalar refractive index, as directionality of energy flow and multiple wavevectors may need to be considered. This is especially significant for materials which support negative refraction, negative phase velocity, and counterposition. By means of a numerical example based on a commonly studied bianisotropic material, our theoretical investigation revealed that: (i) negative (positive) refraction can arise even though the phase velocity is positive (negative); (ii) counterposition can arise in instances of positive and negative refraction; (iii) the phase velocity and time-averaged Poynting vectors can be mutually orthogonal; and (iv) whether or not negative refraction occurs can depend upon the state of polarization and angle of incidence. A further numerical example revealed that negative phase velocity and positive refraction can co-exist even in a simple isotropic dielectric material.
The Lorentz transformations of electric and magnetic fields were implemented to study (i) the refraction of linearly polarized plane waves into a half-space occupied by a uniformly moving material, and (ii) the traversal of linearly polarized Gaussian beams through a uniformly moving slab. Motion was taken to occur tangentially to the interface(s) and in the plane of incidence. The moving materials were assumed to be isotropic, homogeneous, dissipative dielectric materials from the perspective of a co-moving observer. Two different moving materials were considered: from the perspective of a co-moving observer, material A supports planewave propagation with only positive phase velocity, whereas material B supports planewave propagation with both positive and negative phase velocity, depending on the polarization state. For both materials A and B, the sense of the phase velocity and whether or not counterposition occurred, as perceived by a nonco-moving observer, could be altered by varying the observer's velocity. Furthermore, the lateral position of a beam upon propagating through a uniformly moving slab made of material A, as perceived by a nonco-moving observer, could be controlled by varying the observer's velocity. In particular, at certain velocities, the transmitted beam emerged from the slab laterally displaced in the direction opposite to the direction of incident beam. The transmittances of a uniformly moving slab made of material B were very small and the energy density of the transmitted beam was largely concentrated in the direction normal to the slab, regardless of the observer's velocity.
The Maxwell Garnett and Bruggeman formalisms were applied to estimate the effective permittivity dyadic of active dielectric composite materials. The active nature of the homogenized composite materials (HCMs) arises from one of the component materials which takes the form of InAs/GaAs quantum dots. Provided that the real parts of the permittivities of the component materials have the same sign, the Maxwell Garnett and Bruggeman formalisms give physically plausible estimates of the HCM permittivity dyadic that are in close agreement. However, if the real parts of the permittivities of the component materials have different signs then there are substantial differences between the Bruggeman and Maxwell Garnett estimates. Furthermore, these differences becomes enormous--with the Bruggeman estimate being physically implausible--as the imaginary parts of the permittivities of the component materials tend to zero.
The strong-property-fluctuation theory (SPFT) provides a general framework for estimating the constitutive parameters of a homogenized composite material (HCM). We developed the elastodynamic SPFT for orthotropic HCMs, in order to undertake numerical studies. A specific choice of two-point covariance function - which characterizes the distributional statistics of the generally ellipsoidal particles that constitute the component materials - was implemented. Representative numerical examples revealed that the lowest-order SPFT estimate of the HCM stiffness tensor is qualitatively similar to the estimate provided by the Mori-Tanaka mean-field formalism, but the differences between the two estimates vary as the orthotropic nature of the HCM is accentuated. The second-order SPFT provides a correction to the lowest-order estimate of the HCM stiffness tensor and density. The correction, indicating effective dissipation due to scattering loss, increases as the HCM becomes less orthotropic but decreases as the correlation length becomes smaller.
The linear strong--property--fluctuation theory (SPFT) was developed in order to estimate the constitutive parameters of certain homogenized composite materials (HCMs) in the long--wavelength regime. The component materials of the HCM were generally orthorhombic $mm2$ piezoelectric materials, which were randomly distributed as oriented ellipsoidal particles. At the second--order level of approximation, wherein a two--point correlation function and its associated correlation length characterize the component material distributions, the SPFT estimates of the HCM constitutive parameters were expressed in terms of numerically--tractable two--dimensional integrals. Representative numerical calculations revealed that: (i) the lowest--order SPFT estimates are qualitatively similar to those provided by the corresponding Mori--Tanaka homogenization formalism, but differences between the two estimates become more pronounced as the component particles become more eccentric in shape; and (ii) the second--order SPFT estimate provides a significant correction to the lowest--order estimate, which reflects dissipative losses due to scattering.
In a long wavelength regime, the effective properties of particulate composites, including nanocomposites, may be estimated using one of various homogenization formalisms, such as the Bruggeman and Maxwell Garnett formalisms, and the approach of the strong--property--fluctuation theory (SPFT). In the conventional implementations of these formalisms, the constituent particles are treated as point--like scattering centres. However, extended formalisms have been established--which involve integral formulations--that take account of the spatial extent of the constituent particles. In particular, the extended second--order SPFT takes account of both the size of the constituent particles and their statistical distributions. We derive explicit representations of the extended second--order SPFT appropriate to isotropic chiral and uniaxial dielectric homogenized composite mediums. These results may also be employed in extended versions of the Bruggeman and Maxwell Garnett formalisms.
The dyadic Green functions for a uniaxial dielectric-magnetic medium, together with a reversible field transformation, were implemented to derive a formulation of the Huygens principle appropriate to a uniaxial dielectric-magnetic medium with gyrotropic-like magnetoelectric properties.
Describing the phenomenon of total internal reflection in terms of a reflection coefficient of unit magnitude, we found that, not only can propagating plane waves be total internally reflected at the planar interface of two dissimilar, homogeneous, isotropic dielectric-magnetic mediums, but evanescent plane waves can also be. The refracting medium must be the optically denser of the two mediums for total internal reflection of an evanescent plane wave to occur.
Two choices are possible for the refractive index of a linear, homogeneous, isotropic, active, dielectric material. Either of the choices is adequate for obtaining frequency-domain solutions for (i) scattering by slabs, spheres, and other objects of bounded extent; (ii) guided-wave propagation in homogeneously filled, cross-sectionally uniform, straight waveguide sections with perfectly conducting walls; and (iii) image formation due to flat lenses. The correct choice does matter for the half-space problem, but that problem is not realistic.
The four wavenumbers associated with planewave propagation in a Faraday chiral medium (FCM) with relatively huge magnetoelectric coupling give rise to enhanced possibilities for negative-phase-velocity propagation and therefore negative refraction. They can also give rise to the phenomenon of negative reflection. In particular, for a nondissipative example, we deduced that an incident plane wave with positive/negative phase velocity can result in a negatively reflected plane wave with negative/positive phase velocity, as well as a positively reflected plane wave with positive/negative phase velocity.
The strong-property-fluctuation theory (SPFT) provides a sophisticated means of estimating the effective constitutive parameters of a homogenized composite material (HCM), which takes account of the statistical distribution of the component particles. We present an extended version of the third-order SPFT in which the component particles are represented as depolarization regions of nonzero volume. Numerical results are provided for a bianisotropic homogenization scenario wherein the HCM is a Faraday chiral medium. Thereby, convergence of the extended SPFT at the second-order level of approximation is demonstrated within the long-wavelength regime.
The refractive index of a dielectric medium comprising both passive and inverted components in its permittivity was determined using two methods: (i) in the time domain, a finite-difference algorithm to compute the frequency-domain reflectance from reflection data for a pulsed plane wave that is normally incident on a dielectric half-space, and (ii) in the frequency domain, the deflection of an obliquely incident Gaussian beam on transmission through a dielectric slab. The dielectric medium was found to be an active medium with a negative real part for its refractive index. Thereby, a recent controversy in the scientific literature was resolved.
Analysis of electromagnetic planewave propagation in a medium which is a spatiotemporally homogeneous, temporally nonlocal, isotropic, chiral medium in a co-moving frame of reference shows that the medium is both spatially and temporally nonlocal with respect to all non-co-moving inertial frames of reference. Using the Lorentz transformations of electric and magnetic fields, we show that plane waves which have positive phase velocity in the co-moving frame of reference can have negative phase velocity in certain non-co-moving frames of reference. Similarly, plane waves which have negative phase velocity in the co-moving frame can have positive phase velocity in certain non-co-moving frames.
The phase velocity of light is co-parallel to the direction of energy flow in classical vacuum. However, in certain uncommon materials, these two vectors can be oppositely directed, in which case the phase velocity is termed `negative'. This negative phase velocity (NPV) gives rise to many exotic phenomenons, such as negative refraction, inverse Doppler shift and inverse Cerenkov radiation, and has technological allure. According to quantum electrodynamics, the presence of a magnetostatic field makes vacuum an anisotropic medium for the passage of light. Under the influence of a sufficiently strong magnetostatic field, vacuum supports NPV. Such ultrastrong magnetic fields are believed to arise due to dynamo action in newborn neutron stars and in binary neutron star mergers, for examples. In view of the possible occurrence of negative refraction, the influence of ultrastrong magnetostatic fields must be carefully taken into account in astronomical observations relating to neutron stars and associated gamma-ray bursts.