# Fresnel Lens Antennas with smooth phase compensation and manufactured with a very low cost technological process in the 220-330 GHz band

Alexis Goblot, Olivier Lafond, Mohamed Himdi

► To cite this version:

Alexis Goblot, Olivier Lafond, Mohamed Himdi. Fresnel Lens Antennas with smooth phase compensation and manufactured with a very low cost technological process in the 220-330 GHz band. IEEE Access, 2025, 13, pp.176985-176997. 10.1109/access.2025.3621059. hal-05341118

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Submitted on 20 Nov 2025

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Distributed under a Creative Commons Attribution 4.0 International License
Received 5 September 2025, accepted 2 October 2025, date of publication 13 October 2025, date of current version 17 October 2025.

Digital Object Identifier 10.1109/ACCESS.2025.3621059

RESEARCH ARTICLE

# Fresnel Lens Antennas With Smooth Phase Compensation and Manufactured With a Very Low-Cost Technological Process in the 220-330 GHz Band

ALEXIS GOBLOT<sup>1)</sup>, OLIVIER LAFOND, AND MOHAMMED HIMDI

IETR, Université de Rennes, Campus de Beaulieu, 35042 Rennes, France

Corresponding author: Alexis Goblot (alexis.goblot@univ-rennes.fr)

This work was supported in part by European Union through European Regional Development Fund (ERDF); in part by the Ministry of Higher Education and Research, Centre National de la Recherche Scientifique (CNRS); in part by the Brittany Region; in part by the Conseils Départementaux of Ille-et-Vilaine; and in part by the Contrat de Plan Etat-Region (CPER) Project CyMoCod for the measurement equipment.

**ABSTRACT** In this paper, the performance of Fresnel Lens Antennas (FLAs) is investigated in the 220-330 GHz frequency band for future high-data-rate wireless communication systems. The lenses are fabricated through an innovative and highly cost-effective method based on thermally pressed foam material. This technique enables the realization of fully dielectric, inhomogeneous lenses from a single material, allowing smooth phase compensation for the wavefront distortion introduced by a primary feed, in this case a standard horn antenna. After detailing the technological process, the horn antenna is designed and experimentally validated, demonstrating excellent agreement between simulated and measured results in terms of radiation patterns and gain. Several FLAs are then fabricated, confirming the effectiveness of the pressed foam approach over the entire operating band. One of the prototypes, featuring a 30 mm diameter, achieves a narrow half-power beamwidth of 2° and a peak gain of 32 dBi when implemented using three stacked sub-lenses.

**INDEX TERMS** Dielectric compression, Fresnel lens antennas, gain enhancement, low-cost fabrication, phase compensation, sub-terahertz.

## I. INTRODUCTION

High-gain antennas with narrow radiation patterns are well suited for various applications, such as long-range, high-data-rate communications [1] and high-resolution radar systems [2], particularly in the millimeter-wave and sub-millimeter bands, where free-space path loss is significant. A wide operating bandwidth is often desirable in these frequency ranges to support broadband functionalities.

Several antenna technologies have emerged to address the challenge of achieving highly directive beams at sub-millimeter wavelengths. Antenna arrays offer a promising path toward low-profile, integrated solutions using advanced

technologies such as multilayer PCBs [3] or LTCC [4], [5] in the D-band, as well as silicon micromachining for slotted arrays in the W-band [6]. However, these approaches often suffer from limited gain and restricted bandwidth. While diffusion bonding [7] or CNC milling [8] can improve gain, they are relatively complex and costly to implement.

For sub-millimeter antennas, high gain and efficiency can also be achieved using passive architectures that avoid complex feed networks, such as resonant cavity antennas, reflectors, metasurfaces, or dielectric lens systems. A resonant cavity antenna fabricated via additive manufacturing is reported in [9], while a 300 GHz low-cost Fabry-Pérot cavity antenna achieving 15 dBi gain over a 25 GHz bandwidth is reported in [10]. A 50 dBi high-gain offset parabolic antenna operating at 330 GHz with 70 GHz bandwidth is described

The associate editor coordinating the review of this manuscript and approving it for publication was Debabrata K. Karmakar.
in [11], although its bulky size and manufacturing complexity limit practical deployment. Other compact solutions include a dual-reflector system built via CNC milling in [12], achieving 28–29 dBi gain with dual polarization over 80–110 GHz. Metasurfaces are another promising solution for wideband, high-gain, and multibeam antennas, as demonstrated in [13] up to 300 GHz and in [14] using a holographic semiconductor metasurface with 32 dBi directivity at 94 GHz.

Dielectric lenses, particularly homogeneous lenses excited by a single or multiple feeds, also offer attractive features such as beam reconfigurability and broadband behavior. In [15], a hemispherical homogeneous lens with an extension layer operating from 230 to 310 GHz delivers 29 dBi gain using a standard WR3 waveguide. A core-shell lens fabricated with low-cost plastic for the D-band is presented in [16], providing 32 dBi gain with less than 2 dB loss. In [17], an elliptical lens combined with an active focal plane array enables beam steering in the D-band.

Inhomogeneous lenses with gradient index profiles are often used to enable high-gain, reconfigurable antennas at millimeter and sub-millimeter frequencies. Examples include Luneburg and Maxwell Fish-Eye lenses built by combining dielectric materials to achieve the desired refractive index distribution in [18], as well as a Luneburg lens using Teflon with drilled air holes to support beam scanning with active feeds at 60 GHz in [19]. A fully metallic geodesic Luneburg lens is proposed in [20] for improved efficiency and multibeam capabilities.

Among the most widely known gradient-index devices are Fresnel lenses, which can generate narrow beams with high gain when illuminated from the focal point. A Fresnel Zone Plate Lens (FZPL) fabricated via silicon micromachining is presented in [21], achieving 25 dBi gain and 40% fractional bandwidth with circular polarization, albeit through a complex process. The main challenge for such lenses remains the development of low-cost fabrication methods to implement spatially varying refractive indices that are key to their electromagnetic behavior.

A reliable and low-cost process based on composite materials was developed at IETR and successfully applied to manufacture inhomogeneous lenses up to 100 GHz [22], [23], [24]. The technique allows the expulsion of air bubbles from the dielectric mixture, enabling control of the effective permittivity.

The main objective of the present work is to validate and extend this pressed foam technology to the 300 GHz band. This is particularly challenging due to the microstructure of the foam, which is composed of air-filled polymer cells whose size may become comparable to the sub-millimeter wavelengths of interest. With the rapid development of sixth-generation (6G) wireless systems and the growing interest in high-resolution sensing and imaging technologies, there is an urgent need for cost-effective and scalable high-frequency antenna solutions. Fresnel Lens Antennas (FLAs), particularly those fabricated with low-complexity techniques, are strong candidates to meet these requirements. Reducing

the cost and complexity of manufacturing high-gain antennas in the sub-THz range is essential for the democratization of emerging applications in short-range ultra-fast wireless communications, security screening, and biomedical sensing.

Compared to state-of-the-art micromachined FZPLs or metasurface lenses operating above 200 GHz, the proposed lens design offers comparable gain with drastically reduced fabrication cost and complexity. While most high-gain sub-THz lenses rely on silicon processing or CNC-machined parts, our approach bridges the gap between performance and accessibility.

This methodology not only simplifies lens fabrication at sub-THz frequencies, but also opens new directions for passive beam-shaping components using inexpensive and structurally tunable dielectric media. Beyond the current operating band, the process has the potential to support frequency scalability toward the 400–500 GHz range, where dielectric lens solutions remain limited due to manufacturing constraints.

The remainder of this paper is organized as follows:

* Section II introduces the FLA concept and explains the principle of radial variation in dielectric constant to achieve uniform phase and highly directive radiation.

* Section III presents the horn antenna design and its experimental validation using Electrical Discharge Machining (EDM).

* Section IV discusses the realization of FLAs using single or stacked lenses, and provides a comparison between simulated and measured radiation patterns, gain, and beamwidth.

* Section V provides a discussion on the manufacturing process and future improvements.

* Conclusions are drawn in Section VI.

## II. FRESNEL LENS ANTENNA PRINCIPLE AND TECHNOLOGICAL PROCESS USED

### A. FRESNEL LENS ANTENNA PRINCIPLE

As outlined in the introduction, one effective approach to achieve a highly directive antenna is to employ a Fresnel lens that compensates for the phase delay introduced by the spherical wavefront of the primary source. This compensation enables the formation of a uniform-phase electric field at the lens aperture.

A classical configuration of a FLA is illustrated in Fig. 1, where the lens, of diameter D, is discretized into concentric subzones of equal thickness d, illuminated by a primary feed typically a horn antenna, positioned at the focal distance F. For fully dielectric FLAs, phase compensation can be achieved by varying the dielectric constant radially across the lens aperture. Each subzone is assigned a different permittivity value depending on its radial position, such that the phase delay introduced by the dielectric medium compensates the phase difference of the spherical incident wave. The required variation in dielectric constant depends on the lens thickness d.
<figure><img src="image_2.png" /><figcaption>FIGURE 1. Sectional view and top view of the FLA with the focal distance F, diameter D and thickness d of the lens. The lens is illuminated by a primary source positioned at the phase center [24].</figcaption></figure>

In conventional Fresnel Zone Plate Lenses (FZPLs) [23], phase compensation is implemented periodically based on the number of discrete steps per full $2\pi$ phase shift. For instance, the half-wave FZPL uses $Q = 2$ steps per $2\pi$, the quarter-wave FZPL uses $Q = 4$, and the eighth-wave FZPL uses $Q = 8$.

By calculating the optical path difference for two different incident angles across the FLA depicted in Fig. 1, the required phase correction can be verified using (1), where $f_0$ is the working frequency, $c$ is the speed of light in vacuum, $F$ is the focal distance, $\epsilon_{ref}$ is the relative dielectric permittivity at the center of the lens, $d$ is the thickness of the lens, $\Delta$ is the phase shift introduced by the spherical wavefront considered for the incident angle $\theta_i$, $\epsilon_r$ is the relative dielectric permittivity of the lens at $\theta_i$, and $\theta_f$ is the refracted angle corresponding to $\theta_i$. This expression allows the determination of the dielectric constant distribution needed across the subzones to ensure phase alignment at the output plane of the lens.

$$ \frac{2\pi f_0}{c} (F + \sqrt{\epsilon_{ref}} d) = \frac{2\pi f_0}{c} \left( (F + \Delta) + \frac{\sqrt{\epsilon_r} d}{\cos \theta_f} \right) \quad (1) $$

As demonstrated in [24], implementing a smooth phase correction equivalent to an infinite number of infinitesimal subzones enhances both the efficiency and the bandwidth performance of FLAs.

The designs presented in this work are based on this principle, featuring a continuous phase variation across the lens diameter. However, achieving such a smooth phase profile requires a fabrication technology capable of producing a gradual variation in dielectric permittivity, rather than discrete steps.

The technological process developed to fulfill this requirement is described in detail in the following subsection.

## B. A MANUFACTURING TECHNOLOGY FOR FLAS BASED ON A PRESSED FOAM PROCESS

The pressed foam process employed in this study has been used for several years at the IETR laboratory for the fabrication of inhomogeneous lenses, as noted in Section I. However, until now, this process had only been experimentally validated up to 100 GHz, as reported in [24]. The industrial foam material used Airex R82 has an initial

dielectric constant of approximately 1.12 and consists of a polymeric matrix embedded with air bubbles. For the designs presented in this work, the lenses were fabricated following the procedure detailed in [22]. This process allows for controlled variation of the dielectric constant by modifying the foam's internal structure via mechanical compression. Specifically, the process involves pressing the foam at a controlled temperature using a hydraulic heat press, which expels air from the material and reduces its thickness. As illustrated in Fig. 2, a foam sheet with an initial thickness $h_i$ is compressed to a final thickness $h_f$, thereby yielding a compression ratio $\xi = \frac{h_i}{h_f}$. This ratio directly governs the effective dielectric constant. Experimental data and model shown in Fig. 3 reveal that the dielectric constant increases from its original value of 1.12 (uncompressed foam) to as high as 2.65, depending on the compression ratio. This characterization was conducted at 60 GHz using the method presented in [22], while the model is the average dielectric constant equation reported by Plonus in [25], applied to the Airex R82 foam. In order to compensate for the limitation of the foam in term of effective dielectric constant, it might be necessary, for some applications, to increase the thickness of the pressed foam to achieve desired phase compensation.

While this pressed foam technique has proven effective at millimeter-wave frequencies (up to 100 GHz), its extension to higher frequencies, particularly in the 300 GHz range, presents new challenges. Several concerns arise:

1. At 300 GHz, the wavelength is approximately 1 mm, and the presence of internal air bubbles (typically ~ 250 µm in diameter) could lead to scattering or diffraction effects within the foam.

2. These air bubbles may also introduce unwanted local inhomogeneities, leading to local anisotropic properties, affecting the lens's performance.

3. The dielectric behavior of Airex R82 foam has only been characterized at 60 GHz; thus, its permittivity and loss tangent as a function of compression ratio at 300 GHz remain uncertain.

That's why this paper focuses on lens designs in the 220-330 GHz band to push this technological process for these very high frequencies, and it may consider improving the developed process if necessary.

To ensure geometric fidelity during pressing, a custom mold was designed to enforce radial uniformity and minimize shear deformation across the foam slab during heating. Preliminary tests confirmed that mechanical tolerances below 0.2 mm are achievable with the current mold setup, which is essential to reproduce the target permittivity profile across multiple samples.

The proposed technique requires only standard industrial tools such as a hydraulic hot press and metallic molds, enabling repeatable fabrication without cleanroom facilities. The total manufacturing time for one lens remains below one hour, which makes the process attractive for batch production.
<figure><img src="image_3.png" /><figcaption>FIGURE 2. The pressed foam process to change the dielectric constant locally [22].</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>FIGURE 3. Dielectric constant variation versus the compression ratio

$\xi = \frac{h_i}{h_f}$.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>FIGURE 4. Horn antenna design and its dimensions.</figcaption></figure>

For these reasons, this work focuses on exploring the applicability of the pressed foam process in the 220–330 GHz frequency range, with the aim of validating and, if necessary, refining the fabrication method for operation in the sub-terahertz regime.

### III. DESIGN, MANUFACTURING AND MEASUREMENT OF THE HORN ANTENNA USED AS THE PRIMARY SOURCE FOR THE FLA TECHNOLOGICAL PROCESS

The first step in designing an efficient FLA, in terms of gain and radiation pattern quality, involves developing a suitable primary source for lens illumination. For operation within the 220–330 GHz frequency band, a fully metallic horn antenna was designed and fabricated to serve as a low-loss, high-efficiency primary feed.

<figure><img src="image_6.png" /><figcaption>FIGURE 5. Manufactured horn antenna with the EDM process at IETR.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>FIGURE 6. Measured $S_{11}$ parameter of the manufactured horn antenna.</figcaption></figure>

A simple pyramidal horn configuration was selected in order to produce classical radiation patterns in both the E- and H-planes. No extensive optimization was carried out, as the horn design itself was not the main focus of this study. Full-wave electromagnetic simulations were performed using CST Studio Suite. The resulting antenna dimensions are shown in 4: the horn has a width of 2.59 mm, a height of 1.30 mm, and a total length of 8 mm. It is excited via a standard WR3 rectangular waveguide with internal cross-sectional dimensions of 0.8 mm × 0.4 mm. A circular flange was added to facilitate connection with standard WR3 measurement setups for $S_{11}$ and radiation pattern measurements in the IETR anechoic chamber.

The horn antenna was manufactured from a single block of aluminum using EDM, also known as electro-erosion. This technique employs a graphite electrode to form a negative mold of the horn geometry. A photo of the fabricated prototype is shown in Fig. 5, where the metal flange holes for WR3 attachment can also be seen.

The return loss ($S_{11}$) was measured using an R&S vector network analyzer equipped with sub-millimeter frequency extenders. The measured $S_{11}$ response over the 220–330 GHz band is presented in Fig. 6, showing good impedance
<figure><img src="image_8.png" /><figcaption>FIGURE 7. Comparison of simulated and measured radiation patterns (co-polar) of the horn antenna in E and H plane at 270 GHz.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>FIGURE 8. Measured realized gain and simulated directivity of the horn antenna.</figcaption></figure>

matching ($S_{11} < -12$ dB) across the entire band, consistent with simulation results.

Radiation pattern measurements were performed in a Compact Antenna Test Range (CATR) configuration inside the IETR anechoic chamber. Fig. 7 shows the measured and simulated co-polar radiation patterns at 270 GHz in both the E- and H-planes. Excellent agreement is observed between simulation and measurement over the full band. At 270 GHz, the half-power beamwidths are 43° in the E-plane and 30° in the H-plane, with cross-polarization levels below -23 dB in both planes.

The antenna gain was measured using the same CATR setup and is shown in Fig. 8. The measured gain is compared to the simulated directivity to estimate insertion losses. The horn antenna shows an average loss of approximately 1 dB across the band, indicating high fabrication and radiation efficiency. The measured gain increases with frequency, ranging from 12 dBi to 15 dBi within the 220–330 GHz band.

<figure><img src="image_10.png" /><figcaption>FIGURE 9. Fresnel law corresponding to the two first FLAs.</figcaption></figure>

# IV. DESIGN, MANUFACTURING AND MEASUREMENT OF DIFFERENT FLAS

## A. INTRODUCTION AND EXPLANATION OF FLA DESIGN

This section presents the design, fabrication, and experimental characterization of various FLAs operating in the 220–330 GHz band. The lenses were manufactured using the pressed foam process described in Section II and were illuminated by the horn antenna developed in Section III. Since this is the first time this fabrication technique is applied at sub-millimeter wavelengths, multiple prototypes were produced in order to evaluate and compare their performance in terms of radiation patterns and gain.

As discussed in Section II-A, fully dielectric FLAs were considered in this work. Phase compensation to generate a plane wave at the lens output was achieved by smoothly varying the dielectric constant along the lens diameter. All fabricated FLAs had similar diameters of approximately 30 mm (corresponding to $30\lambda_0$ at 300 GHz), with focal lengths ranging from 35 mm to 42 mm depending on the prototype.

As described in Section II-B, the pressed foam process allows control over the dielectric constant by adjusting the compression ratio, defined as the ratio between the initial and final thickness of the foam. By combining the dielectric profile (Fig. 9) with the compression curve (Fig. 3), a spatially varying thickness profile can be designed for the foam slab, which after compression produces the desired permittivity distribution across the lens aperture.

The following section examines several FLA prototypes, with the main distinction being whether they were fabricated as a single monolithic lens or assembled from multiple stacked sub-lenses.

The dielectric constant profile used for phase correction is shown in Fig. 3, where it varies continuously from 1.0 to 2.3. Given that the uncompressed foam has an initial dielectric constant of 1.12, the outermost portion of the lens must be trimmed, as depicted in Fig. 3, to satisfy the required index profile.
<figure><img src="image_11.png" /><figcaption>**FIGURE 10.** Initial smooth profile of the first FLA before the pressing process.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>**FIGURE 11.** Initial smooth profile of the only lens constituting the first FLA (A) before the pressing process, (B) after the pressing process.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>**FIGURE 12.** Rohacell foam mechanical support with two pieces (one for lens and one for achieving the focal distance).</figcaption></figure>

## B. FLA REALIZED IN ONE UNIQUE PIECE OF FOAM

The first and most straightforward approach for fabricating a Fresnel lens consists in producing the structure as a single piece, with a continuously varying thickness profile prior to compression. This initial thickness profile is shown in Fig. 10 and is designed to achieve the desired dielectric constant variation across the lens diameter, targeting a final compressed thickness of 5 mm.

Photographs of the initial foam profile before compression (Fig. 11(a)) and the final lens after pressing (Fig. 11(b)) reveal

<figure><img src="image_14.png" /><figcaption>**FIGURE 13.** S<sub>11</sub> parameter of the first and second manufactured FLAs, both illuminated by the primary source.</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>(a) E plane.</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>**FIGURE 14.** Measured and simulated radiation patterns of the first lens (A) E plane at 270 GHz, (B) H plane at 270 GHz.</figcaption></figure>

that the resulting structure is neither perfectly cylindrical nor entirely flat at the edges or top surface. Such deviations are
<figure><img src="image_17.png" /><figcaption>**FIGURE 15.** Measured and simulated realized gain of the first FLA between 220 and 330 GHz.</figcaption></figure>

<figure><img src="image_18.png" /><figcaption>**FIGURE 16.** Impact of a 200 microns gap between the two sub-lenses on the simulated $S_{11}$ parameter of the second FLA, illuminated by the primary source.</figcaption></figure>

expected to introduce non-ideal phase compensation, which could impact both the radiation pattern and gain performance.

For characterization, the dielectric lens was mounted within a two-part mechanical support made of Rohacell foam ($\epsilon_r$ = 1.07 at 26.5 GHz). This fixture was designed to ensure the optimal focal distance of 42 mm between the lens and the horn antenna. To minimize dielectric losses, the Rohacell structure was drilled out along the optical axis between the horn and lens, leaving only a 5 mm thick rim to mechanically hold the lens in place, as shown in Fig. 12.

The return loss ($S_{11}$), presented Fig. 13, of the lens-fed antenna remains excellent across the entire band, with values better than 15 dB between 225 and 330 GHz, closely matching that of the standalone horn. Radiation pattern and gain measurements were conducted using the CATR setup at IETR over the 220–330 GHz range. Fig. 14 shows the comparison between simulated and measured co-polar radiation patterns at 270 GHz in both E- and H-planes. A very low cross-polarization level ($< -25$ dB) was observed for

<figure><img src="image_19.png" /><figcaption>(a) E plane.</figcaption></figure>

<figure><img src="image_20.png" /><figcaption>(b) H plane.</figcaption></figure>

<figure><img src="image_21.png" /><figcaption>**FIGURE 18.** Impact of a 200 microns gap between the two sub-lenses on the simulated realized gain of the second FLA.</figcaption></figure>

both planes. The half-power beamwidths vary from 2.8° to 1.8° in the E-plane and from 3° to 2° in the H-plane across
<figure><img src="image_22.png" /><figcaption>(a) Sub-lens before press.</figcaption></figure>

<figure><img src="image_23.png" /><figcaption>(b) Sub-lens after press.</figcaption></figure>

<caption>**FIGURE 19.** Smooth profile of a sub-lens of the second FLA (A) before the pressing process, (B) after the pressing process.</caption>

the frequency band. Concerning the side lobes at ± 30°, they indicate losses caused by spillover, because the primary source illuminates a surface area greater than the lens. Given the primary source has a greater aperture in the E-plane than the H-plane, the spillover is more important in the E-plane, explaining why the sides lobes at ± 30° are higher in the E-plane than the H-plane in Fig. 14.

The overall agreement between simulation and measure-
ment is good in terms of symmetry, main lobe direction,
and beamwidth. However, the manufactured antenna exhibits
higher side lobe levels (-9 dB) than predicted by simulations
(-15 to -20 dB). This discrepancy is likely due to non-ideal
phase compensation caused by uncertainties in the dielectric
constant versus compression ratio, which was originally
characterized at 60 GHz (Section II-B) and may not hold
precisely in the 220-330 GHz band.

Additionally, this first lens design involved a substantial
uncompressed central thickness (55 mm), and the pressed
foam process is generally less suitable for thicker structures,
especially at higher frequencies.

Fig. 15 presents the measured and simulated realized gain of the antenna system. For the measurements, losses from the horn antenna (≈1 dB) and the 5 mm Rohacell support were accounted for. The simulations also include losses in the Airex R82 foam, using dielectric loss tangents (0.008 < tan δ < 0.016) measured at 60 GHz. These values likely underestimate the actual losses at 300 GHz, partially explaining the 2–3 dB gain discrepancy between simulation and measurement.

Furthermore, mechanical alignment errors during assem-
bly may contribute additional loss, and it is observed that the
lens performs better at lower frequencies (220–260 GHz) than
at the upper end of the band (270–330 GHz). This degradation
is likely related to increased scattering from air bubbles
within the foam, whose sizes become more significant as the
wavelength decreases.

C. FLA MADE WITH TWO IDENTICAL SUB-LENSES
STacked together

To overcome the limitations imposed by the manufacturing
process due to the relatively thick lens in the initial

<figure><img src="image_24.png" /><figcaption>(a) E plane.</figcaption></figure>

<figure><img src="image_25.png" /><figcaption>(b) H plane.</figcaption></figure>

<figure><img src="image_26.png" /><figcaption>**FIGURE 21.** Measured and simulated realized gain of the second FLA between 220 and 330 GHz.</figcaption></figure>

design (5 mm), a different approach was chosen. This
involves taking the height profile calculated for the lens,
<figure><img src="image_27.png" /><figcaption>**FIGURE 22.** Initial smooth profile of the third FLA before pressing process, before the division into sub-lenses.</figcaption></figure>

<figure><img src="image_28.png" /><figcaption>(b) Comparison of the compression quality of the different manufactured FLAs.</figcaption></figure>

<caption>**FIGURE 23.** Smooth profile of a sub-lens of the third FLA (A) before the pressing process, (B) a comparison of the compression quality of the different manufactured FLAs.</caption>

but halving it, while also halving the final height. This allows us to reduce the amount of foam to be pressed, while maintaining the compression ratio. Two lenses were manufactured using this approach, as shown in Fig. 19, which were then stacked to reconstruct the desired lens. Compared to the single-piece configuration described in Section IV-B, the resulting sub-lenses appear significantly flatter after the pressing process, which is expected to improve phase uniformity and reduce fabrication-induced imperfections.

Prior to fabrication, full-wave simulations were performed to assess the impact of a potential air gap (up to 200 µm) between the stacked layers. It can be seen on Fig. 16 that the return loss conserves the same curve profile despite the gap. At 270 GHz, the gap causes the side lobe level in both planes to increase (2.5 dB in the E plane, 3 dB in the H plane), as shown in Fig. 17. However, the impact on the realized gain (Fig. 18) is minimal, as maximal loss of gain across the entire band is 0.4 dB, reached between 290 and 300 GHz. Overall, the performances of the simulated FLA remain excellent despite the introduced gap.

<figure><img src="image_29.png" /><figcaption>**FIGURE 24.** $S_{11}$ parameter of the third manufactured FLA, illuminated by the primary source.</figcaption></figure>

The measured and simulated co-polar radiation patterns for the stacked-lens configuration are presented in Fig. 20 at 270 GHz in both the E- and H-planes. The realized gain of the antenna is plotted in Fig. 21. The new configuration yields improved results compared to the single-lens design. Specifically, the first side lobe level is reduced to approximately –11 dB, compared to –9 dB in the initial design. Additionally, the measured gain increases by at least 1.5 dB across the band while the return loss remains better than 15 dB between 225 and 330 GHz, as shown Fig. 13.

The measured gain grows steadily with frequency, ranging from 30 dBi at 225 GHz to 32 dBi at 330 GHz. The half-power beamwidths vary from 2.8° to 1.7° in the E-plane and from 3.0° to 1.9° in the H-plane over the 220–330 GHz range. As with the previous design, the cross-polarization levels remain very low, with values better than –29 dB in both planes at 270 GHz.

Encouraged by these improved results, a third prototype was developed using a similar strategy, this time consisting of three stacked sub-lenses. This configuration and its corresponding measurements are discussed in the following section.

## D. FLA MADE WITH THREE IDENTICAL SUB-LENSES STACKED TOGETHER

In this third design, the same reasoning as in the Section IV-C was applied, dividing the lens into three sub-lenses instead of two. However, the lens design has been slightly changed to reduce bulk. The total final thickness was increased to 6 mm, corresponding to 2 mm per sub-lens after compression. Consequently, the focal length was reduced to 35 mm. The adjusted smooth thickness profile, adapted to this new focal configuration, is illustrated in Fig. 22.

Three sub-lenses have been manufactured using the divided thickness profile, as illustrated in Fig. 23(a). After thermal compression, the resulting sub-lens exhibits an even flatter profile than the previous two designs, as it can be
<figure><img src="image_30.png" /><figcaption>(a) E plane.</figcaption></figure>

<figure><img src="image_31.png" /><figcaption>(b) H plane.</figcaption></figure>

<caption>FIGURE 25. Measured and simulated radiation patterns of the third FLA (A) in the E plane at 270 GHz, (B) in the H plane at 270 GHz.</caption>

seen in Fig. 23(b), indicating improved uniformity in dielectric distribution and suggesting enhanced electromagnetic performance.

Fig. 24 presents the return loss of the third manufactured FLA. As it is the case for the first and second FLAs presented in this work, this FLA also has a return loss better than 15 dB between 225 and 330 GHz.

Fig. 25 presents the simulated and measured co-polar radiation patterns at 270 GHz in both the E- and H-planes. The realized gain results are shown in Fig. 26. Overall, this configuration delivers the best performance among the three tested prototypes. Specifically, the half-power beamwidths vary from 2.6° to 1.6° in the E-plane and from 2.7° to 1.8° in the H-plane across the 220–330 GHz range.

As in the previous designs, cross-polarization levels remain consistently low, staying below –23 dB in both planes at 270 GHz. The measured gain is close to or exceeds 32 dBi across most of the band.

Between 220 and 250 GHz, the measured gain closely matches the simulated values, confirming the effectiveness

<figure><img src="image_32.png" /><figcaption>FIGURE 26. Measured and simulated realized gain of the third FLA between 220 and 330 GHz.</figcaption></figure>

of the technological process within this frequency range. To further validate this conclusion, Fig. 27 compares the simulated and measured radiation patterns at 220 GHz and 240 GHz in both the E-plane and the H-plane. While some discrepancies remain in side lobe levels, the overall agreement is significantly improved compared to earlier designs, indicating better phase compensation and reduced manufacturing-induced distortions.

This experimental validation confirms that the pressed foam technique remains effective at frequencies three times higher than those previously reported, despite the increased sensitivity to microstructural features such as air bubble scattering. The method shows potential scalability to even higher frequencies, provided that foam microstructure and losses are further optimized and characterized.

Since dielectric properties such as loss tangent and permittivity dispersion can vary significantly above 100 GHz, a dedicated measurement campaign is underway to extend the material database for compressed foam up to 330 GHz.

Accurate dielectric modeling at these frequencies is crucial for predicting lens performance, especially as scattering and absorption become increasingly dominant.

V. DISCUSSION ABOUT RESULTS

The pressed foam process has demonstrated strong potential for the fabrication of FLAs operating in the sub-millimeter wave range. Despite the promising results, several avenues for improvement remain in order to further optimize antenna efficiency and reduce side lobe levels particularly at the upper end of the frequency band (270–330 GHz). As discussed earlier, the phase compensation strategy relies on controlling the dielectric constant via the compression ratio $\frac{h_i}{h_f}$, based on material characterization performed at 60 GHz. This introduces uncertainties when extrapolated to higher frequencies, such as 300 GHz. Therefore, future work should include a comprehensive dielectric characterization of the foam material within the 220–330 GHz range to enhance phase accuracy.
<figure><img src="image_33.png" /><figcaption>FIGURE 27. Measured and simulated radiation patterns of the third FLA (A) in the E plane at 220 GHz, (B) in the H plane at 220 GHz, (C) in the E plane at 240 GHz and (D) in the H plane at 240 GHz.</figcaption></figure>

<table><caption>TABLE 1. Comparison between the designed FLAs and the state of the art.</caption><thead><tr><th>Reference paper</th><th>Frequency (GHz)</th><th>Diameter (λ)</th><th>Bandwidth (GHz)</th><th>Gain (dBi)</th><th>Phase compensation</th><th>Manufacturing process</th></tr></thead><tbody><tr><td>[21]</td><td>625</td><td>17</td><td>250</td><td>25</td><td>Stepped</td><td>Silicon micro-machining</td></tr><tr><td>[24]</td><td>92</td><td>36.8</td><td>29.25</td><td>38.9</td><td>Smooth</td><td>Pressing foam process</td></tr><tr><td>[26]</td><td>300</td><td>19</td><td>55</td><td>27.4</td><td>Partially smooth</td><td>Dielectric 3D printing</td></tr><tr><td>[27]</td><td>230</td><td>19</td><td>25</td><td>22</td><td>Stepped</td><td>Conical lens and flat dielectric rings</td></tr><tr><td>[28]</td><td>300</td><td>300</td><td>NA</td><td>45</td><td>Stepped</td><td>PTFE rings</td></tr><tr><td>[29]</td><td>75, 120</td><td>24</td><td>Dual band</td><td>21.3 (120 GHz)</td><td>Stepped</td><td>Additive Dielectric printing</td></tr><tr><td>This paper</td><td>270</td><td>30</td><td>110</td><td>32</td><td>Smooth</td><td>Pressing foam process</td></tr></tbody></table>

Preliminary sensitivity analyses have indicated that axial misalignments between the horn antenna and the lens may lead to a measurable degradation in gain and increased side-lobe levels. Thus, precise mechanical alignment remains a key requirement for performance stability.

Additionally, the mechanical aspects of the pressing process could be refined. The current method uses a metal

mold with a cylindrical cavity matching the lens diameter and a piston to apply pressure (Fig. 28). Introducing small vent holes at the bottom of the mold could facilitate the escape of trapped air during compression, thereby improving uniformity and alignment between the target and actual thickness profiles, as compression flaws will impact the index gradient within the lens, which will deviate from
<figure><img src="image_34.png" /><figcaption>FIGURE 28. Metal mold used to press the three sub-lenses of the third FLA.</figcaption></figure>

Fresnel's law, causing a loss of focus and thus reducing gain.

An additional advantage of the proposed foam-based process lies in its extremely low manufacturing cost. The total material and fabrication cost for one lens much lower than comparable dielectric or metallic structures manufactured with CNC or micromachining techniques. The process also shows excellent repeatability and does not require cleanroom environments or complex alignment steps, further highlighting its suitability for industrial upscaling.

Experimental results indicate that lenses composed of stacked sub-lenses outperform those fabricated as a single unit. This suggests that fabricating lenses from thinner, individually pressed layers may further enhance performance, while also offering greater flexibility in shaping the dielectric gradient.

Although initial estimations were based on 60 GHz loss tangent values, the effective dielectric losses at 300 GHz are likely underestimated. High-frequency material characterization will allow refinement of the electromagnetic simulation models and better prediction of radiation efficiency. A dedicated measurement campaign is currently under preparation to characterize the dielectric behavior of compressed foam samples across the full 220–330 GHz band. These data will enable more accurate modeling of the dielectric constant and loss tangent as a function of the compression ratio and frequency.

In conclusion, the proposed technological process is remarkably low-cost and shows excellent promise for scalable sub-millimeter lens fabrication. A comparison with recent sub-millimeter FLA designs reported in the literature is provided in Table 1, focusing on implementations operating above 100–150 GHz. However, To the best of our knowledge, only [24] and the work presented in this article achieve smooth phase compensation above those frequencies.

## VI. CONCLUSION

This paper has presented the design, fabrication, and characterization of three fully dielectric FLAs operating in

the 220–330 GHz frequency band. The work focuses on an innovative and highly cost-effective manufacturing technique without any post-fabrication coating or chemical treatment that employs a single commercially available foam, thermally pressed to achieve a spatially varying dielectric constant for smooth phase compensation. The lenses are illuminated by a metallic horn antenna fabricated using EDM, ensuring high-quality primary excitation. To the best of our knowledge, this is the first demonstration of a FLA operating in the 220–330 GHz band using a such approach.

Among the three proposed configurations, the design based on the stacking of three thin sub-lenses demonstrated the best overall performance, achieving a measured gain of up to 32.5 dBi, validating the suitability of the pressed foam process for high-frequency lens-based antennas. Stacking thin sub-lenses enables better control of the dielectric gradient and improves phase uniformity, making it particularly effective in the lower portion of the targeted frequency range (220–270 GHz). This low-cost lens technology holds strong potential for future high-frequency systems such as 6G, high-resolution imaging radar, and secure THz communications.

Future research will aim to optimize the lens fabrication process through improved material characterization and enhanced mechanical control during compression, while also exploring integration into compact, low-cost, multi-beam or electronically reconfigurable antenna systems for next-generation THz applications. Future work, using this technological process, will also explore hybrid designs with active or switchable metasurface layers for dynamic beam steering, non-planar geometry for curved surfaces, and tailored aperture profiles to enable advanced beam-shaping capabilities such as asymmetric coverage and orbital angular momentum (OAM) generation.

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<figure><img src="image_35.png" /></figure>

**ALEXIS GOBLOT** was born in Rouen, France, in 1998. He received the degree in electrical engineering and radio communications from the École Supérieure d'ingénieurs de Rennes (ESIR), France, and the master's degree in telecommunication and electronics from the University of Rennes, France, in 2022. He is currently pursuing the Ph.D. degree in electronics with the Institut d'Electronique et des Technologies du numéRique (IETR), University of Rennes.

<figure><img src="image_36.png" /></figure>

**OLIVIER LAFOND** received the Ph.D. degree in signal processing and telecommunications from the University of Rennes 1, Rennes, France, in 2000. Since October 2002, he has been an Associate Professor with the Institut d'Electronique et des Technologies du numéRique (IETR), University of Rennes. Since 2020, he has been a Full Professor with IETR. He has authored or co-authored 50 journal articles and 70 papers in conference proceedings. He has also authored/co-authored four book chapters. He holds nine patents in the area of antennas. His research activities concern passive and active millimeter-wave and sub-millimeter wave antennas, quasi-optical systems (inhomogeneous lens or plasma antennas).

<figure><img src="image_37.png" /></figure>

**MOHAMMED HIMDI** received the Ph.D. degree in signal processing and telecommunications from the University of Rennes 1, France, in 1990. Since 2003, he has been a Professor with the University of Rennes 1. He has been the Head of the High Frequency and Antenna Department, since 2013, and IETR, since 2024. He has authored or co-authored 176 journal articles and over 350 papers in conference proceedings. His H-index is 41. He has also co-authored 12 book chapters. He holds 49 patents. His research activities concern passive and active millimeter-wave antennas. His research interests include the development of new architectures of antenna arrays and new three-dimensional (3-D) antenna technologies. He was a Laureate of the 2nd National Competition for the Creation of Enterprises in Innovative Technologies in 2000 (Ministry of Industry and Education). In March 2015, he received the JEC-AWARD in Paris on a pure composite material antenna embedded into a motorhome roof for the Digital Terrestrial Television Reception. He received the Innovation Trophy 2021 from the University of Rennes 1. In 2024, he received the Gold Award for the invention/innovation category from iMTC 9.0 at the Universiti Putra Malaysia.