Acoustic Bessel-like beam formation by an axisymmetric grating

Abstract

We report Bessel-like beam formation of acoustic waves by means of an axisymmetric grating of rigid tori. The results show that the generated beam pattern is similar to that of Bessel beams, characterized by elongated non-diffracting focal spots. A multiple foci structure is observed, due to the finite size of the lens. The dependence of the focal distance on the frequency is also discussed, on the basis of an extended grating theory. Experimental validation of acoustic Bessel-like beam formation is also reported for sound waves. The results can be generalized to wave beams of different nature, as optical or matter waves. PACS numbers: 43.20.Mv, 43.20.Hq,43.20.Fn Bessel beams, originally proposed in optics 1,2 , are now at the basis of many applications due to their unusual propagation properties 3-8 . The most celebrated property of a Bessel beam is that, in the ideal case, the field propagates invariantly, i.e. without any diffracting broadening, in contrast to the other canonical case, the Gaussian beam, where the beam experiences diffractive broadening in free space propagation. As a consequence, the field pattern in a Bessel beam possesses an infinitely extended focal line.Strictly speaking, Bessel beam is a solution of the wave equation in the form of a monochromatic wave with a transverse profile given by a Bessel function of the first kind, which by definition presents an infinite spatial extension. This ideal case cannot be realized in practice (in the same way as ideal, infinitely extended plane waves cannot exist). However, approximate or imperfect Bessel beams of finite transverse extent can be excited by different means, displaying not an infinite but an extremely elongated focal line.In optics, Bessel-like beams are usually formed by focusing a Gaussian beam by an axicon 9 , a transparent refractive element of conical shape, as shown in Fig. 1(a). The beam in propagation through the axicon acquires linearly tilted (conical) wave-fronts, which results in an elongated focus behind the axicon. As the axicon is not infinitely extended in transverse space, the resulting Bessel beam is not perfect, and displays a focal line of finite extent. Optical Bessel beams have been also obtained by acoustic gradient index lenses 10 . In electromagnetism, Bessel-like beams have been generated from a subwavelength aperture by adding a metallic circular grating structure in front of the aperture 11 . Such imperfect Bessel beams find multiple applications, e.g. in optics for laser inscription of patterns deep into transpar-m=1 m=2 m=3 M (a) (b) f(r)| n=2 f(r)| n=1 a n=2 n=1 FIG. 1. (Color online) (a) Illustration of the formation of Bessel beam by an axicon resulting in imperfect Bessel beam showing a focus-line of finite extent; (b) Illustration of the formation of Bessel-like beams by a plane of concentric rings, where converging diffracted waves result in two elongated foci.ent materials, or for etching of deep narrow holes in laser manufacturing of opaque materials, among others 3,4,6 . In acoustics, Bessel beam...

Formation of high-order acoustic Bessel beams by spiral diffraction gratings

“…In the case of a pure axisymmetric grating [7] where the sources are distributed in concentric circles separated at a distance a,…”

“…3(a) for the case of the truncated systems (blue line) the amplitude grows up to a given distance z = z F . This distance can be estimated geometrically through the zeroth-order Bessel beams as [7] …”

“…Solutions of such kinds are of infinite transverse extent and thus cannot be generated experimentally. However, it is possible to generate finite size approximations for Bessel beams which propagate over extended distances in a diffraction-free manner providing potential applications for the wave physics community [2][3][4][5][6][7]. Whereas zeroth-order Bessel beams present a bright central maximum and can be useful for applications that require focusing of energy [8], the vortex beams generated by the HOBBs can be useful for manipulating particles in both optics [9] and acoustics [10].…”

Achromatic reflected metalens for highly directional and long-distance acoustic probing

“…Various kinds of acoustic lenses have been designed for focusing of transmitted waves, such as GRIN (gradient index) sonic lenses [6,7], GRIN lenses using cross-shaped scatterers [8], coiled up space [9][10][11], rigid toroidal scatterers [12] and orifice-type metamaterial [13,14], acoustic Fresnel lenses [15][16][17][18], planar diffractive acoustic lenses [19][20][21][22]. Most of the above works focused on designing ultra-thin lenses [8,10,11,[16][17][18][19][20][21][22], resulting in the focal length highly dependent on frequency due to the refractive index (or the properties of diffractive elements) sensitive to frequency, whereas the GRIN lenses using orifice-type metamaterial [13,14] demonstrated near-frequencyindependent characteristics, with its thickness being on the order of wavelength. Different from GRIN lenses, which rely on gradually varying refractive index to obtain phase delay, diffractive lenses are realized by controlling local phases of transmitted waves to generate interference and diffraction patterns.…”

Design of Acoustical Bessel-Like Beam Formation by Tunable Angular Spectrum in Soret Zone Plate Lens

“…In any case, the most convenient way to form acoustic Bessel beams is by using annular transducer arrays [40,41]. The acoustic Bessel-like beam by means of an axisymmetric grating of rigid tori was reported in [42]. The radii are obtained from the following Fresnel construction equation,…”