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Ray chaos, manifested by the exponential divergence of trajectories originating from an originally thin ray bundle, can occur even in linear electromagnetic propagation environments, due to the inherent nonlinearity of ray-tracing (eikonal) maps. In this paper, extending our previous study of a two-dimensional planar ray-chaotic prototype scenario, we consider a cylindrical scatterer made of a perfectly electric-conducting azimuthally corrugated boundary coated by a radially inhomogeneous (ray-trapping) dielectric layer. For this configuration, we carry out a comprehensive parametric study of the ray-dynamical and full-wave scattering (monostatic and bistatic radar-cross-section) signatures, with emphasis on possible implications for high-frequency wave asymptotics ('ray-chaotic footprints'). Index Terms--High-frequency, radar cross-section, ray chaos.

This paper is concerned with a study of the two-dimensional (2-D) time-harmonic scattering by aperiodically-ordered 1-D planar strip arrays based on two-symbol substitutional sequences, under Kirchhoff physical-optics approximation. In this connection, theoretical results from solid-state physics, dwelling on concepts from discrete geometry and number theory, are briefly reviewed and applied to the characterization of the scattering signatures of the above physical configuration. Parametric studies are presented in order to flesh out some of the above concepts and to highlight wave-features which are thought as being representative of a fairly broad class of regular non-periodic scatterers. Potential applications are also envisaged. Index Terms--Aperiodic order, quasicrystals, scattering, substitutional sequences.

The development of exotic new materials, such as metamaterials, has created strong interest within the electromagnetics (EM) community for possible new phenomenologies and device applications, with particular attention to periodicity-induced phenomena, such as photonic bandgaps. Within this context, motivated by the fairly recent discovery in X-ray crystallography of 'quasi-crystals,' whose diffraction patterns display unusual characteristics that are associated with 'aperiodic order,' we have undertaken a systematic study of how these exotic effects manifest themselves in the radiation properties of aperiodically configured antenna arrays. The background for these studies, with promising example configurations, has been reported in a previous publication [V. Pierro et al., IEEE Trans. Antennas Propag., vol. 53, pp. 635-644, Feb. 2005]. In this paper, we pay attention to various configurations generated by Rudin-Shapiro (RS) sequences, which constitute one of the simplest conceivable examples of deterministic aperiodic geometries featuring random-like (dis)order. After presentation and review of relevant background material, the radiation properties of one-dimensional RS-based antenna arrays are analyzed, followed by illustrative numerical parametric studies to validate the theoretical models. Design parameters and potential practical applications are also given attention. Index Terms--Antenna array, aperiodic order, random-like geometries, Rudin-Shapiro sequences.

The fairly recent discovery of 'quasi-crystals,' whose X-ray diffraction patterns reveal certain peculiar features which do not conform with spatial periodicity, has motivated studies of the wave-dynamical implications of 'aperiodic order.' Within the context of the radiation properties of antenna arrays, an instructive novel (canonical) example of wave interactions with quasi-periodic order is illustrated here for one-dimensional array configurations based on the 'modified-Fibonacci' sequence, with utilization of a two-scale generalization of the standard Poisson summation formula for periodic arrays. This allows for a 'quasi-Floquet' analytic parameterization of the radiated field, which provides instructive insights into some of the basic wave mechanisms associated with quasi-periodic order, highlighting similarities and differences with the periodic case. Examples are shown for quasi-periodic infinite and spatially-truncated arrays, with brief discussion of computational issues and potential applications. Index Terms--Antenna arrays, aperiodic order, Fibonacci sequence, generalized Poisson summation.

Two-dimensional aperiodic tilings are collections of polygons, devoid of any translational symmetries, capable of covering a plane without gaps and overlaps. Although aperiodic, these structures can exhibit order and symmetry in an extended sense. In this paper, we study the radiation properties of planar antenna arrays based on certain categories of two-dimensional aperiodic tilings that illustrate diverse aspects of aperiodic order. Background material on aperiodic tilings and their known electromagnetic properties is reviewed. Results are illustrated to highlight the effects of aperiodic order in the antenna array radiation properties. Potential applications are also envisaged. Index Terms--Antenna arrays, aperiodic tilings, radiation, quasi-crystals.

Ray chaos, manifested by the exponential divergence of trajectories in an originally thin ray bundle, can occur even in linear electromagnetic propagation environments, due to the inherent nonlinearity of ray-tracing maps. In this paper, we present a novel (two-dimensional) test example of such an environment which embodies intimately coupled refractive wave-trapping and periodicity-induced multiple scattering phenomenologies, and which is amenable to explicit full-wave analysis. Though strictly nonchaotic, it is demonstrated that under appropriate conditions which are inferred from a comprehensive parametric database generated via the above-noted rigorous reference solution, the high-frequency wave dynamics exhibits trends toward irregularity and other peculiar characteristics; these features can be interpreted as 'ray-chaotic footprints,' and they are usually not observed in geometries characterized by 'regular' ray behavior. In this connection, known analogies from other disciplines (particularly quantum physics) are briefly reviewed and related to the proposed test configuration. Moreover, theoretical implications and open issues are discussed, and potential applications are conjectured. Index Terms--Ducted-type modes, Floquet theory, ray chaos.

In this paper, we use higher order impedance boundary conditions (HOIBCs) for studying high frequency asymptotic two-dimensional (2-D) scattering of truncated aperture-generated electromagnetic fields from planar conducting surfaces coated by multiple layers of homogeneous bi-anisotropic media. The reflected field syntheses are carried out via asymptotic reduction of rigorous plane-wave spectral integrals, which are subsequently discretized and transformed to the spatial domain through use of a Gabor-based narrow-waisted (NW) Gaussian beam (GB) algorithm. In this discretized algorithm, the GB propagators are approximated by previously explored standard and modified (uniform) complex-source-point paraxial asymptotic techniques. Example applications are restricted to zeroth and second order IBCs for single- and multilayer complex coatings, with emphasis on the adaptation of the NW-GBs to the HOIBC launch conditions in the presence of localizing (e.g., focused and/or abruptly truncated) illumination. The results confirm that the previously established utility of the NW-GB algorithm with respect to accuracy and computational feasibility continues to hold for this fairly general combination of environmental complexity and strongly inhomogeneous (localizing) illumination. Index Terms--Bianisotropic layered media, Gaussian beam asymptotics, higher order impedance boundary conditions.

We study a simple (ray optical, scalar) model of mode-stirred electromagnetic reverberating enclosures. Extensive numerical simulations reveal consistently that spatial-field homogeneization and (wide-sense) deterministic chaos occur together, as the time-harmonic peak displacement of the mode-stirring wall becomes comparable to the electromagnetic wavelength. Reverberation properties can thus be synthetically gauged by Lyapounov exponents. Semiquantitative design optimization criteria are obtained and possible generalizations are discussed. Index Terms - Chaos, electromagnetic compatibility measurements, electromagnetic shielding measurements, ray tracing, reverberation enclosures.