Werner S. Weiglhofer

The negative index of refraction demystified

We study electromagnetic wave propagation in media in which the effective relative permittivity and the effective relative permeability are allowed to take any value in the upper half of the complex plane. A general condition is derived for the phase velocity to be oppositely directed to the power flow. That extends the recently studied case of propagation in media for which the relative permittivity and relative permeability are both simultaneously negative, to include dissipation as well. An illustrative case study demonstrates that in general the spectrum divides into five distinct regions.

On Light Propagation in Helicoidal Bianisotropic Mediums

We have shown liquid crystals to be members of the more general class of helicoidal bianisotropic mediums (HBMs) and have discussed physical realizations of HBMs as liquid crystals, cross-linked polymer networks and solid thin films. Solutions of the time-harmonic Maxwell postulates for axial propagation in a HBM have been derived in terms of the eigenvalues and eigenvectors of a 4 x 4 matrix. We have given a procedure to obtain the response of a HBM slab to a normally incident plane wave and exemplified our analytical results by application to four mediums.

MAXWELL GARNETT AND BRUGGEMAN FORMALISMS FOR A PARTICULATE COMPOSITE WITH BIANISOTROPIC HOST MEDIUM

We present here the application of Maxwell Garnett and Bruggeman formalisms to homogenize very general bianisotropic-in-bianisotropic particulate composites, assuming the inclusion particles to be ellipsoidal.

Are linear, nonreciprocal, biisotropic media forbidden?

Using a covariance argument due to Post (1962) for linear media, it is shown that biisotropic media must be reciprocal in electromagnetic theory. >

Analytic methods and free‐space dyadic Green's functions

A number of mathematical techniques are presented which have proven successful in obtaining analytic solutions to the differential equations for the dyadic Greens functions of electromagnetic theory. The emphasis is on infinite-medium (or free-space) time-harmonic solutions throughout, thus putting the focus on the physical medium in which the electromagnetic process takes place. The mediums properties enter Maxwells equations through the constitutive relations, and a comprehensive listing of dyadic Greens functions for which closed-form solutions exist, is given. Presently, the list of media contains (achiral) isotropic, biisotropic (including chiral), generally uniaxial, electrically (or magnetically) gyrotropic, diffusive and moving media as well as certain plasmas. A critical evaluation of the achievements, successes, limits, and failures of the analytic techniques is provided, and a prognosis is put forward about the future place of analytic methods within the general context of the search for solutions to electromagnetic field problems.

Further results on light propagation in helicoidal bianisotropic mediums: oblique propagation

The recent fabrication of thin-film helicoidal bianisotropic mediums (HBMs) has created an impetus for understanding their electromagnetic response. Using the Oseen transformation, we have derived a 4×4 matrix ordinary differential equation for oblique (i.e. non–axial) propagation in general linear HBMs. A perturbational technique is presented for almost-axial propagation; and two other techniques—one semi–analytic and the other analytic—are presented for general oblique propagation. All three techniques yield exact closed-form results for axial propagation. Our use of the Oseen transformation amounts to viewing oblique propagation not by itself but as a graft on axial propagation, and is thus responsible for the stability of all three techniques.

Electromagnetic depolarization dyadics and elliptic integrals

Depolarization dyadics are essential for the characterization of electromagnetic fields in source regions. As such they are key ingredients in the formulation of homogenization theories of composite media. Explicit expressions for the depolarization dyadics for a biaxial dielectric anisotropic medium (encompassing orthorhombic, monoclinic and triclinic crystallographic classes) are presented here. The results are expressed in terms of elliptic functions of the first and second kind.

Homogenisation of similarly oriented, metallic, ellipsoidal inclusions using the bilocally approximated strong-property-fluctuation theory

The homogenisation of a two-phase composite medium comprising metallic, ellipsoidal inclusions embedded in a non-conducting host medium is carried out via the bilocally approximated strong-property-fluctuation theory. Comparison is made against the results obtained via the Bruggeman formalism. The correlated actions of neighbouring inclusions result in a considerable mitigation of the percolation threshold anisotropy due to inclusion shape alone. Furthermore, the choice of covariance function may only have a secondary influence in relation to the effects of the correlation length.

Lorentz covariance, Occam's razor, and a constraint on linear constitutive relations

Abstract The constitutive relations of a spatially and temporally non-local linear medium are shown to be constrained by the structure of modern electromagnetic theory. A constraint reflecting this fact is derived by resorting to the Lorentz covariance of the Maxwell postulates as well as by using Occams razor to arrive at a parsimonious description of general linear media.

Incremental and differential Maxwell Garnett formalisms for bi-anisotropic composites

Abstract We present, compare and contextualize two approaches to the homogenization of bi-anisotropic-in-bi-anisotropic particulate composite medias: (i) the incremental Maxwell Garnett (IMG) formalism, in which the composite medium is built incrementally by adding the inclusions in N discrete steps to the host medium; and (ii) the differential Maxwell Garnett (DMG) formalism, which is obtained from the IMG in the limit N →∞ . Both formalisms are applicable to arbitrary inclusion concentration and are well-suited for computational purposes. Either of the two formalisms may be used as an alternative to the well-known Bruggeman formalism. Numerical results for the homogenization of a uniaxial dielectric composite medium and of a chiroferrite are presented.