Radiation properties of one-dimensional random-like antenna arrays based on Rudin-Shapiro sequences

Abstract

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 (PBG). Within this context, motivated by the fairly recent discovery in X-ray crystallography of "quasicrystals," 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 Propagat., vol. 53, No. 2, pp. 635-644, Feb. 2005]. In the present 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 quasirandom (dis)order. After presentation and review of relevant * V. Galdi, V. Pierro, G. Castaldi, and I.M. Pinto are with the Waves Group, ). background material, the radiation properties of one-dimensional RSbased 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.

Suppression of Backscattering From 2-D Aperiodically-Ordered Thinned Patch Array Using Rudin-Shapiro Sequences

“…More recently, RS sequences have found important practical applications as signal processing tools for spreading spectrum communication and encryption systems [11,12]. One of the first applications of RS sequence and polynomials in electromagnetics was in [13] where the time-harmonic radiation properties of 1-D RS-based antenna array configurations have been investigated.…”

Radiation and Scattering from One-Dimensional Aperiodically-Ordered Structures Based on Two-Letter Substitutional Sequences

“…These investigations, pioneered by Bombieri and Taylor [5], have demonstrated intriguing connections between diffraction physics and number theory (algebraic integers, prime numbers). Within this context, for the two-letter substitution rules of interest here, a key role is played by the so-called substitution matrix r[ s] (4) which describes the symbol distribution in (3) [5][6][7]. It can be shown that, for the case of primitive substitution rules, the substitution matrix in (4) admits two real eigenvalues Al and A2, with Al> 1A21 [6].…”

“…* The discrete (Bragg-type) spectrum generally depends on the eigenvalues of the substitution matrix in (4), and on the scale ratio d. Idb It is interesting to note that the substitution matrix depends only on the number of letters in the substitution rules, and not on their ordering. For rational values of the scale ratio, there exist also "trivial" Bragg-type modes whose wavenumbers do not depend on the substitution rules.…”

“…They are typically associated with intermediate forms of aperiodic order, and generally exhibit multifractal character [6]. Conversely, absolutely-continuous constituents can be viewed as noise-like flat background spectra, typically associated with random or quasirandom geometries (see, e.g., the Rudin-Shapiro sequence in [4]). …”

“…Along these lines, in an ongoing series of investigations [2][3][4], we have concentrated on the radiation properties of representative classes of one-dimensional (I-D) and 2-D aperiodic configurations, and on the similarities and differences between the resulting wave-dynamical characteristics and their well-known periodic counterpart. In the present paper, we consider a fairly broad category of 1-D aperiodically-ordered geometries based on substitutional sequences, for which rigorous theoretical results are available in the crystallography and discrete-geometry literature (see, e.g., [5][6][7]).…”