Periodic Array Of Scatterers Research Articles

Band Structure in a Sustainable Sonic Crystal

During the last few decades many researchers have been interested in acoustic wave propagation in artificial periodic composites known as sonic crystals. Sonic crystals have received renewed attention because they exhibit acoustic band gaps where there are only evanescent waves. Sonic crystals consist of a periodic array of scatterers embedded in a host medium. The host medium and/or scatterers are fluids. We investigate the band structure of acoustic waves propagating in a sustainable sonic crystal composed by miriti fibers and air, regarding square and triangular lattices. Miriti fibers are extracted from buriti palm petiole (Mauritia flexuosa Mart.), which is a typical specie that grows in Amazonian region. We also study the influence of miriti fiber cross section, i.e. circular, hollow circular, square and rotated square with a 45° angle of rotation with respect to x, y axes. Plane wave expansion method is used to solve the wave equation. Acoustic band gaps are observed for all miriti fiber cross sections and lattices. The best performances of the sustainable sonic crystal are for triangular lattice, regarding circular and rotated square miriti fiber cross sections, and for square lattice with circular miriti fiber cross section. We suggest that the sustainable sonic crystal should be feasible for noise management.

Collectively enhanced optomechanical coupling in periodic arrays of scatterers

We investigate the optomechanical properties of a periodic array of identical scatterers placed inside an optical cavity and extend the results of [A. Xuereb, C. Genes, and A. Dantan, Phys. Rev. Lett. 109, 223601 (2012)]. We show that operating at the points where the array is transmissive results in linear optomechanical coupling strengths between the cavity field and collective motional modes of the array that may be several orders of magnitude larger than is possible with an equivalent reflective ensemble. We describe and interpret these effects in detail and investigate the nature of the scaling laws of the coupling strengths for the different transmissive points in various regimes.

Linear momentum quantization in periodic structures II

Fraunhofer interference of a single particle by a periodic array of scatterers, usually treated with a wave picture, can be fully explained on the basis of linear momentum quantization, as pointed out in a previous study by Van Vliet (1967) [4]. This analysis is now extended to scattering (or passing through slits) involving a finite number N of equidistantly spaced entities comprising the interferometer. The usual intensity probability distribution for W ( sin θ ) is obtained, noting that total momentum is conserved (as in the Compton effect), while the interferometer is treated as a quantum object—rather than a classical measuring apparatus, as perceived in the Copenhagen interpretation. Various aspects of the ‘orthodox view’ are examined and renounced.

Extraordinary Transmission Through Arrays of Electrically Small Holes From a Circuit Theory Perspective

Extraordinary optical transmission of light or electromagnetic waves through metal plates periodically perforated with subwavelength holes has been exhaustively analyzed in the last ten years. The study of this phenomenon has attracted the attention of many scientists working in the fields of optics and condensed matter physics. This confluence of scientists has given rise to different theories, some of them controversial. The first theoretical explanation was based on the excitation of surface plasmons along the metal-air interfaces. However, since periodically perforated dielectric (and perfect conductor) slabs also exhibit extraordinary transmission, diffraction by a periodic array of scatterers was later considered as the underlying physical phenomenon. From a microwave engineering point of view, periodic structures exhibiting extraordinary optical transmission are very closely related to frequency-selective surfaces. In this paper, we use simple concepts from the theory of frequency-selective surfaces, waveguides, and transmission lines to explain extraordinary transmission for both thin and thick periodically perforated perfect conductor screens. It will be shown that a simple transmission-line equivalent circuit satisfactorily accounts for extraordinary transmission, explaining all of the details of the observed transmission spectra, and easily gives predictions on many features of the phenomenon. Although the equivalent circuit is developed for perfect conductor screens, its extension to dielectric perforated slabs and/or penetrable conductors at optical frequencies is almost straightforward. Our circuit model also predicts extraordinary transmission in nonperiodic systems for which this phenomenon has not yet been reported.

Water-wave scattering by a periodic array of arbitrary bodies

An algebraically exact solution to the problem of linear water-wave scattering by a periodic array of scatterers is presented in which the scatterers may be of arbitrary shape. The method of solution is based on an interaction theory in which the incident wave on each body from all the other bodies in the array is expressed in the respective local cylindrical eigenfunction expansion. We show how to efficiently calculate the slowly convergent terms which arise in the formulation and how to calculate the scattered field far from the array. The application to the problem of linear acoustic scattering by cylinders with arbitrary cross-section is also discussed. Numerical calculations are presented to show that our results agree with previous calculations. We present some computations for the case of fixed, rigid and elastic floating bodies of negligible draft concentrating on presenting the amplitudes of the scattered waves as functions of the incident angle.

Acoustic barriers based on periodic arrays of scatterers

It is well known that certain periodic structures built by repetition of elements produce sound attenuation effects as a consequence of the destructive interference of the scattered waves by these elements. The sound attenuation results that we got from transmission experiments with these kind of structures, so-called sonic crystals (SCs), led us to think that SCs could be used as an acoustic barrier. Until now, most of the transmission experiments with these periodic arrays of scatterers have been performed under controlled conditions, so how they would behave outdoors is still not well known. In this letter we present outdoor-experimental results for two-dimensional SCs and from these it can be concluded that periodic arrays of scatterers are a suitable device to reduce noise in free-field conditions.

Electron pinball and commensurate orbits in a periodic array of scatterers.

We have introduced an artificial array of scatterers into a macroscopic two-dimensional conductor nearly devoid of intrinsic defects. This generates pronounced structure in the magnetoresistance, anomalous low-field Hall plateaus, and a quenching of the Hall effect about B=0. Our calculations show that the predominant features in the data arise from commensurate classical orbits impaled upon small groups of the imposed scatterers.

Iterative-based computational methods for electromagnetic scattering from individual or periodic structures

In this paper we review the use of iterative approaches for the numerical analysis of many electromagnetic scattering problems. In a variety of cases, iteration can be used to greatly extend the range of problems easily treated by a numerical solution of the conventional integral equations. Since the resulting matrix equations are not sparse, a special structure must be built into the discrete system in order to reduce the storage requirements. Two distinct discretization procedures are presented that provide the necessary structure when treating individual scatterers and infinite periodic arrays of scatterers. Since many additional problems of interest do not fall into this category, some recent efforts to treat more general problems are reported. In addition, we include a brief overview of preconditioning methods for the improvement of the convergence rates of iterative algorithms.