# Experimental Comparison of Wireless Near-Field Links based on Gaussian and Bessel Beams

Jérôme Taillieu, Walter Fuscaldo, Mauro Ettorre, D. Gonzalez-Ovejero

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Jérôme Taillieu, Walter Fuscaldo, Mauro Ettorre, D. Gonzalez-Ovejero. Experimental Comparison of Wireless Near-Field Links based on Gaussian and Bessel Beams. 2025 IEEE Wireless Power Technology Conference and Expo (WPTCE), Jun 2025, Rome, Italy. pp.1-4, 10.1109/wptce62521.2025.11062256. hal-05158310

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# Experimental Comparison of Wireless Near-Field Links based on Gaussian and Bessel Beams

1st Jérôme Taillieu

IETR, UMR CNRS 6164

Université de Rennes

Rennes, France

jerome.taillieu@univ-rennes.fr

2th Walter Fuscaldo

CNR-IMM

Consiglio Nazionale delle Ricerche

Rome, Italy

walter.fuscaldo@cnr.it

3th Mauro Ettorre

ECE, College of Engineering

Michigan State University

East Lansing, MI, USA

mauro.ettorre@msu.edu

4th David González-Ovejero

IETR, UMR CNRS 6164

Université de Rennes, CNRS

Rennes, France

david.gonzalez-ovejero@univ-rennes.fr

**Abstract**—Gaussian beams are considered excellent candidates for wireless near-field links thanks to their well-known focusing properties. The latter, however, are maintained only up to the Rayleigh range because of diffraction. In this context, the limited-diffraction and self-healing properties of Bessel beams gained increasing interest in wireless data links and power transfer applications. Here, we provide for the first time an experimental comparison of the performance of Bessel beams and Gaussian beams for realizing a wireless link in the sub-terahertz range, specifically in the W-band. Bessel beams are generated through all-metal spline horns, whereas Gaussian beams are generated through commercial WR10 horns. Measurements, even in presence of obstacles across the link and a ground plane in proximity, reveal the superior performance of Bessel beams.

**Index Terms**—Bessel beams, Gaussian beams, wireless links, submillimeter waves.

## I. INTRODUCTION

Following the first experimental evidence of Bessel beams in optics [1], a long-standing debate (see [2]–[5]) began regarding their superiority over Gaussian beams. However, a general conclusion cannot be drawn without focusing on a specific application context and clearly defining the required performance [5]. In this respect, a recent work [6] revisited this problem and introduced a figure of merit for measuring the performance of focused beams in wireless power transfer (WPT) scenarios. In particular, the analysis shows that Bessel beams consistently outperform Gaussian beams when the goal is to achieve the farthest propagation distance with the minimum beam waist using the smallest aperture.

Still, no experimental validation is currently available in the open literature to support this claim. Remarkably, Bessel and Gaussian beams are extensively used in the optical domain [7], but significantly fewer realizations exist in the microwave and millimeter-wave domains (see, e.g., [8]–[10] and refs. therein), where WPT links have major applications. In this context, it has been demonstrated that all-metal spline horns represent a valid platform for generating Bessel beams in the millimeter-wave and sub-terahertz domains [11], [12]. Recently, the same

devices have been used to establish a high data-rate wireless link even in the presence of metallic obstacles [9], [13]. This marked the first demonstration of error-free transmission in the sub-THz range under non-line-of-sight conditions, leveraging the self-healing property of Bessel beams [14].

Here, taking advantage of the aforementioned technology, we experimentally compare for the first time the performance of wireless links based on Bessel beams or Gaussian beams under various operating conditions. Bessel beams are generated using all-metal spline horns, whereas Gaussian beams are generated by means of commercial WR10 horns. Specifically, we compare the transmission coefficient $S_{21}$ as a function of frequency for different distances, both in the presence and absence of a ground plane and of a metallic obstacle. The measurements clearly show that Bessel beams outperform Gaussian beams in terms of $S_{21}$ levels in all cases.

The paper is organized as follows. Section II reviews the properties of Bessel and Gaussian beams and briefly describes the two technologies used here for their sub-THz-wave generation. Section III presents the experimental setup and the measurements. Conclusions are drawn in Section IV.

## II. BESSEL BEAMS AND GAUSSIAN BEAMS

Gaussian beams emerge as exact solutions of the paraxial Helmholtz equation, characterized by a central main lobe described by a Gaussian distribution with a maximum along the propagation axis [15]. As the beam propagates, the energy within the main lobe spreads radially due to diffraction. The Rayleigh range is defined as the distance from the aperture plane at which the on-axis intensity drops to half of its peak value. Gaussian beams are thus diffractive in nature but exhibit excellent focusing properties, as most of the energy is concentrated within the beam waist.

Bessel beams are monochromatic solutions of the Helmholtz equation in a cylindrical reference system. While Bessel beams exist for any order [7], here we refer specifically to zeroth-order Bessel beams, as they are the only ones that exhibit a
<figure><img src="image_2.png" /><figcaption>Fig. 1: Pictures of (a) the WR10 horn and (b) the spline horn, mounted to the waveguide flange of the virginia diodes extenders for W-band.</figcaption></figure>

maximum in the center. As opposed to Gaussian beams, Bessel beams do not generally carry most of their energy within the main lobe, which is usually surrounded by an arbitrary number, say $N$, of concentric annular rings. For large $N$, the energy carried within the main beam is $1/N$ the total energy [2], [6]. However, the presence of such annular rings allows the beam to reconstruct itself after encountering an obstacle along the propagation axis, this is known as the self-healing property. In contrast to Gaussian beams, Bessel beams do not diffract as they propagate. This property is maintained up to a finite distance (as required by the energy conservation law) referred to as the nondiffractive range.

The properties of Bessel and Gaussian beams are fully determined once the aperture size, the beam waist, and the frequency are defined. The beam efficiency is determined by the ratio between the beam waist and the aperture size, whereas the coverage distance (namely, the Rayleigh range for Gaussian beams and the nondiffractive range for Bessel beams) can always be expressed as a function of the beam waist and the wavelength (see the formulas in [6]).

In WPT scenarios, the goal is typically to maximize the beam efficiency and coverage distance with the minimum beam waist and aperture size. By introducing a figure of merit defined as the product of the beam efficiency and the coverage distance divided by the product of the beam waist and the aperture size, it is found that Bessel beams are superior with respect to Gaussian beams [6].

### III. ALL-METAL SPLINE HORNS VS. WR10 HORNS

Gaussian beams can easily be realized at sub-THz frequencies by means of waveguide horns. In this work, we focus on generating a Gaussian beam in the W-band, i.e., 75–110 GHz, and thus we employ commercial WR10 horns, such as the one shown in Fig. 1(a). The radiating properties of these antennas are well known and well documented in the literature, and are therefore not discussed in this work.

Bessel beams can be generated using various devices (see, e.g., [10], [16]–[18] and references therein). Here, we consider the antenna element proposed in [9], [13] which consists of an all-metal spline-profile horn as shown in Fig. 1(b). Following the design rules provided in [11], it is easy to obtain a TE-polarized Bessel beam from a conical horn by suitably tapering the spline profile. The near-field profiles of this antenna have already been experimentally characterized in [9], [13] through THz frequency-domain spectroscopy and are not repeated here for the sake of brevity.

#### A. Setup

We wish to measure the transmission coefficient $S_{21}$ between two identical WR10 horns and two identical all-metal spline horns in three different scenarios: i) a line-of-sight (LOS) link, ii, a non-line-of-sight (nLOS) link with an obstacle (a metallic disk with a diameter of 7 mm) centered on the propagation axis, positioned 9.4 mm from one of the two apertures, and iii) the same configuration as in ii), but with the addition of a finite ground plane in proximity of the link, placed 5 cm to the side of the propagation axis. The pictures in Fig. 2(a) and (b) show the link between the spline horns in scenarios ii) and iii), respectively, whereas Fig. 2(c) shows the link between the two WR10 horns in scenario iii). Both the transmitting and the receiving antennas are connected to W-band Virginia Diodes extenders to perform the measurements using a vector network analyzer (VNA). The calibration was performed at the output waveguides of the extenders, so the $S_{21}$ results presented in the next section account for the insertion losses introduced by both the WR10 and spline horns.

#### B. Measurements

For all scenarios, $S_{21}$ measurements are taken for various distances between the antennas, ranging from 0 to 120 mm in steps of 10 mm over the entire W-band. The results are reported in Fig. 3(a)–(f) as contour plots. A direct comparison between the results of the top row (links between the spline horns) and those of the bottom row (links between the WR10 horns) clearly reveals the superiority of Bessel beams with respect to Gaussian beams in all conditions.

In the simplest scenario of an LOS link (see Figs. 3(a) and (d)) Bessel beams are capable of maintaining an $S_{21} > -3$ dB up to 100 mm for all frequencies, whereas Gaussian beams can ensure this performance only up to 40 mm and in the lower part of the W-band. This effect is due to the diffractive spreading of Gaussian beams that becomes more pronounced at higher frequencies. In addition, standing waves are more prominent in the link based on Gaussian beams. It should also
<figure><img src="image_3.png" /><figcaption>Fig. 2: (a) An nLOS link between two spline horns with a metallic obstacle centered on the propagation axis. (b) As in (a) with the addition of a ground plane in proximity of the link. As in (c), but for a link between WR10 horns.</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>Fig. 3: Contour plot of the $S_{21}$ measurements (in dB) vs. frequency (in GHz) and link distance (in mm). The top(bottom) row shows the results for spline(WR10) horns. (a) and (d) show the $S_{21}$ for an LOS link, (b) and (e) show the $S_{21}$ for an nLOS link with a metallic obstacle at 9.4 mm from one of the antenna, and (c) and (f) show the $S_{21}$ for an nLOS link with the same obstacle and the addition of a ground plane at a lateral distance of 50 mm from the propagation axis.</figcaption></figure>

be noted that the WR10 horn we used has a poor $S_{11}$ in the 90–95 GHz band which explains the lower $S_{21}$ in that range. Even excluding this portion of the spectrum, the results reveal that Gaussian beams have an average penalty of at least 5 dB with respect to Bessel beams for almost all distances.

When a metallic obstacle was introduced, as shown in Fig. 2(a), the $S_{21}$ was severely affected for the link based on Gaussian beams. In contrast, the link based on Bessel beams was able to recover almost the same performance as the LOS link after a distance of approximately 20 mm (see Fig. 3(b) and (e)). Remarkably, this distance agrees well with the shadow

region of the obstacle, as predicted by ray optics.

Finally, the results in Fig. 3(c) and (f) show the combined effect of the obstacle and the proximity of a finite ground plane. Once again, the link based on Bessel beams (Fig. 3(c)) shows strong resilience to the presence of the ground plane, the $S_{21}$ being barely affected, but for very short distances. Conversely, the link based on Gaussian beams (Fig. 3(f)) is sensitive to the presence of the ground plane, the $S_{21}$ being lowered of few dBs at short distances.
IV. CONCLUSION

In this work, we compared the performance of wireless links based on Bessel beams and Gaussian beams by measuring the transmission through a VNA at W-band. Bessel beams were generated through spline horns whereas commercial WR10 horns were used for generating Gaussian beams. Measurements were collected for various distances up to 120 mm and considering either a free-space link or the presence of metallic obstacles and ground planes in the path. Results confirmed the resilience of Bessel beams to the presence of metallic obstacles on the beam path and to the proximity of ground planes. Conversely, Gaussian beams were proven to be more sensitive to the presence of obstacles and ground planes. In general, the link based on Bessel beams showed a superior $S_{21}$ performance with respect to that based on Gaussian beams.

ACKNOWLEDGMENT

This work has received support from the French National Research Agency (ANR) through the project LinkAll with reference ANR-21-CE25-0014, and from the French Government through the Labex CominLabs Excellence Laboratory, managed by ANR in the Investing for the Future Program under Reference ANR-10-LABX-07-01. W. Fuscaldo wishes to acknowledge the project PRIN 2022 "SAFE" (Spiral and Focused Electromagnetic fields) 2022ESAC3K, Italian Ministry of University and Research (MUR), financed by the European Union, Next Generation EU.

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