Uniaxial Medium Research Articles

Incremental and differential Maxwell Garnett formalisms for bi-anisotropic composites

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.

Observation of magnetoelectric jones birefringence

In 1948, Jones showed that uniaxial media can in general show four different fundamental optical phenomena, each of which can appear in refraction and absorption. Three of these are well established: isotropic refraction and absorption, linear birefringence and dichroism, and circular birefringence and dichroism. The fourth effect, predicted by Jones, has remained unobserved so far. In this Letter, we report the first experimental observation of this missing fourth, so-called Jones effect, as an additional, tilted linear birefringence. In our experiments, this effect was induced in liquids by parallel external magnetic and electric fields perpendicular to the propagation direction.

Electromagnetic Waves in a Material with Simultaneous Mirror-Conjugated and Racemic Chirality Characteristics

A material combining both mirror-conjugated and racemic chirality properties is characterized and classified within the context of linear bianisotropic mediums. Planewave propagation in the chosen material is studied with particular emphasis on the interaction of different and no handedness along certain specified directions. Comparison is made with isotropic chiral mediums as well as uniaxial bianisotropic mediums.

Dielectric cavity QED between photonic crystals: An effective uniaxial medium approach

The spontaneous-emission rate is evaluated for dipole emitters situated in the thin slab region between two semi-infinite one-dimensionally periodic photonic crystals, a situation reminiscent of planar cavity laser structures. It is pointed out that the long-wavelength electromagnetic fields supported by such complex structures can be directly quantized provided that the pair of semi-infinite photonic crystals are treated within the effective-medium approach, in which each photonic crystal is represented by a truncated uniaxial medium whose dielectric tensor components are determinable in terms of layer thicknesses and dielectric functions of the individual photonic crystal components. The spontaneous-emission rate is evaluated for a dipole emitter situated in the slab region, and oscillating at a frequency resonant with one of the modes that are localized within the slab and exponentially decaying within the photonic crystals. Both symmetric and asymmetric structures are discussed. Interesting features are predicted when the variations of the adjustable parameters are examined, including suppression and enhancement of the spontaneous rate.

Radiative transfer in a plane parallel slab of anisotropic uniaxial semi-transparent medium

The apparent emissivities emerging from an absorbing–emitting grey semi-transparent uniaxial crystal slab, and the temperature and radiative flux fields inside a crystal slab bounded by two black or transparent interfaces at radiative–conductive coupling have been determined with the help of a ray-tracing technique. The exact expressions of the temperature field and the radiative flux field for positive and negative uniaxial crystals have been obtained. Results display a strong influence of the crystal's positivity on the temperature and flux fields when the two boundary surfaces are transparent.

Field representations in general rotationally uniaxial anisotropic media using spherical vector wave functions

Electromagnetic fields in general rotationally uniaxial media are studied. Six components of the fields are solved using the method of separation of variables. By grouping the proper terms, the electromagnetic fields are finally expressed in a very compact form by introducing the modified spherical vector wave functions. The dyadic Green's function in an infinite uniaxial medium is subsequently derived and expanded in terms of the same vector wave functions. It is shown that the expressions of both the fields and the dyadic Green's function are reducible to those of simpler cases. © 2000 John Wiley & Sons, Inc. Microwave Opt Technol Lett 25: 159–162, 2000

Uniqueness in a frequency-domain inverse problem of a stratified uniaxial bianisotropic medium

An inverse problem for a stratified uniaxial bianisotropic slab is considered in the frequency domain. The problem is treated as an analytic factorization problem in the frequency complex plane. Uniqueness in the parameter reconstruction is discussed and illustrated under a particular choice of a priori information.

Investigation of solid state surfaces by non-linear polaritons

The dispersion characteristics of the TM-type non-linear surface electromagnetic waves at the boundary of a magnetoactive semiconductor and a uniaxial non-linear medium (Voigt geometry) have been studied. A new type of wave, i.e. a non-resonance non-linear surface wave, has been revealed. The exact criteria for their existence have been formulated. The means to control their characteristics have been shown and the ranges of multivalues of their dispersion curves have been determined. Calculation of a three-mirror open resonator with a non-linear boundary has been carried out. The domains of the system parameters corresponding to the emergence of unstable solutions have been defined. In addition, their correlation with the surface concentrations and the mobility of the major charge carriers in the semiconductor and the open resonator coupling coefficient with the semiconductor under investigation has been established. The results of experimental studies of the surface characteristics of narrow-gap n-type Cd x Hg 1− x Te samples are discussed.

Optical properties of a deformed short pitch helical structure

We analyse via a homogeneous description the optical properties of a deformed short pitch helical structure, which consists of an uniaxial mesoscopic medium in which the helical axis does not coincide with the direction of periodicity. We find that the effective medium is generally anisotropic, biaxial and gyrotropic. Its dielectric tensor is isotropic only in the limiting case of a proper chiral smectic C at its critical tilt angle.

The Perfectly Matched Layer as a Synthetic Material with Active Inclusions

The perfectly matched layer is a successful concept used in finite difference numerical techniques. It can be also considered as a uniaxial medium whose tensor material parameters are subject to certain requirements. Here we demonstrate that such a medium is in principle physically realizable as a composite material with small inclusions, but the inclusions must be active, which means that they can only be realized as active electronic circuits, e.g., circuits based on operational amplifiers.

Displacement of the refracted wave in presence of inhibited reflection

A displacement of the transmitted wave for a uniaxial crystalisotropic medium interface is found, when the angle of incidence is larger than the limiting inhibited reflection angle. The phenomenon treated is a generalization of the well-known Goos—Hünchen effect [1] which is the longitudinal displacement of the reflected wave associated with total reflection in isotropic interfaces. Nevertheless, because of the crystal anisotropy, the displacement vector here has both a longitudinal and a transverse component even when the incident beam is linearly polarized. Expressions for these components are given and their meaning is analysed

Electromagnetic scattering by a conducting cylinder coatedwith a uniaxial chiral layer of varying thickness: generalized mode-matching method

Based on the concept of characteristic waves and the method of angular spectral expansion, cylindrical vector wave functions are developed to represent the electromagnetic waves in a uniaxial chiral medium. To illustrate how to use the present cylindrical vector wave functions in a practical way, a generalized mode-matching method is proposed to study the electromagnetic scattering of a conducting circular cylinder coated with a uniaxial chiral layer of varying thickness. The excellent convergence property of the bistatic echo width is numerically verified, which establishes the reliability and applicability of the present cylindrical vector wave functions and generalized mode-matching method for a two-dimensional problem with a curved surface coating of a uniaxial chiral medium.

Scattering By an Arbitrarily Shaped Rotationally Uniaxial Anisotropic Object: Electromagnetic Fields and Dyadic Green's Fucntions - Abstract *

The electromagnetic scattering by a three-dimensional arbitrarily shaped rotationally uniaxial anisotropic object is studied. Electromagnetic fields in a uniaxial medium are solved for first using the method of separation of variables, and then expressed in a very compact form by introducing the modified spherical vector wave functions. The equivalence theorem and the T-matrix method are applied in the analysis of the scattering problem. The scattered fields and the dyadic Green's functions both external and internal to the scatterer are derived in terms of spherical vector wave functions and matrix-form coefficients. Through making use of the dyadic Green's functions obtained, numerical results are provided for an incident field excited by an infinitesimal dipole. The scatterers are assumed to be prolate and oblate dielectric spheroids with the rotational z-axis. The angular scattering intensities in far-zone are plotted for all these cases. And some conclusions are also drawn eventually from numerical discussions.

Scattering by an Arbitrarily Shaped Rotationally Uniaxial Anisotropic Object: Electromagnetic Fields and Dyadic Green's Fucntions

The electromagnetic scattering by a three-dimensional arbi- trarily shaped rotationally uniaxial anisotropic object is studied. Elec- tromagnetic fields in a uniaxial medium are solved for first using the method of separation of variables, and then expressed in a very com- pact form by introducing the modified spherical vector wave functions. The equivalence theorem and the T-matrix method are applied in the analysis of the scattering problem. The scattered fields and the dyadic Green's functions both external and internal to the scatterer are de- rived in terms of spherical vector wave functions and matrix-form coef- ficients. Through making use of the dyadic Green's functions obtained, numerical results are provided for an incident field excited by an in- finitesimal dipole. The scatterers are assumed to be prolate and oblate dielectric spheroids with the rotational z-axis. The angular scatter- ing intensities in far-zone are plotted for all these cases. And some conclusions are also drawn eventually from numerical discussions.

On Anomalous Propagation in Transversely Uniaxial Bianisotropic Mediums

We consider the propagation of a plane electromagnetic wave in transversely uniaxial bianisotropic mediums (TUBMS). Anomalous propagation takes place when a certain condition is fulfilled by the constitutive parameters of the medium. A detailed field analysis for this anomalous behaviour is provided.

Numerical treatment of UV-pumped, white-light-seeded single-pass noncollinear parametric amplifiers

A technique for numerically simulating second-order nonlinear interactions of light waves modulated spatially and temporally in both amplitude and phase in a uniaxial medium with arbitrary polarization and propagation directions is presented. A three-dimensional grid technique that automatically adapts grid parameters to the evolving sampled amplitudes by means of an analytical fit function is described. By means of spatiotemporal split-step fast-Fourier-transform propagation, diffraction and group-velocity dispersion can be included. We employ this technique for femtosecond noncollinear white-light-seeded parametric amplification in experimental designs presented earlier [Opt. Lett.22, 1494 (1997); Opt. Lett.23, 1283 (1998)]. The dependence of phase mismatch on signal wavelength provides a quantitative measure of the achromaticity of phase matching. Our results indicate that the pump pulse characteristics and not phase mismatching limit the amplification and the bandwidth of the parametric amplifier.

Electromagnetic scattering by a reciprocal uniaxial bianisotropic cylinder with arbitrary cross section: extended mode-matching method

Based on the eigenfunction expansion of electromagnetic waves in a reciprocal uniaxial bianisotropic medium, an extended mode-matching method is proposed to study the scattering of an infinitely long reciprocal uniaxial bianisotropic cylinder with arbitrary cross section. Excellent convergence of the echo width is numerically verified, which establishes the reliability and applicability of the present extended mode-matching method for the two-dimensional single-body problem in which the reciprocal uniaxial bianisotropic medium has a curved surface.

Vector Wave Functions in Gyromagnetic Uniaxial Chiral Medium and Applications - Abstract

The gyromagnetic uniaxial chiral medium, which is a generalization of the well-studied reciprocal chiral material, can be created by mixing three sets of small metal helices in a host gyromagnetic medium (e.g., magnetically biased ferrite), with the axes of two sets perpendicular and parallel to a fixed direction, respectively, and the other set distributed in random orientations and locations. Based on the concept of characteristic waves and the method of angular spectral expansion, vector wave functions are rigorously developed to represent the electromagnetic fields in a source-free gyromagnetic uniaxial chiral medium. The analysis reveals that the solutions of the source-free vector wave equation for the gyromagnetic uniaxial chiral medium, which are composed of two transverse waves and a longitudinal wave, can be represented in sum-integral forms of the cylindrical vector wave functions. Addition theorem of the vector wave functions for gyromagnetic uniaxial chiral medium can be directly obtained from its counterpart for isotropic medium. To apply the present formulations for practical applications, an extended mode-matching method is proposed to study the two-dimensional electromagnetic scattering of a gyromagnetic uniaxial chiral cylinder with arbitrary cross section and a conducting circular cylinder with an inhomogeneous coating thickness. To check the convergence of the present cylindrical vector wave functions for multiple-body problem, electromagnetic scattering of two circular cylinders of gyromagnetic uniaxial chiral media is also investigated. Excellent convergence properties of the cylindrical vector wave functions in these application examples are numerically verified, which

Electric dipole fields over an anisotropic seafloor: theory and application to the structure of 40Ma Pacific Ocean lithosphere

Seismic anisotropy has been detected in the oceanic crust and upper mantle, and likewise it is geologically reasonable to expect that a certain amount of lateral anisotropy exists in seafloor electrical properties. Anisotropy in Earth properties can often lead to surprising effects on geophysical responses that are not anticipated from simple isotropic theories. Here, we investigate the effects of lateral anisotropy on the frequency-domain, controlled-source electromagnetic (CSEM) response of a uniaxially conducting, non-magnetic seafloor excited by a horizontal electric dipole whose moment is oriented obliquely with respect to the electrical strike direction. A ‘paradox of anisotropy’ is observed, in which the seafloor electric field strength is enhanced in the most conductive direction of the seafloor. This enhancement is opposite to what one would expect based on naive isotropic theory. We also show that it is possible in certain circumstances to extract the along-strike electrical conductivity from marine controlled-source electromagnetic data using only isotropic modelling. The extraction of across-strike conductivity, however, requires full anisotropic modelling. The physical insight into electromagnetic induction in uniaxial media that is presented here should greatly assist the geological interpretation of marine CSEM experimental data. Applying our algorithm to the PEGASUS data set (CSEM data collected over 40Ma Pacific Ocean lithosphere) produces a model with conductivity in the fossil spreading direction that is seven × greater than the conductivity perpendicular to spreading. Strain-aligned mineralogical fabric, as predicted by tectonic modelling, would explain our result, with enhanced conductivities caused by hydrogen conduction along the olivine a-axis or connected accumulations of trace conductors such as graphite or magnetite.

On Anomalous Propagation in Axially Uniaxial Bianisotropic Mediums

Propagation of a plane electromagnetic wave in axially uniaxial bianisotropic mediums (AUBMs) is investigated. It is shown that anomalous behaviour arises when a certain condition is fulfilled by the constitutive parameters of the medium.