# Design and Experimental Validation of an E-Band Wideband Bessel-Beam Launcher on Quartz

Edoardo Negri, Jérôme Taillieu, Walter Fuscaldo, Malo Robin, Xavier Morvan, Olivier de Sagazan, Paolo Burghignoli, Alessandro Galli, David González-Ovejero

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To cite this version:

Edoardo Negri, Jérôme Taillieu, Walter Fuscaldo, Malo Robin, Xavier Morvan, et al., Design and Experimental Validation of an E-Band Wideband Bessel-Beam Launcher on Quartz. IEEE Journal of Microwaves, 2025, 5 (6), pp. 1329-1338. 10.1109/JMW.2025.3610404. doi:10.54124/je.microwaves.2025.5.6.1329-1338

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Distributed under a Creative Commons CC BY 4.0 - Attribution - International License
Received 12 May 2025; revised 3 August 2025; accepted 11 September 2025. Date of publication 9 October 2025; date of current version 7 November 2025.

Digital Object Identifier 10.1109/JMW.2025.3610404

# Design and Experimental Validation of an E-Band Wideband Bessel-Beam Launcher on Quartz

EDOARDO NEGRI Ⓓ<fnref n="1" />,<fnref n="2" /> (Member, IEEE), JÉRÔME TAILLIEU<fnref n="3" /> (Graduate Student Member, IEEE), WALTER FUSCALDO Ⓓ<fnref n="1" /> (Senior Member, IEEE), MALO ROBIN<fnref n="3" />, XAVIER MORVAN Ⓓ<fnref n="3" />, OLIVIER DE SAGAZAN<fnref n="3" />, PAOLO BURGHIGNOLI Ⓓ<fnref n="2" /> (Senior Member, IEEE), ALESSANDRO GALLI Ⓓ<fnref n="2" /> (Member, IEEE), AND DAVID GONZÁLEZ-OVEJERO Ⓓ<fnref n="3" /> (Senior Member, IEEE)

(Regular Paper)

CORRESPONDING AUTHOR: Edoardo Negri (e-mail: edoardonegri@cnr.it).

The work of Edoardo Negri and Walter Fuscaldo was supported by the Project PRIN 2022 "SAFE" (Spiral and Focused Electromagnetic fields) under Grant 2022ESAC3K, Italian Ministry of University and Research (MUR), through European Union, Next Generation EU. The work of Jérôme Taillieu, Malo Robin, Xavier Morvan, Olivier de Sagazan, and David González-Ovejero was supported in part by the European Union through European Regional Development Fund (ERDF), in part by the Ministry of Higher Education and Research, in part by CNRS, in part by Brittany Region, in part by Conseils Départementaux d'Ille-et-Vilaine, in part by Côtes d'Armor, in part by Rennes Métropole, and in part by Lannion Trégor Communauté, through the CPER Projects CyMoCod and PhotBreizh. The work was also supported in part by the Agence Nationale de la Recherche (ANR) through the AROMA under Project ANR-22-CE24-0013 and in part by the Labex CominLabs Excellence Laboratory through the ANR Investing for the Future Program under Project ANR-10-LABX-07-01. The work of Alessandro Galli was supported by European Union through Italian National Recovery and Resilience Plan (NRRP) of NextGenerationEU, partnership on "Telecommunications of the Future" PE00000001 - Program "RESTART".

**ABSTRACT** Radially periodic Bessel-beam launchers are typically fed with coaxial probes, as they provide a simple and effective means to obtain TM-polarized Bessel beams. However, as the frequency increases, coaxial feeders become increasingly expensive and fragile. Therefore, the realization of Bessel-beam launchers at (sub)millimeter-wave frequencies calls for alternative technologies. To illustrate this challenge and propose an effective solution, an E-band (81–86 GHz), radially periodic, leaky-wave Bessel-beam launcher is designed and experimentally validated in this work. The device is realized using a grounded dielectric slab with an annular metal strip grating on top and is fed through a waveguide mode converter. Specifically, the input fundamental mode of a standard rectangular waveguide is converted into the higher-order TM₀₁ mode of a circular waveguide, which feeds the launcher, thereby generating a TM-polarized Bessel beam. Full-wave and measurement results show impressive agreement with those theoretically predicted by an established leaky-wave approach.

**INDEX TERMS** Bessel beams, E-band, leaky waves, near-field focusing, periodic structures.

## I. INTRODUCTION

The 'chimera' of point-to-point wireless communications is to transfer the largest amount of information at the farthest distance, with minimal power waste, low interference, and resilience to obstacles. These requirements call for devices capable of radiating focused beams (to minimize diffraction and thus power waste) over long distances at high frequencies (to maximize the available bandwidth). Near-field

focusing at (sub)millimeter-wave frequencies has indeed recently attracted significant interest in various application contexts, such as wireless power transfer [1], [2], [3], [4], tomography [5], imaging [6], and secure point-to-point wireless communication links [7], [8], [9], [10], [11]. One of the most efficient ways to generate a near-field link is through *Bessel beams* [12]. These beams are monochromatic solutions of the Helmholtz equation in a cylindrical reference system,

<footnote n="1">¹Istituto per la Microelettronica e Microsistemi, Consiglio Nazionale delle Ricerche, 00133 Rome, Italy</footnote>

<footnote n="2">²Department of Information Engineering, Electronics and Telecommunications, Sapienza University of Rome, 00184 Rome, Italy</footnote>

<footnote n="3">³Univ. Rennes, CNRS, Institut d'Electronique et des Technologies du numérique (IETR), UMR 6164, 35000 Rennes, France</footnote>
exhibiting intriguing properties such as self-healing [13], focusing [14], and limited-diffraction [15]. These remarkable features can be maintained over a given distance, commonly referred to as *nondiffractive range* $z_{ndr}$ [16], [17].

The generation of Bessel beams at microwave and millimeter-wave frequencies has been widely investigated and experimentally validated through different techniques [18], such as radial line slot array (RLSA) [19], [20], [21], [22], spline horns [23], [24], arrays [25], [26], subwavelength apertures [27], or metamaterial lenses [28]. Among the possible solutions, *leaky-wave* Bessel-beam launchers (BBLs) stand out for their single-feeder, low-profile, and cost-effective structure [29]. These devices are typically categorized as either *resonant* [30], [31], [32] or *wideband* [33], [34] BBLs, depending on their working principle. The former operate based on a radial resonance, which allows them to maintain a compact structure but results in a narrowband behavior [35]. The latter rely on the excitation of an *outward* cylindrical leaky wave, which is converted into an *inward* cylindrical leaky wave through a periodic structure. This mechanism enables the generation of a Bessel-beam distribution over a broad frequency range, leveraging an electrically large aperture, an aspect of little concern at high frequencies [34].

As a result, the millimeter and sub-millimeter frequency ranges remain relatively unexplored, offering fertile ground for leaky-wave BBL development. In particular, in October 2003, the Federal Communications Commission (FCC) ruled that the spectrum from 71 to 76 GHz, 81 to 86 GHz, and 92 to 95 GHz would be available for high-density fixed wireless services in the United States, creating an ideal operating scenario for Bessel beams [36]. In this context, we present the theoretical analysis, design, and experimental validation of a wideband BBL working in the 81–86 GHz frequency range, capable of generating a near-field focused and limited-diffractive beam. A key innovation of our approach, compared to the previously studied and experimentally validated leaky-wave BBLs [31], [32], [33], [37], lies in the feeding scheme and the working bandwidth. At microwave frequencies, as in [33], a coaxial connector serves as a physical representation of a vertical electric dipole (VED). However, while this kind of connectors are commercially available up to 110 GHz [38], they become fragile and expensive at frequencies beyond 40 GHz [35]. Specifically, due to their extremely small size, these connectors are not only difficult to handle but also prone to damage during assembly, potentially leading to very high replacement costs (see, e.g., [39]). Moreover, since wideband BBLs consist of a subwavelength-thick grounded dielectric slab with an annular metal strip grating printed on top, exciting the device with a coaxial connector is challenging, as inserting it into the dielectric would risk damaging both the probe and the substrate.

To overcome this critical limitation, the proposed wideband BBL is excited through a circular slot on the ground plane, fed by an appropriate mode converter. This transducer transforms (with a mode-conversion efficiency above 90% in the working bandwidth) the fundamental transverse-electric TE₁₀

mode of a standard rectangular waveguide (WR10) into the higher-order transverse-magnetic TM₀₁ mode of a circular waveguide (CW), which extends up to the circular slot in the device ground plane [40], [41].

The experimental validation of the latter in the E band is crucial not only for the implementation of the proposed BBL but also for addressing the long-standing challenge of achieving an azimuthally symmetric, effective, TM source at high frequencies.

Another crucial consideration at E band and higher frequencies is the choice of substrates with a low loss tangent. Most wideband BBLs at lower frequencies rely on ceramic laminates and PTFE composites [33]; however, their high losses significantly reduce efficiency as frequency increases. Therefore, alternative materials must be explored. In this work, we demonstrate that fused quartz is an excellent candidate for E-band wideband BBLs and, in general, for high-frequencies leaky-wave radiating devices based on a dielectric slab. An alternative low-loss solution for the generation of E-band Bessel beams is represented by all-metal spline horns (see, e.g., [11]). This solution, however, appears bulkier than the proposed planar device, even when considering the inclusion of its feeding block.

This paper is organized as follows. Section II presents the theoretical designs of the wideband BBL and of its feeder. Their physical implementation and the experimental-validation setup are discussed in Section III. In Section IV, the measurement results are compared with those obtained from both full-wave simulations and a well-established leaky-wave approach. Finally, conclusions are drawn in Section V.

## II. DESIGN WORKFLOW

This section deals with the design of the proposed wideband launcher from both theoretical and numerical perspectives, showing the design steps from the leaky-wave analysis to the realization of the device. In particular, the design of the radially periodic launcher and the original feeder are presented in Section II-A and Section II-B, respectively.

### A. RADIALLY PERIODIC BESSEL-BEAM LAUNCHER

As mentioned in the Introduction, a wideband BBL consists of a grounded dielectric slab with an annular, radially periodic, metal strip grating printed on top (see Fig. 1). This grating is carefully designed to support the propagation of a first-order, backward, fast leaky-wave harmonic [33], which is strictly needed for generating a focused, Bessel-beam distribution [42]. As is well known, the leaky mode is described by a complex radial wavenumber $k_ρ = β - jα$, where β and α are the phase and attenuation constants [43], respectively. The correct evaluation of $k_ρ$ is crucial for the theoretical prediction of the Bessel-beam performance and for evaluating the near-field distribution [29]. This analysis can be simplified by leveraging the azimuthal symmetry of the device and considering its linearized counterpart, as illustrated in the inset of Fig. 2 [44]. In this manner, a simple, one-dimensional, partially open, parallel-plate waveguide problem, for which
<figure><img src="image_3.png" /><figcaption>**FIGURE 1.** Schematic representation of the proposed wideband Bessel-beam launcher based on a grounded fused quartz slab with an annular metal strip grating printed on top. A qualitative profile of the absolute value of the vertical component of the electric field *E*<sub>*z*</sub> is represented, normalized with respect to its maximum, through a dB color map.</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>**FIGURE 2.** Dispersion curves of the leaky phase $\hat{\beta}$ (solid black line) and attenuation $\hat{\alpha}$ (dashed black line) constants normalized with respect to the vacuum wavenumber $k_0$ as a function of frequency *f*. The inset on top represents the linearized counterpart of the metal strip grating which has been considered for the Bloch analysis evaluation.</figcaption></figure>

various Bloch-analysis techniques have been proposed in the literature [45], [46], [47], [48], holds. In this work, we applied the transfer-matrix method [49], assuming a 1-D linearized counterpart of the wideband launcher with perfect magnetic conductors on the lateral walls to correctly represent the TM surface-wave mode in propagation. Specifically, the values of $\beta$ and $\alpha$ have been extrapolated by considering the unit-cell transfer matrix $T$, obtained as the product of the $T$ matrix for $N = 7$ periods and the inverse of the $T$ matrix for $N = 6$ [50]. Using this approach, the period $p$ and the strip width $w$ of the metal grating on top of the grounded dielectric slab have been designed in order to maximize $\alpha$ while maintaining a low but nonvanishing $\beta$.

On the one hand, the attenuation-constant value has to be carefully chosen to maximize the aperture efficiency for a given BBL. As is well known [29], the efficiency in 1-D leaky-wave radiators is given by $\eta_r = 1 - e^{-2\alpha\rho_{ap}}$, where $\rho_{ap}$ represents the radius of the circular substrate. For fused

quartz substrates, the lateral dimension of the device is constrained by the available substrates aperture radius $\rho_{ap} \simeq 25$ mm [51]. On the other hand, the phase constant must be sufficiently small, but not vanish, to avoid the open-stopband phenomenon [52], ensuring a large nondiffractive range. This range is approximately given through the ray-optics formula $z_{ndr} = \rho_{ap} \cot \theta_0$, where $\theta_0$, known as the axicon angle, is defined as $\theta_0 = \arcsin \hat{\beta}$, with $\hat{\beta} = \beta/k_0$ being the normalized leaky phase constant relative to the vacuum wavenumber $k_0$.

After conducting a parametric analysis of the dispersion curves using a MATLAB live link to control the CST simulation environment [53], a good trade-off solution has been identified. The latter corresponds to a unit-cell configuration with a periodicity of $p = 1.8$ mm and a strip width of $w = 0.9$ mm, yielding the dispersion curves shown in Fig. 2. The resulting attenuation- and phase-constant values correspond to an average radiation efficiency of about $\eta_r \simeq 80\%$ and a nondiffractive range of $z_{ndr} \simeq 110$ mm at the central frequency $f_0 = 83.5$ GHz. The designed metal strip grating has been printed on top of a fused quartz dielectric slab with a height of $h = 0.76$ mm and a complex relative permittivity of $\epsilon_r = 3.789(1 - j0.001)$ at $f_0$. This relative permittivity value has been achieved through interpolation based on physical models [54], incorporating data from the fused quartz datasheet [51] as well as its characterization at higher frequencies [55].

## B. FEEDER IMPLEMENTATION

The previous design of the radially periodic metal strip grating is necessary to achieve an inward, TM-polarized cylindrical leaky wave from the outward traveling wave generated by the source [29]. The latter is typically implemented by means of a coaxial connector [33]. However, to operate in the E band and above, an innovative feeding structure is considered here. In particular, the device is excited by a circular slot on the ground plane, which is, in turn, fed by a CW. To achieve the excitation of an azimuthally symmetric TM surface-wave mode, the CW must support only the higher-order $TM_{01}$ mode. For this purpose, a mode converter has been designed to transform the fundamental $TE_{10}$ mode in the standard WR10 input rectangular waveguide (width $a = 2.54$ mm and height $b = 1.24$ mm) into the higher-order $TM_{01}$ mode in the CW (see the modal distributions in Fig. 3). This device consists of an E-plane power-divider connected to the rectangular-waveguide feeder (see Fig. 4(a)). Each of the two branches of the divider is followed by a 180° bend (as shown in Fig. 4(c)) and symmetrically connected to the CW [56] (see Fig. 4(b)). Since the branches are out of phase, one of the branches (the right one in Fig. 3) is made longer to introduce a phase shift of $\Delta\phi = \lambda_g/2$, where $\lambda_g$ is the operating wavelength in the rectangular waveguide (see the additional section in red in Fig. 4(c)). Although this aspect may limit the bandwidth over which the desired mode conversion is achieved, it did not affect performance within the band of interest, as later confirmed by simulations and measurements. In addition, sectors with different heights in the two rectangular waveguide branches
<figure><img src="image_5.png" /><figcaption>**FIGURE 3.** Pictorial representation of the proposed mode converter able to transform the fundamental TE₁₀ mode (see inset) in a standard WR10 rectangular waveguide in the higher-order TM₀₁ mode (see inset) in the CW.</figcaption></figure>

(see Figs. 4(d) and (e)) and a backshort with a decreasing stepped diameter in the –z direction of the CW (see Fig. 4(b)) have been added for matching purposes when the feeder is connected to the launcher. It is worth noting that more sophisticated or alternative approaches could be considered for implementing the transducer. However, the choice of using a simple E-plane power divider combined with waveguide bends is driven by the goal of minimizing leakage caused by imperfect contact between metal blocks. Cutting along the E-plane ensures better electromagnetic sealing (since surface currents do not cross this plane) and allows for a structure that remains straightforward to fabricate, which is particularly important at high operating frequencies. Specifically, the proposed design requires only a couple of metal blocks, as detailed in Section III.

The design procedure of the mode converter has been carried out in two main steps. First, the power-divider parameters, the branch and bends dimensions, and CW length and radius have been chosen in order to achieve a satisfactory performance of the feeder in terms of mode conversion when the output CW is matched (see Fig. 3). In particular, the circular waveguide diameter, $D_{CW} = 3.18$ mm, has been specifically designed to suppress the propagation of higher-order modes, ensuring that only the desired TM₀₁ is supported, while the dominant CW mode TE₁₁ is not actually excited. [57].

However, although useful for a mode transducer, the optimization of the working bandwidth of the device with an ideal CW output port is of limited significance in the context of exciting a BBL. In this scenario, the mode converter works as the feeding scheme for the proposed TM-polarized, high-frequency, wideband BBL through a circular slot on its ground plane. As a result, the load impedance experienced

<figure><img src="image_6.png" /><figcaption>**FIGURE 4.** Schematic representations of the components of the proposed feeding scheme for the E-band Bessel-beam launcher: (a) power divider, (b) mode converter, (c) bend, and the matching steps for the (d) upper and (e) lower part. It is worthwhile to point out that the bend radius between two different guide heights has been always assumed equal to 0.25 mm, a value which is strictly related to the fabrication process. Moreover, the additional waveguide segment of length $l_t$ [represented in red in (c)], whose value is reported in Table 1, is present only on one side of the feeding scheme since it is needed as additional signal path to properly phase the two waveguide branches.</figcaption></figure>

by the feeding device differs from the wave impedance of the CW TM₀₁ mode. To account for this aspect, the design parameters of different rectangular-waveguide sections and additional CW segments (see Figs. 4(b), (d), and (e)) have been carefully optimized in the second step of the design procedure. The latter has been carried out through the simultaneous exploitation of semi-analytical techniques [58], circuitual representations [56], and full-wave parametric analyses [53].

The design goal was to achieve a simulated reflection coefficient below –15 dB across the entire bandwidth. This ensures a 5-dB margin relative to the typical $S_{11} = -10$ dB threshold before proceeding with fabrication. The resulting magnitude of the input reflection coefficient, obtained with the design parameters reported in Table 1, is shown as a blue solid curve in Fig. 5. Once the optimal configuration has been identified and the tolerance analyses have been carried out, the proposed wideband BBL has been prototyped and characterized, as thoroughly discussed in Section III.

It is worth noting that the proposed excitation scheme has easily been implemented using a split-block fabricated through computerized-numerical-control (CNC) milling. For this reason, the effectiveness of the proposed feeder is of great importance not only for the specific wideband BBL but also for any device requiring pure azimuthally symmetric TM-polarized excitation at high frequencies. Although additional sections have been added for matching purposes, the good
<table><caption>TABLE 1. Geometrical Parameters of the Proposed TE₁₀–TM₀₁ Mode Converter in mm.</caption><thead><tr><th>a</th><th>b</th><th>b<sub>1</sub></th><th>b<sub>2</sub></th><th>b<sub>3</sub></th><th>b<sub>4</sub></th><th>L<sub>1</sub></th></tr></thead><tbody><tr><td>2.54</td><td>1.27</td><td>1.4</td><td>1.81</td><td>2.25</td><td>2.54</td><td>0.87</td></tr><tr><td>L<sub>2</sub></td><td>L<sub>3</sub></td><td>L<sub>4</sub></td><td>L<sub>5</sub></td><td>L<sub>FW</sub></td><td>l<sub>PD</sub></td><td>w</td></tr><tr><td>0.79</td><td>0.71</td><td>0.64</td><td>2.86</td><td>2.54</td><td>3.57</td><td>0.23</td></tr><tr><td>ρ<sub>1</sub></td><td>ρ<sub>2</sub></td><td>ρ<sub>3</sub></td><td>ρ<sub>4</sub></td><td>ρ<sub>in5</sub></td><td>ρ<sub>out5</sub></td><td>ρ<sub>in6</sub></td></tr><tr><td>0.53</td><td>0.61</td><td>0.62</td><td>0.60</td><td>1.59</td><td>2.85</td><td>1.59</td></tr><tr><td>ρ<sub>out6</sub></td><td>b<sub>CW</sub></td><td>l<sub>CW</sub></td><td>h<sub>CW</sub></td><td>h<sub>BS</sub></td><td>h<sub>BS1</sub></td><td>h<sub>BS2</sub></td></tr><tr><td>2.85</td><td>0.94</td><td>1.99</td><td>4.38</td><td>3.31</td><td>0.71</td><td>0.88</td></tr><tr><td>D<sub>CW</sub></td><td>D<sub>BS1</sub></td><td>D<sub>BS2</sub></td><td>h<sub>B</sub></td><td>l<sub>B</sub></td><td>ρ<sub>in</sub></td><td>ρ<sub>out</sub></td></tr><tr><td>3.18</td><td>2.6</td><td>1.68</td><td>8.77</td><td>3.04</td><td>1.27</td><td>2.54</td></tr><tr><td>l<sub>L</sub></td><td>b<sub>S1</sub></td><td>b<sub>S2</sub></td><td>l<sub>S1</sub></td><td>l<sub>S2</sub></td><td>b<sub>SL1</sub></td><td>b<sub>SL2</sub></td></tr><tr><td>1.27</td><td>1.05</td><td>1.18</td><td>1.45</td><td>1.61</td><td>1.18</td><td>1.23</td></tr></tbody></table>

<figure><img src="image_7.png" /><figcaption>FIGURE 5. Absolute value of the simulated (blue solid line) and measured (red solid line) $S_{11}$ parameter of the proposed wideband BBL vs. frequency f. The vertical black lines show the limits of the desired working bandwidth.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>FIGURE 6. Absolute value of the simulated S parameters vs. frequency f in a two-port network constituted by the mode converter. The input and output ports are the WR10 and the CW, respectively. The insets, corresponding to the respective $S_{ij}$ curves displayed in color-code format, show the electric-field profile at port i normalized with respect to its maximum. ($S_{21}^{\text{TE11x}}$ and $S_{21}^{\text{TE11y}}$ indicate the $S_{21}$ parameters related to the TE₁₁ mode with the electric field mainly polarized along the x and y direction, respectively)</figcaption></figure>

performance of the device in terms of mode conversion is corroborated by Fig. 6, which presents the simulated scattering parameters of a two-port network device consisting of the stand-alone mode converter (see Fig. 3). In these simulation

<figure><img src="image_9.png" /><figcaption>FIGURE 7. Photograph of the prototype of the proposed wideband Bessel-beam launcher connected to the vector network analyzer. The insets show the two blocks that constitute the feeder prior to assembly and machining of the output circular waveguide.</figcaption></figure>

results, the input port is placed on the feeding WR10 rectangular waveguide, whereas the output port is positioned on the circular waveguide.

In Fig. 6, since modes with cutoff frequencies higher than that of the TM₀₁ are not propagating for the $D_{CW}$ choice, the $S_{21}$ parameters of the two-port configuration shown in Fig. 3 are reported only for the CW fundamental TE₁₁ mode (with two polarizations) and for the desired TM₀₁ mode. As can be easily inferred from Fig. 6, the designed converter is satisfactorily working for two main reasons: first, the transmission coefficient from the input rectangular-waveguide port to the desired TM₀₁ mode of the output CW is almost unitary (viz., $S_{21}^{\text{TM01}} = 0$ dB) across the entire operating bandwidth; second, there is no transmitted power to the undesired TE₁₁ CW mode in either polarization. Moreover, when the output port is matched to the wave impedance of the considered modes, one can also observe a good matching over the entire bandwidth (viz., $|S_{11}| < -10$ dB in the 81–86 GHz frequency range).

### III. FABRICATION PROCESS AND EXPERIMENTAL SETUP

In this section, the fabrication process and experimental validation of the device are discussed. The proposed wideband BBL consists of two main components: a grounded dielectric slab with an annular metal strip grating on top and the feeder. The former is fabricated using a standard aluminum lift-off process on a fused quartz substrate [51], whereas the latter is realized as a split-block through CNC milling. Specifically, two metal blocks have been machined through CNC milling (see the blue-contoured insets in Fig. 7) to form the rectangular waveguide sections. These two blocks were then aligned using dowel pins and joined together using screws. After assembly, the output circular waveguide section and the circular back-short were drilled using the same CNC machine for better accuracy. The fused quartz slab, featuring the annular metal strip grating on top, was then manually aligned using the output circular waveguide as a reference and secured
<figure><img src="image_10.png" /><figcaption>**FIGURE 8.** Schematic representation and picture (gray inset) of the measurement setup for the near-field characterization of devices working at high frequencies. The prototype of the Bessel-beam launcher (green inset) is connected to the free-space-to-waveguide excitation scheme on one side (red inset) and radiates on the other side. The electric near-field distribution is then evaluated through a electric-field probe mounted on a three-directional stage (blue inset).</figcaption></figure>

to the feeder assembly through a clamping aluminum frame screwed into the metal blocks. After assembly, the reflection coefficient of the proposed wideband BBL is measured using a vector network analyzer (VNA) with a W-band extension module (see Fig. 7). The measured magnitude of the input reflection coefficient, shown as a red solid line in Fig. 5, is in an impressive agreement with the simulated one. Minor discrepancies appear in the considered working bandwidth (81–86 GHz), marked by the black vertical lines in Fig. 5, however, the magnitude of the input reflection coefficient in dB remains lower than the –10 dB threshold, owing to the design margin accounted for during the simulation stage.

Fig. 8 illustrates a schematic representation and a picture (gray inset) of the lock-in detection setup, adapted from [11], [59] and used in this study to characterize the near-field distribution of the proposed BBL. The sub-THz carrier is generated photonically by employing two fiber-coupled, free-running distributed-feedback (DFB) laser diodes that produce optical tones separated by a frequency corresponding to the E-band carrier (81–86 GHz). These tones are combined and intensity modulated using a 102 kHz sinusoidal signal sourced from a lock-in amplifier. The optical signal is then heterodyned to the E-band frequency using a photomixing module connected to the BBL (visible as the black component in the red inset in Fig. 8). To measure the launcher near-field distribution, a WR10 waveguide probe, connected to a zero-bias Schottky barrier diode (ZSBD), detects a voltage proportional to the millimeter-wave power captured by the probe. The probe is mounted on a 3-axis motorized stage programmed to systematically scan the xz-plane (blue inset in Fig. 8). Finally, the lock-in amplifier provides a readout of the voltage amplitude of the 102-kHz signal. An alternative detection scheme using a single frequency converter (see Fig. 8(a)) would be feasible; however, its weight and bulkiness make it unsuitable for our 3-D scanner. Since only the power distribution is of interest, the combination of a ZSBD and a lock-in detector is sufficient,

providing a dynamic range of 30 dB, which is sufficient for accurately characterizing the near-field distribution. The probe is oriented to capture $|E_x|^2$ at $y = 0$ on the xz-plane (see Fig. 8). Since the synthesized Bessel-beam features azimuthal symmetry with TM polarization, this is equivalent to measuring $|E_\rho|^2$, which corresponds to the magnitude of the total tangential electric field. It is worth noting that misalignment effects could slightly deteriorate the correct evaluation of $E_\rho$ through the measurement of $E_x$. However, as confirmed through a 3-D scan of both $E_x$ and $E_\rho$ components, the alignment was nearly perfect. The obtained results are discussed and compared with full-wave and theoretical ones in Section IV.

## IV. NEAR-FIELD DISTRIBUTIONS

The radial component of the electric-field distribution on the xz plane has been evaluated at $f = 81, 83.5, 86$ GHz (minimum, central, and maximum frequency in the operational bandwidth, respectively) through the measurement setup discussed in the previous Section III. It is worth noting that the nondiffractive range varies with frequency due to the dispersive nature of the leaky phase constant, which is directly linked to the nondiffractive range, as clearly illustrated in Fig. 2. Consequently, the predicted nondiffractive ranges are approximately $z_{ndr} \simeq 78, 110, \text{ and } 150 \text{ mm}$ for $f = 81, 83.5, \text{ and } 86$ GHz, respectively.

The measurement results are presented in Fig. 9(a)–(c). Notably, the radial profile closely follows the first-order Bessel function of the first kind $J_1(\cdot)$, as predicted from the theory [29], [33]. A closer analysis of the near-field distributions further confirms the effect of the dispersive behavior of the leaky phase constant. As the frequency increases, the leaky phase constant decreases in absolute value, leading to an increase of the nondiffractive range. This trend is highlighted in Fig. 9(a)–(c) by the white dashed lines, with the maximum nondiffractive range reaching $z_{ndr} = 150 \text{ mm}$, which is also the farthest z-distance at which the field has been evaluated.

The measured field distributions are compared to the numerically predicted results. Fig. 9(d)–(f) present the radial electric field distribution on the xz-plane in dB, normalized with respect to its maximum, as obtained through full-wave simulations at the same frequencies as the measured results. These full-wave results have been obtained using the time-domain solver of CST Microwave Studio [53] by implementing the 3-D model of the device. Specifically, the waveguiding feeder has been modeled by inserting the designed structure (see Fig. 3) into a solid aluminum block. The latter is then placed beneath the grounded dielectric slab, ensuring perfect alignment between the circular slot on the ground plane and the output CW of the mode converter. Fig. 9(g)–(i) instead show the near-field distributions evaluated by means of an established leaky-wave approach, as detailed in [29], [34], [60]. This method assumes the dominance of the leaky-wave contribution on the aperture plane. Therefore, by leveraging leaky-wave theory [61], cylindrical leaky waves are assumed at the radiating aperture, with their leaky wavenumber determined through the previously
<figure><img src="image_11.png" /><figcaption>FIGURE 9. Near-field distribution in dB of the electric-field radial component normalized with respect to its maximum at $f = 81$ GHz (first column), $f = 83.5$ GHz (second column), and $f = 86$ GHz (third column). The fields have been evaluated through measurements (first row), full-wave simulations (second row), and the leaky-wave approach (third row). White dashed lines represent the nondiffractive ranges.</figcaption></figure>

mentioned Bloch analysis (see also the dispersion diagram in Fig. 2). These leaky waves are then used to numerically evaluate the near-field distributions via the Huygens–Fresnel radiation integral and the equivalence theorem [57].

It is worth noting that, due to finite power discretization, the measurement setup cannot capture extremely low power levels. As the distance increases, the detected power beyond

the nondiffractive range drops more than 30 dB below that on the aperture plane. Nevertheless, both the simulated and theoretical near-field distributions show excellent agreement with the measurements.

Another interesting analysis can be made by observing Fig. 10, where the variation of the radial electric-field component along the aperture radius is shown through 1-D plots. In
<figure><img src="image_12.png" /><figcaption>FIGURE 10. Measured absolute value in dB of the electric-field radial component normalized with respect to its maximum vs. *x* at (a)–(c) different *z* distances from the aperture plane (the color of the lines goes from black to yellow as the distance from the aperture plane increases from *z* = 0 mm to *z* = *z*<sub>ndr</sub>) and (d)–(e) at half of the nondiffractive range (*z* = *z*<sub>ndr</sub>/2). The electric-field evaluation of the proposed wideband Bessel-beam launcher has been carried out at *f* = 81, 83.5, and 86 GHz and reported on the first, second, and third column, respectively.</figcaption></figure>

particular, the radial envelope of the normalized $E_\rho$ is reported at different distances from the aperture plane using different colors (color shading from black to yellow as the evaluation $z$-plane moves away from the aperture plane $z=0$ mm to $z=z_{ndr}$) at $f=81$, 83.5, and 86 GHz, in Fig. 10(a), (b), and (c), respectively. Regardless the working frequency, the Bessel-beam behavior is clearly confirmed, as the transverse profile remains almost unaltered in the central radial region, even though the field amplitude decreases with increasing $z$, as expected. This trend further confirms the propagation-invariant nature of these field solutions.

The effect of the working frequency and, in turn, of the leaky-wave dispersion curve is instead more clearly visible by observing Fig. 10(d)–(f). These figures show the measured $E_\rho$ field distribution, normalized with respect to its maximum, at $z=z_{ndr}/2$, where the Bessel-beam profile is expected from $x=-\rho_{ap}/2$ to $x=\rho_{ap}/2$ based on the ray-optics approximation presented in [33]. Interestingly, as the frequency increases, the number of the nulls decreases. This is due to the fact that, as $f$ increases, the modulus of the leaky phase constant $\beta$ decreases (see Fig. 2), requiring a larger radius to reach the value of the nulls of the first-order Bessel function of the first kind $j_1 n$.

## IV. CONCLUSION

The theoretical design and experimental validation of an E-band, radially periodic, wideband Bessel-beam launcher have been presented in this work. The device consists of a grounded

dielectric slab with an annular metal strip grating printed on top through a standard metal lift-off process and is fed through a mode converter. The latter has been implemented as a split-block, providing an effective, TM-polarized, azimuthally symmetric source at high frequencies. Measured results show an impressive agreement with theoretical and full-wave predictions, both in terms of near-field distribution and input reflection coefficient. Therefore, this works paves the way for the implementation of innovative, effective, near-field links at millimeter and submillimeter-wave frequencies based on limited-diffractive, self-healing, and focusing Bessel beams excited through a compact, low-profile, single-feeder launcher.

## IV. ACKNOWLEDGMENTS

The authors thank the NanoRennes-IETR platform belonging to RENATECH+ (French National Network of Facilities for Micro nanotechnology) for manufacturing the fused quartz antennas in clean room.

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