Bessel-Gauss Beams Through Leaky Waves: Focusing and Diffractive Properties

Abstract

Bessel-Gauss beams have been mainly proposed in optics as a solution for reducing the on-axis intensity oscillations typical of Bessel beams. Previous investigations on Bessel-Gauss beams are based on a scalar theory in the paraxial approximation, and thus cannot be extended to the microwave range where a fully vectorial approach is needed. Here, the generation of Bessel-Gauss beams through leaky waves is investigated. First, the nondiffractive and focusing properties of Bessel-Gauss generated through leaky waves are extensively examined in the frame of a vectorial approach. Useful design criteria are derived to optimize both the radiation and the focusing efficiency of such beams. On this basis, leaky-wave radiators synthesized to support the generation of a Bessel-Gauss beam over a given frequency band in the microwave range are presented. Full-wave results corroborate the concept.

Microwave synthesis of Bessel, Bessel–Gauss, and Gaussian beams: a fully vectorial electromagnetic approach

“…2(c) that requires the simultaneous variation of Λ and FF. We should highlight that this is a considerable difference with respect to the approach proposed in [10], where the period was assumed to be fixed (at which corresponds a path that follows a straight horizontal line over the color maps in Fig. 2(c)), and there were no degrees of freedom for reducing the variation of the leaky phase constant.…”

“…In this light, the following section only aims at showing conditions for correctly synthesizing the aperture fields to obtain along the longitudinal component of the electric field either a BB, or a BGB, or a GB, in the near-field region. This approach is demonstrated to be effective within a limited region located in the near field of the radiating aperture (criteria to determine this region are provided in [10]).…”

“…(It is worth noting here that the excitation of a backward cylindrical wave, i.e., with βα < 0, allows for recovering the required inward character of the Hankel function characterizing the aperture distribution.) The synthesis technique for obtaining a BGB has been described in [10] taking cues from the standard leaky-wave approach originally applied to 1-D periodic LWAs [25] to obtain a target far-field radiation pattern, and more recently to 2-D radially periodic LWAs [26,27] to obtain focused beams in the radiative near-field region.…”

“…1, middle, right). Thus, the resulting equations for the tangential field components are [10]:Equation (3) represents the tangential aperture distribution that is required to obtain a TM-polarized BGB for E z and within the nondiffractive range.…”

“…[9] and refs. therein) BGBs have been discussed only recently on a rigorous theoretical basis [10] (although the benefits arising from the application of amplitude tapering functions on the aperture distribution were yet highlighted in [11]). On the other hand, GBs are commonly generated at microwaves, but mostly by means of bulky devices such as corrugated horn feeders for reflector antennas [12, 13].…”