Analysis of limited-diffractive and limited-dispersive X-waves generated by finite radial waveguides

Abstract

In this work, we analyze the spatial and temporal features of electromagnetic X-waves propagating in free space and generated by planar radiating apertures. The performance of ideal X-waves is discussed and compared to practical cases where the important effects related to the finiteness of the radiating aperture and the wavenumber dispersion are taken into account. In particular, a practical device consisting of a radial waveguide loaded with radiating slots aligned along a spiral path is considered for the practical case in the millimeter-wave range. A common mathematical framework is defined for a precise comparison of the spatiotemporal properties and focusing capabilities of the generated X-wave. It is clearly shown that the fractional bandwidth of the radiating aperture has a key role in the longitudinal confinement of an X-wave in both ideal and practical cases. In addition, the finiteness of the radiating aperture as well as the wavenumber dispersion clearly affect both the transverse and the longitudinal profiles of the generated radiation as it travels beyond the depth-of-field of the generated X-wave. Nevertheless, the spatiotemporal properties of the X-wave are preserved even in this "dispersive-finite" case within a defined region and duration related to the nondiffractive range and fractional bandwidth of the spectral components of the generated X-wave. The proposed analysis may open new perspectives for the efficient generation of X-waves over finite radiating apertures at millimeter waves where the dispersive behavior of realistic devices is no longer negligible

Propagation of nondiffracting pulses carrying orbital angular momentum at microwave frequencies

“…Note that similar results have been obtained for zeroth-order X-waves in Ref. 25. As a consequence, the nondiffractive range also represents the distance for which the OAM is effectively carried by the pulse.…”

“…Such a standing-wave distribution is inherently narrow-band 10 , whilst the generation of efficiently confined localized pulses requires wideband capabilities, as discussed in detail in Ref. 25. However, it has recently been demonstrated 27 that an inward traveling-wave aperture distribution can generate a Bessel beam in a biconical region close to the axis of symmetry of the aperture.…”

“…In particular, as already done in Ref. 25, we consider here a second-order Taylor expansion of the radial wavenumber around the operating angular frequency ω 0 as follows…”

A new class of nondiffracting pulses based on focusing leaky waves

“…therein). Just very recently, theoretical and numerical results have been reported in [7][8][9], whereas experimental results just appeared in [10].…”

“…In this connection, it has been shown that leaky waves (LWs) can profitably be used for generating Bessel beams with considerably narrower spot-sizes in both microwave [12,13] and millimeter-wave ranges [1]. However, both these leaky-wave antennas (LWAs) exhibit a narrow operating fractional bandwidth, and thus they are not suitable for the generation of polychromatic nondiffracting waves, such as XWs [7]. This narrow-band feature is due to the resonant character of the radiation mechanism, which is typically based on the superposition of an outward and an inward cylindrical wave [14].…”