Bianisotropic Slab Research Articles

Electromagnetic characterization of strong-coupled Omega-type bianisotropic metamaterials using the state transition matrix method

A feasible extraction procedure is proposed to retrieve the diagonal tensor elements of the permittivity and permeability, and the magnetoelectric coupling coefficient of Omega-type biansiotropic metamaterials (MMs). The procedure is based on the state transition matrix approach and uses non-iterative closed-form expressions between constitutive parameters and scattering (S-) parameters to achieve such determination using S-parameters for normal incidence and oblique incidence of TE and TM modes (a desirable feature from practical point of view). S-parameter simulations of a bianisotropic MM slab constructed by edge-coupled resonators are performed using a 3D electromagnetic simulator program and used to validate the proposed procedure and compare its accuracy against previously developed extraction procedures. The effects of incidence angle, S-parameters' noise, and dimensional variations (fabrication tolerances) on the extracted parameters of the examined MM slab are investigated.

Finite element modeling of electromagnetic properties in photonic bianisotropic structures.

Given a constitutive relation of the bianisotropic medium, it is not trivial to study how light interacts with the photonic bianisotropic structure due to the limited available means of studying electromagnetic properties in bianisotropic media. In this paper, we study the electromagnetic properties of photonic bianisotropic structures using the finite element method. We prove that the vector wave equation with the presence of bianisotropic is self-adjoint under scalar inner product. we propose a balanced formulation of weak form in the practical implementation, which outperforms the standard formulation in finite element modeling. Furthermore, we benchmark our numerical results obtained from finite element simulation in three different scenarios. These are bianisotropy-dependent reflection and transmission of plane waves incident onto a bianisotropic slab, band structure of bianisotropic photonic crystals with valley-dependent phenomena, and the modal properties of bianisotropic ring resonators. The first two simulated results obtained from our modified weak form yield excellent agreements either with theoretical predictions or available data from the literature, and the modal properties in the last example, i.e., bianisotropic ring resonators as a polarization-dependent optical insulator, are also consistent with the theoretical analyses.

Casimir forces on a bi-anisotropic absorbing magneto-dielectric slab between two parallel conducting plates

A fully canonical quantization of electromagnetic field in the presence of a bi-anisotropic absorbing magneto-dielectric slab is demonstrated. The electric and the magnetic polarization densities of the magneto-dielectric slab are defined in terms of the dynamical variables modeling the slab and the coupling tensors that couple the electromagnetic field to the slab. The four susceptibility tensors of the bi-anisotropic magneto-dielectric slab are expressed in terms of the coupling tensors that couple an electromagnetic field to the slab. It is shown that the four susceptibility tensors of the bi-anisotropic magneto-dielectric slab satisfy Kramers–Kronig relations. The Maxwell’s equations are exactly solved in the presence of the bi-anisotropic magneto-dielectric slab. The tangential and the normal components of the Casimir forces exerted on the bi-anisotropic magnet-dielectric slab exactly are calculated in the vacuum state and thermal state of the total system. It is shown that the tangential components of the Casimir forces vanish when the bi-anisotropic slab is converted to an isotropic slab.

Reflection/transmission calculation of complex particle slabs for normal incidence through dipole approximation

The computation of the reflection/transmission coefficients from normally illuminated bianisotropic metamaterial slabs through a rigorous method is presented in this paper. The bianisotropic particles that compose finite slabs are approximated as electric and magnetic dipoles. Modeling these slabs as a succession of 2D arrays, the interaction of all dipoles is described via Green’s function series, for a given wave illumination on each array, and the excited dipole moments are obtained by the resulting linear system. Finally, the reflection/transmission coefficients are derived in terms of summing the scattering from the equivalent surfaces that comprise the slab. The new algorithm is applied to a bianisotropic and a complicated chiral particle, while all results are compared to numerically simulated ones.

Scattering parameter analysis of cascaded bi-anisotropic metamaterials

Forward and backward reflection and transmission scattering (S-) parameters of a metamaterial (MM) structure of bi-anisotropic slabs in cascade are analyzed. Signal flow graph technique is applied in this analysis for a cascaded connection of two and three bi-anisotropic MM slabs with different orientations. We also investigated effects of geometrical parameters (fabrication tolerances) of individual MM cells on forward and backward reflection and transmission S-parameters of cascade connection of MM cells. We note from our analysis the following important points. First, forward and backward reflection S-parameters become equal to one another for a MM structure composed of an even number of bi-anisotropic MM slabs (individually characterized by non-identical forward and backward reflection S-parameters) with proper orientations only if there exists symmetry of the structure in the propagation direction. Second, it is noted that it is not possible to obtain identical forward and backward reflection S-parameters of a MM structure composed of an odd number of bi-anisotropic MM slabs. Finally, reflection asymmetry (bi-anisotropy) of cascade connection of MM cells generally is enhanced for a change in geometrical parameters of individual MM cells.

Technique for inversion of an inhomogeneous bianisotropic slab through an optimisation approach

An electromagnetic inversion method is presented to reconstruct the constitutive parameters of an inhomogeneous bianisotropic slab. The measured co- and cross-reflection and transmission coefficients are used to extract the electromagnetic parameters profiles of the inhomogeneous bianisotropic media from the proposed method, using truncated Fourier series expansion and Gravitational Search Algorithm (GSA). GSA is used to improve the speed and accuracy of the optimisation process because of the complexity of inhomogeneous bianisotropic media, highly non-linearity of optimisation problem, and extremely large search space. Finally, the accuracy and robustness of the proposed reconstruction method are validated using some typical examples.

Focusing light in a bianisotropic slab with negatively refracting materials

We investigate the electromagnetic response of a pair of complementary bianisotropic media, which consist of a medium with positive refractive index (+ε, +μ, +ξ) and a medium with negative refractive index(−ε, −μ, −ξ). We show that this idealized system has peculiar imaging properties in that it reproduces images of a source, in principle, with unlimited resolution. We then consider an infinite array of line sources regularly spaced in a 1D photonic crystal (PC) consisting of 2n layers of bianisotropic complementary media. Using coordinate transformations, we map this system into 2D corner chiral lenses of 2n heterogeneous anisotropic complementary media sharing a vertex, within which light circles around closed trajectories. Alternatively, one can consider corner lenses with homogeneous isotropic media and map them into 1D PCs with heterogeneous bianisotropic layers. Interestingly, such complementary media are described by scalar, or matrix valued, sign-shifting parameters, which satisfy a new version of the generalized lens theorem of Pendry and Ramakrishna. This theorem can be derived using Fourier series solutions of the Maxwell–Tellegen equations, or from space–time symmetry arguments. Also of interest are 2D periodic checkerboards consisting of alternating rectangular cells of complementary media which are such that one point source in one cell gives rise to an infinite set of images with an image in every other cell. Such checkerboards can themselves be mapped into a class of 3D corner lenses of complementary bianisotropic media. These theoretical results are illustrated by finite element computations.

Metamaterials with custom emissivity polarization in the near-infrared

Metamaterials have been previously studied for their ability to tailor the dispersive infrared (IR) emissivity of a surface. Here, we investigate metamaterial coatings based on an electromagnetic band-gap surface for use as near-IR emitters with custom polarization selectivity. A genetic algorithm is successfully employed to optimize the metamaterial structures to exhibit custom linear, circular, and elliptical polarization. A study is also conducted on a bi-anisotropic slab, showing that anisotropic chirality is required in the metamaterial structure in order to achieve circular or elliptical emissivity polarization.

Experimental Characterization of Chiral Uniaxial Bianisotropic Composites at Microwave Frequencies

This paper presents an experimental procedure for retrieving the effective constitutive parameters of chiral materials. Unlike past research that primarily deals with isotropic materials, this study considers a lossy uniaxial bianisotropic slab with a nonzero chirality along its axial direction. First, plane-wave scattering off the uniaxial slab in a free-space environment is studied analytically. This forward analysis gives insight into the problem and the choice of proper independent measurements required for the inverse process, i.e., retrieving the slab constitutive parameters from its S-parameters. Based on this analysis, three sets of co-polarized and cross-polarized S-parameters are required, including both the transmission and reflection coefficients of the slab. Given the measured scattering data, the complex permittivity, permeability, and chirality tensors are determined numerically using the results of the analytic study. To test the performance of the new retrieval method, an array of 2 × 56 long, metallic helices is designed and fabricated for operation at C-band. Having the same handedness, the helices are closely spaced and held in parallel to each other in a wooden frame in order to create an effective uni-axial chiral medium. A conventional transmission/reflection setup measures the array scattering parameters, which are fed into the retrieval process to obtain the effective parameters. The measured parameters well model the array scattering response, exhibiting a significant averaged chirality of ~0.4 over 5.5-8.7 GHz and a plasmonic behavior at ~7.1GHz.

On interaction of electromagnetic waves with infinite bianisotropic layered slab

AbstractA stratified general bianisotropic medium is considered, consisting of several infinite slabs either between two half‐spaces filled with isotropic material, or grounded. The slab is illuminated by an incident plane wave from one of the half‐spaces. The excited electromagnetic field inside the bianisotropic slab and in the isotropic domains is described. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

OPTIMIZATION APPROACH TO THE RETRIEVAL OF THE CONSTITUTIVE PARAMETERS OF SLAB OF GENERAL BIANISOTROPIC MEDIUM

The reconstruction of the frequency-dispersive constitu- tive parameters of general bianisotropic media is achieved by an opti- mization approach. The constitutive parameters are optimized in order to match the measured reflection and transmission data for plane wave incidence onto bianisotropic slabs. Two optimization methods, in our case the differential evolution (DE) algorithm and the Nelder-Mead simplex method, are used for the reconstruction at low frequencies. The Nelder-Mead simplex method is then used to obtain the solutions at higher frequencies, where the initial guess is obtained by the linear extrapolation of the solutions at previous frequencies. The proposed reconstruction method is tested with both noiseless and noisy data, and is proven feasible and robust.

Time-domain direct and inverse scattering for bi-anisotropic slabs at obliqueincidence

Using the Cayley–Hamilton theorem and unique solubility of scalar Volterraconvolution equations of the second kind, the inverse problem of determiningthe four time-dependent susceptibility dyadics of a linear, homogeneous,bi-anisotropic slab from generic scattering data at oblique incidence isshown to be well posed. An explicit formula for the crucial step is given.

Scattering from a Frequency Selective Surface Supported by a Bianisotropic Substrate

In this paper a method for the analysis of a frequency selective surface (FSS) supported by a bianisotropic substrate is presented. The frequency selective structure is a thin metallic pattern — the actual FSS — on a plane supporting substrate. Integral representations of the fields in combination with the method of moments carried out in the spatial Fourier domain are shown to be a fruitful way of analyzing the problem with a complex substrate. This approach results in a very general formulation in which the supporting substrate can have arbitrary bianisotropic properties. The bianisotropic slab can be homogeneous,stratified, or it can have continuously varying material parameter as a function of depth. The analysis presented in this paper is illustrated in a series of numerical examples. Results for isotropic,anisotropic and bianisotropic substrates are given. (Less)

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.

Scattering From a Frequency Selective Surface Supported By a Bianisotropic Substrate - Abstract

In this paper a method for the analysis of a frequency selective surface (FSS) supported by a bianisotropic substrate is presented. The frequency selective structure is a thin metallic pattern - the actual FSS - on a plane supporting substrate. Integral representations of the fields in combination with the method of moments carried out in the spatial Fourier domain are shown to be a fruitful way of analyzing the problem with a complex substrate. This approach results in a very general formulation in which the supporting substrate can have arbitrary bianisotropic properties. The bianisotropic slab can be homogeneous, stratified, or it can have continuously varying material parameter as a function of depth. The analysis presented in this paper is illustrated in a series of numerical examples. Results for isotropic, anisotropic and bianisotropic substrates are given.

Propagation in bianisotropic media — reflection and transmission

A systematic analysis for solving the wave propagation problem in a general bianisotropic, stratified medium is presented. The method utilises the concept of propagators, and the representation of these operators is simplified by introducing the Cayley–Hamilton theorem. The propagators propagate the total tangential electric and magnetic fields in the slab and only outside the slab do the up- and down-going parts of the fields need to be identified. This procedure makes the physical interpretation of the theory intuitive. The reflection and the transmission dyadics for a general bianisotropic medium with an isotropic (vacuum) half-space on both sides of the slab are presented in a co-ordinate-independent dyadic notation, as well as the reflection dyadic for a bianisotropic slab with perfectly electric backing (PEC). In the latter case the current on the metal backing is also given. Some numerical computations that illustrate the algorithm are presented.

Unbounded and scattered field representations of the Dyadic Green's functions for planar stratified bianisotropic media

This paper presents a rigorous formulation of the spectral-domain dyadic Green's functions for planar stratified bianisotropic media. The media may consist of any number of layers bounded by optional impedance/admittance walls. Both electric and magnetic dyadic Green's functions for arbitrary field and source locations are derived simultaneously. Based on the principle of scattering superposition, these dyadics are decomposed into unbounded and scattered parts. The scattered dyadic Green's functions are determined without cumbersome operations using the concepts of effective reflection and transmission of outward-bounded and inward-bounded waves. The scattering coefficient matrices are expressed in compact and convenient forms involving global reflection and transmission matrices. Corresponding to the impedance/admittance boundary walls, the global reflection matrices are related directly to the wall impedance/admittance dyadics. For illustration, the general expressions of dyadic Green's functions are applied to the configuration of a grounded bianisotropic slab embedded in isotropic halfspace.

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.

Reply to comment on `Reflection and transmission by a uniaxial bi-anisotropic slab under normal incidence of plane waves

This is a reply to the preceding comment by Weiglhofer and Lakhtakia on `Reflection and transmission by a uniaxial bi-anisotropic slab under normal incidence of plane waves' (1998 J. Phys. D: Appl. Phys. 31 2458).

Comment on `Reflection and transmission by a uniaxial bi-anisotropic slab under normal incidence of plane waves

In the detailed numerical study reported in `Reflection and transmission by a uniaxial bi-anisotropic slab under normal incidence of plane waves' by Semchenko et al (1998 J. Phys. D: Appl. Phys. 31 2458), most of the presented results pertain to regions of the constitutive parameter space where, according to the Post constraint, physical materials do not have electromagnetically recognizable existence.