Bianisotropic Media Research Articles

Cylindrical Vector Wave Function Representation of Green's Dyadic in Gyrotropic Bianisotropic Media

This paper presents an eigenfunction expansion of the electric-type dyadic Green's function (DGF) for unbounded gyrotropic bianisotropic media in terms of cylindrical vector wave functions. The DGF is obtained based on the well-known Ohm-Rayleigh method together with dyadic identities formed by the differential, curl and dot product of the constitutive tensors and the cylindrical vector wave functions. Utilization of the dyadic identities greatly simplifies the process of finding the vector expansion coefficients of the DGF for gyrotropic bianisotropic media. The DGF derived is expressed in terms of the contribution from the irrotational vector wave functions and another contribution from the solenoidal vector wave functions, with the λ-domain integrals removed using the residue theorem. This result can be used to characterise electromagnetic waves in gyrotropic bianisotropic media and the idea can be extended to the development of DGF for some other media.

THE THEORY OF UNIAXIAL BI-ANISOTROPIC MEDIA: THE QUASI-STATIC CASE

The problem of unbounded uniaxial bi-anisotropic media in the presence of both static electric and magnetic point charges is investigated. For this purpose scalar electric and magnetic potentials in these media are introduced. Using these potentials, the corresponding electric and magnetic fields are then determined. The similar problem of static electric and magnetic current sources with the goal of finding the electromagnetic fields is carried out. It is observed that either of static electric or magnetic point charge produces both electric and magnetic fields. Furthermore, it is observed that only the transverse components of current sources with respect to axis of the medium produce the axial field components.

CYLINDRICAL VECTOR WAVE FUNCTION REPRESENTATION OF GREEN'S DYADIC IN GYROTROPIC BIANISOTROPIC MEDIA — Abstract

This paper presents an eigenfunction expansion of the electric-type dyadic Green's function (DGF) for unbounded gyrotropic bianisotropic media in terms of cylindrical vector wave functions. The DGF is obtained based on the well-known Ohm-Rayleigh method together with dyadic identities formed by the differential, curl and dot product of the constitutive tensors and the cylindrical vector wave functions. Utilization of the dyadic identities greatly simplifies the process of finding the vector expansion coefficients of the DGF for gyrotropic bianisotropic media. The DGF derived is expressed in terms of the contribution from the irrotational vector wave functions and another contribution from the solenoidal vector wave functions, with the λ-domain integrals removed using the residue theorem. This result can be used to characterise electromagnetic waves in gyrotropic bianisotropic media and the idea can be extended to the development of DGF for some other media.

Comment: Analytical investigation of electromagnetic waves in bianisotropic media

Presents a comment on a paper by Vytovtov (IEE Proc. Microw. Antennas Propag. vol.148, no.4, p.257-60, 2001). Vytovtov examined certain aspects of electromagnetic wave propagation in specific types of linear bianisotropic media. The present comment gives some clarifications, especially with respect to the practical relevance of the considered type of bianisotropy.

Homogenization of Planar Bianisotropic Arrays on the Dielectric Interface

A model for the electromagnetic properties of a dielectric half-space covered by a regular array of planar bianisotropic particles is described. The model allows us to homogenize the structure, presenting it as a half-space covered by a finite-thickness layer of bianisotropic medium. The array particles' mutual coupling is studied within the frame of the assumption of "electric and magnetic dipole," which implies the rather sparse arrays of particles, though the presented approach can be generalized to the case of dense arrays taking into account the higher multipoles. The model is numerically tested for the case of a bianisotropic array in free space.

Electromagnetics and exotic media: a quest for the holy grail

During the past eight years, the authors have extensively studied the properties of linear homogeneous bianisotropic media. They have studied the Green's dyadics, the factorization of the Helmholtz determinant operator, the field and source decomposition, and plane-wave propagation in various classes of these media. We give an overview of our findings, and we place these findings in historical order. The results we found provide insight into the nature of Maxwell's equations, in general, and into the field propagation mechanisms in the different media, in particular. Finally, we mention that closed-form solutions are valuable as benchmarking results for numerical solutions.

Conditions for Circularly Polarized Plane Wave Propagation in a Linear Bianisotropic Medium

Derived here are four conditions that must be satisfied by the constitutive parameters of a linear, homogeneous, bianisotropic medium for it to support the propagation of a circularly polarized plane wave along a fixed axis.

Vector wave function expansions of dyadic Green's functions for bianisotropic media

An alternative set of Cartesian vector wave functions is presented to simplify the development of eigenfunction expansions of electromagnetic fields and dyadic Green's functions for bianisotropic media. With the eigenfields expanded using these functions, the determination of their expansion coefficients is facilitated via a concise 4×4 matrix method. Based on the complete dyadic discontinuity relations, the source consequents of dyadic Green's functions are also explicitly expressed in terms of these functions. By incorporating the modified reciprocity theorem into the discontinuity relations, more compact source consequents are found to be related directly to the eigenfields in a complementary medium. These complementary eigenfields, in turn, can be deduced readily from their original counterparts by performing certain simple transformations. This manner of incorporating reciprocity provides a clear insight into the significance of each discontinuity relation and reveals the connections between the singularities, discontinuities and the complementary eigenfield components. For illustration, the vector wave functions expansions of the eigenfields for isotropic and uniaxial bianisotropic media are discussed.

Onsager-Casimir Principle and the Constitutive Relations of Bi-Anisotropic Media

In this paper we establish relation between the microscopic and macroscopic Onsager-Casimir principles. It is demonstrated that because of certain symmetries with respect to the space reversal operation, which are intrinsic to any form of the linear constitutive relations, it follows that the symmetries under time reversal expressed by the Onsager-Casimir principle are valid both on the microscopic and macroscopic levels. As one of the possible applications we show that the property of the general bi-anisotropic media to be reciprocal or non-reciprocal does not depend on the constitutive formalism.

Wave Equations for Bi-Anisotropic Media in Differential Forms

Differential-form formalism appears to be an ideal tool for electromagnetic analysis because it allows one to express the basic electromagnetic laws in a most compact and elegant form. In fact, the Maxwell equations for the two electromagnetic two-forms are represented by two differential equations of first-order in the simplest possible form. Connection between the two-forms in a homogeneous and time-invariant linear medium is given by a simple algebraic equation. However, constructing the wave equation for a single electromagnetic two-form through elimination appears to be cumbersome and such an equation corresponding to the general bianisotropic medium could not be found in the literature. The present paper gives one possibility for its derivation based on operations in multivector and dyadic algebra. Two special media are considered in more detail leading to wave equations with scalar second-order and factorized fourth-order operators.

Antisymmetric Six-Dyadics and Bi-Anisotropic Media

Novel analytical methods are introduced for antisymmetric six-dyadics which form a linear space of 15 dimensions. By defining new multiplication operations analogous to those of the classical Gibbsian dyadics, algebraic handling of equations is greatly simplified. As an application, time-harmonic electromagnetic fields expressed in concise six-vector form are considered. A certain class of bi-anisotropic media, labeled as A media, is defined for which the six-dyadic Maxwell operator can be expressed in terms of an antisymmetric operator. It is shown that, applying six-dyadic identities, the corresponding antisymmetric six-dyadic Green function can be straightforwardly expressed in explicit form.

Artificial Uniaxial Bianisotropic Media at Oblique Incidence of Electromagnetic Waves

The response of uniaxial bianisotropic slabs to obliquely incident electromagnetic waves is studied, and the exact solution of this boundary-value problem is derived. This includes the calculation of all characteristics of reflected and transmitted waves. The study is relevant to recent experimental studies of arrays of parallel spirals. The present theory gives an analytical model of such artificial bianisotropic media.

Propagation characteristics of a plane wave in an unbounded nonlocal omega medium

AbstractIn this paper, we derive the main propagation characteristics and the polarization properties of plane waves propagating inside a nonlocal bianisotropic medium. An original condition of circular polarizability is also derived and studied. The nonlocal omega medium can, in principle, be thought of as a spreading of a large number of nonlocal omega elements in an otherwise simple isotropic dielectric host medium. A nonlocal omega element is an electrically conducting microstructure having its stem parallel to the electric field at a given point, and its loop axis parallel to the magnetic field at another point that is somewhat displaced from the first along the direction of the wave propagation. © 2002 John Wiley & Sons, Inc. Microwave Opt Technol Lett 32: 183–186, 2002.

Nominal model for structure-property relations of chiral dielectric sculptured thin films

The Bruggeman formalism is implemented to estimate the permittivity dyadics of chiral dielectric sculptured thin films (STFs), called thin-film helicoidal bianisotropic mediums (TFHBMs), modelled as helicoidally arranged stacks of ellipsoidal inclusions in vacuum. Spectral maximums of several observable optical properties of axially excited TFHBM slabs are examined as functions of inclusion shape, volume fraction and orientation. Changes in the transverse aspect ratio of the ellipsoidal inclusions significantly affect the predicted optical properties of the TFHBM. A critical value for the transverse aspect ratio of the ellipsoids can be found such that optical activity disappears when all other parameters are fixed. The orientation of the inclusions significantly affects the value of optical property maximums, and can be made to suppress optical activity completely. A distribution of orientations decreases various measures of optical activity.

Axial electromagnetic wave propagation in inhomogeneous dielectrics

We review the mathematical description of axial propagation in inhomogeneous dielectrics, focusing on two canonical examples: scalar Bragg gratings and thin film helicoidal bianisotropic media (TFHBM). Coupled wave analysis is reviewed for the former, and exact methods based on rotational transforms are discussed for the latter. There are many similarities between the physical descriptions that are emphasised in reviewing the modelling techniques, although the transform which allows the TFHBM case to be solved exactly is shown to be inapplicable in the scalar case.

U‐patch antenna loaded by complex substrates for multifrequency operation

AbstractIn this paper, the analysis of patch antennas with U‐shaped metalization loaded by bianisotropic media is developed. A theoretical study is performed to obtain transmission‐line equations for bianisotropic materials, and then a method‐of‐lines (MoL) procedure is applied to obtain the radiative characteristics. Presented results assure, for particular patch dimensions and feed application geometry, a multifrequency operation in the microwave range, even for isotropic substrates. The application of bianisotropic materials gives better performances for bandwidth and input impedance at the central frequency, but degrades other frequency operation performances. © 2002 John Wiley & Sons, Inc. Microwave Opt Technol Lett 32: 3–5, 2002.

Author's reply to “Comments on ‘Onsager–Casimir Principle and Reciprocity Relations for Bianisotropic Media’”

Ž . Ž . and it is apparent that 15 18 are equivalent to 3 5 . Therefore, there is no difference between the ‘‘dynamical Ž . constitutive symmetry relations,’’ summarized in 1, eq. 6 , Ž . Ž . and the Lorentz adjointness 3 5 . Since these two set of relations are equivalent, we can conclude that both the Lorentz adjointness relations and the macroscopic generalized reciprocity theorem can be derived, as usual, from the Onsager Casimir principle, even in the most general case of a bianisotropic medium.

Comments on “Onsager–Casimir Principle and Reciprocity Relations for Bianisotropic Media”

Comments on “Onsager–Casimir Principle and Reciprocity Relations for Bianisotropic Media”

Cylindrical vector wave function representation of Green's dyadics for uniaxial bianisotropic media

This paper presents a novel and rigorous eigenfunction expansion of electric‐type dyadic Green's function for an unbounded uniaxial bianisotropic medium in terms of the cylindrical vector wave functions. The Green's dyadic is obtained on the basis of the well‐known Ohm‐Rayleigh method together with some newly developed vector and tensor identities formed by the differential, curl, and dot product of the constitutive dyadics and the cylindrical vector wave functions. The above identities greatly simplify the process of finding the vector expansion coefficients of the dyadic Green's function of the uniaxial bianisotropic media. The dyadic Green's function derived is expressed in terms of the contribution from the irrotational solenoidal types of vector wave functions, with the λ integrals removed using the residue theorem.

Beltrami field phasors are eigenvectors of 6×6 linear constitutive dyadics

AbstractWhen the constitutive parameters of a linear, homogeneous, bianisotropic medium are arranged in a certain way as a 6×6 dyadic, it is shown that the eigenvectors of that dyadic may yield admissible Beltrami field phasors whose wavenumbers are directly proportional to the corresponding eigenvalues. © 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 30: 127–128, 2001.