Bianisotropic Scatterers Research Articles

Direct and inverse electromagnetic scattering problems for bi-anisotropic media**This paper is dedicated to the memory of Professor Armin Lechleiter.

This paper is concerned with the direct and inverse scattering of time-harmonic electromagnetic waves from bi-anisotropic media. For the direct problem, we establish an integro-differential equation formulation, its Fredholm property, and the uniqueness of a weak solution. Using this integro-differential formulation we study a fast spectral Galerkin method for the numerical solution to the direct problem. Numerical examples are presented and convergence of the spectral method is proved via Gårding estimates for (strongly singular) integro-differential equations. We solve the inverse problem of recovering bi-anisotropic scatterers from far-field data using orthogonality sampling methods. These methods aim to construct imaging functionals which are robust to noise, computationally cheap, and require data for only one or a few incident fields. We provide some theoretical analysis as well as numerical simulations for the proposed imaging functionals.

Purely bianisotropic scatterers

The polarization response of molecules or meta-atoms to external electric and magnetic fields, which defines the electromagnetic properties of materials, can either be direct (electric field induces electric moment and magnetic field induces magnetic moment) or indirect (magnetoelectric coupling in bianisotropic scatterers). Earlier studies suggest that there is a fundamental bound on the indirect response of all passive scatterers: It is believed to be always weaker than the direct one. In this paper, we prove that there exist scatterers which overcome this bound substantially. Moreover, we show that the amplitudes of electric and magnetic polarizabilities can be negligibly small as compared to the magnetoelectric coupling coefficients. However, we prove that if at least one of the direct-excitation coefficients vanishes, magnetoelectric coupling effects in passive scatterers cannot exist. Our findings open a way to a new class of electromagnetic scatterers and composite materials.

Experimental realisation of all-dielectric bianisotropic metasurfaces

All-dielectric reciprocal metasurface based on bianisotropic scatterers operating at microwave frequencies is demonstrated experimentally. Experimental studies of a single bianisotropic particle supporting both electric and magnetic Mie-type resonances are performed, and reveal that the particle with a broken symmetry exhibits different back-scattering for the opposite excitation directions. A metasurface composed of the all-dielectric bianisotropic particles is fabricated and experimentally investigated in the frequency range of 4–9 GHz. The measured data demonstrate that the metasurface is characterized by different reflection phases when being excited from the opposite directions. At the frequency 6.8 GHz, the metasurface provides a 2π phase change in the reflection spectrum with the amplitude close to 1.

Robust technique for the polarisability matrix retrieval of bianisotropic scatterers via their reflection and transmission coefficients

A consistent algorithm for extracting the polarisability matrix of bianisotropic meta-atoms directly from their reflection and transmission properties is introduced in this study. Considering a two-dimensional periodic distribution of the scatterer under study, illuminated by properly-polarised, normally-incident, plane waves, the point-dipole approximation is successfully applied in order to analytically compute the scattered field of the array in terms of the particle polarisabilities. Then, simulated or measured S-parameters can be employed for the inversion of the resulting non-linear system of equations, leading to the desired dynamic polarisability matrix and, especially, the magneto-electric coupling term. Finally, the featured technique is applied to an assortment of important structures, frequently utilised for various metamaterial applications and the outcomes are extensively compared with previously existing techniques, thus verifying the merits of the novel approach.

Generalized non-local surface susceptibility model and Fresnel coefficients for the characterization of periodic metafilms with bianisotropic scatterers

A non-local surface susceptibility model for the consistent description of periodic metafilms formed by arbitrarily-shaped, electrically-small, bianisotropic scatterers is developed in this paper. The rigorous scheme is based on the point-dipole approximation technique and is valid for any polarization and propagation direction of an electromagnetic wave impinging upon the metafilm, unlike existing approaches whose applicability is practically confined to very specific cases of incidence. Next, the universal form of the resulting surface susceptibility matrix is employed for the derivation of the generalized Fresnel coefficients for such surfaces, which enable the comprehensive interpretation of several significant, yet relatively unexamined, physical interactions. Essentially, these coefficients include eight distinct terms, corresponding to the co-polarized and cross-polarized reflection and transmission coefficients for the two orthogonal eigenpolarizations of a linearly-polarized incident plane wave. The above formulas are, then, utilized for the prediction of the scattering properties of metafilms with different planar and non-planar resonators, which are characterized via the featured model and two previously reported local ones. Their comparison with numerical simulation outcomes substantiates the merits of the proposed method, reveals important aspects of the underlying physics, and highlights the differences between the various modeling procedures.

Consistent Modeling of Periodic Metasurfaces With Bianisotropic Scatterers for Oblique TE-Polarized Plane Wave Excitation

In this paper, a new method for the consistent analysis of periodic metasurfaces with bianisotropic particles is introduced. The proposed technique combines a microscopic modeling approach at the level of the constituting meta-atoms with a macroscopic equivalent surface characterization, to unambiguously determine a set of surface susceptibilities that properly predict the reflection and transmission properties of the metasurface. Comparisons with alternative schemes and full-wave simulation results for bianisotropic scatterers, frequently utilized as building blocks of realistic metasurfaces, are provided in order to validate the featured algorithm.

COMPREHENSIVE SOLUTION TO SCATTERING BY BIANOSOTROPIC OBJECTS OF ARBITRARY SHAPE

This paper presents a method of moments (MoM) solution for the problems of electromagnetic scattering by inhomogeneous three- dimensional bianisotropic scatterers of any shape. The electromagnetic response of bianisotropy has been described by the constitutive relations of the most general form composed of four 3 £ 3 matrices or tensors. The volume equivalence principle is used to obtain a set of mixed potential formulations for a proper description of the original scattering problem. Here, the total flelds are separated into the incident flelds and the scattered flelds. The scattered flelds are related to the electric and magnetic potentials which are excited by electric and magnetic bound charges and polarization currents. The body of the scatterer is meshed through the use of tetrahedral cells with face-based functions used to expand unknown quantities. At last, the Galerkin test method is applied to create a method of moments (MoM) matrix from which the numerical solution is obtained. Implemented in a MATLAB program, the numerical formulation is evaluated and verifled for various types of scatterers. The results are compared with those of previous work, and a good agreement is observed. Finally, a scattering from a two-layered dispersive chiroferrite sphere is presented as the most general example.

Extended discrete dipole approximation and its application to bianisotropic media

In this research we introduce the formalism of the extension of the discrete dipole approximation to a more general range of tensorial relative permittivity and permeability. Its performance is tested in the domain of applicability of other methods for the case of composite materials (nanoshells). Then, some early results on bianisotropic nanoparticles are presented, to show the potential of the Extended Discrete Dipole Approximation (E-DDA) as a new tool for calculating the interaction of light with bianisotropic scatterers.

Electromagnetic Scattering from an Arbitrarily Shaped Three-dimensional Inhomogeneous Bianisotropic Body

This paper presents a numerical solution to scattering problems that involve 3D inhomogeneous bianisotropic scatterers of an arbitrary shape. The constitutive relations are assumed to be of the most general form and composed of four 3 £ 3 matrices or tensors. The problem is described through a mixed potential formulation. The electric and magnetic potentials are related to electric and magnetic bound charges and polarization currents and then to the electric and magnetic polarizations. The electric fleld and magnetic fleld integral equations are constructed. The method of moments technique is then applied to obtain a numerical solution to the problem. The volume of the scatterer is meshed by tetrahedral cells and face-based functions are applied to expand unknown quantities. The proposed formulation has been evaluated and verifled through examples of scattering by various chiral and gyrotropic scatterers illuminated by a plane electromagnetic wave. Numerical results of scattering from a chiroferrite sphere are also presented showing the ∞exibility of the proposed method.

A condition imposed on the electromagnetic polarizability of a bianisotropic lossless scatterer

In the dipole and local field approximations, electromagnetic scatterers are modeled in terms of the polarizability tensor. The matrix elements of this tensor, which are determined by the scatterer geometry, are complex even in the absence of losses in the material. There is a criterion that the polarizability tensor must obey if the scatterers possess no dissipative losses. This condition, derived here for bianisotropic scatterers, can be applied to analytical modeling of periodic structures composed of such scattering inclusions.

Recursive de-embedding procedure for computation of mutual coupling between bianisotropic or complex sources and scatterers

A previously developed method for computing mutual coupling between two bianisotropic scatterers is extended here to include an arbitrary number of complex radiating or scattering centres using multipole modelling. A recursive algorithm is presented that allows for the computation of the total electromagnetic interaction in the complete system. The technique is based on a de-embedding procedure. It yields modified multipole moments and modified multipolarisability polyadics that characterise the interacting sources or scatterers. The method presented here is practically useful to account for mutual coupling in a variety of complex electromagnetic systems: composite materials, smart structures, antenna systems, . . . and in more general hybrid systems consisting of antennas and scatterers of arbitrary number, shape and configuration.

On polarizability properties of bianisotropic spheres with noncomplete magnetoelectric dyadics

AbstractThe polarizability expressions for bianisotropic scatterers are often complicated expressions of the material parameters. This communication treats the question of how the dyadic inversion operations needed in the expressions can be carried out such that they perform well. The particular polarizabilities of the biaxial chiral sphere are shown in component form. © 1994 John Wiley & Sons, Inc.

General theory of the Purcell-Pennypacker scattering approach and its extension to bianisotropic scatterers

Coupled volume integral equations and the long-wavelength approximation have been used to generalize the Purcell-Pennypacker technique (PPT) and the method of moments (MOM) for inhomogeneous bianisotropic scatterers. The interrelationship between the generalized PPT and the MOM has been established. The dyadic functions employed throughout can be easily interpreted in terms of matrices or as Cartesian tensors of the second rank

STRONG AND WEAK FORMS OF THE METHOD OF MOMENTS AND THE COUPLED DIPOLE METHOD FOR SCATTERING OF TIME-HARMONIC ELECTROMAGNETIC FIELDS

Algorithms based on the method of moments (MOM) and the coupled dipole method (CDM) are commonly used to solve electromagnetic scattering problems. In this paper, the strong and the weak forms of both numerical techniques are derived for bianisotropic scatterers. The two techniques are shown to be fully equivalent to each other, thereby defusing claims of superiority often made for the charms of one technique over the other. In the final section, reductions of the algorithms for isotropic dielectric scatterers are explicitly given.

New theorems for bianisotropic media

The general volume equivalence theorem for bianisotropic scatterers is presented, where the equivalent electric and magnetic currents are determined by a pair of coupled vector integral equations. Moreover, using the general volume equivalence theorem and conventional image principle, image theory is developed for a bianisotropic body over an infinite perfect electric or magnetic conducting ground plane.