High-Gain Circularly Polarized 500–750 GHz Lens Antenna Enabled by Silicon Micromachining

This article introduces an innovative silicon-micromachined, low-profile, high-gain antenna designed for wideband performance in the whole 500–750-GHz waveguide band. The novel antenna concept is based on an elliptical Fresnel zone planner lens (FZPL) with optimized distribution of the zone dimensions. Furthermore, without requiring any extra phase compensating components, the design ensures circular polarization (CP), which was measured to an axial ratio of better than 2.5 over the whole waveguide band (40% fractional bandwidth). The measured gain ranges from 24.3 to 25.7 dBi, and the return loss is better than 15 dB over the whole 250 GHz band. The <inline-formula> <tex-math notation="LaTeX">$8.25\times7.62$ </tex-math></inline-formula> mm large and only <inline-formula> <tex-math notation="LaTeX">$526~\mu \text{m}$ </tex-math></inline-formula> thick antenna can be directly mounted onto a standard WM-380 waveguide flange. The measured radiation patterns for CP, the gain, the axial ratio, and the return loss are excellently matching the simulated antenna performance. This work shows that all-dielectric antennas at THz frequencies easily outperform metal-based designs due to drastically reduced loss with only −0.85 dB average radiation efficiency in the overall frequency band.


I. INTRODUCTION
T ERAHERTZ (THZ) frequencies, ranging from 0.3 to 3 THz within the electromagnetic spectrum, have gained significant attention in recent years due to their potential for ultrahigh-speed wireless communications and radar applications [1], [2].The THz frequency range enables novel applications and promises advancements in various fields.However, to fully harness the potential of THz technology, high-gain antennas are crucial to compensate for propagation losses and to extend transmission distances.Various approaches for high-gain antennas at THz frequencies have been explored, including the use of silicon lenses fed by leaky wave waveguides [3], flat aperture arrays [4], leaky wave antennas with pillbox feeds [5], and metallic printed horns [6].Designing antennas in the THz range presents a unique challenge, primarily due to the reduced size of the wavelength, which affects the size of all components.While common high-gain antennas like reflectors and horns are typically suitable for use up to the THz range, their bulkier nature, and the requirement for micrometer-level accuracy during fabrication make them challenging to implement at these frequencies [7].Lens antennas have emerged as a promising solution for achieving high-gain performance in THz applications.These antennas utilize the principles of focusing and collimating electromagnetic waves, resulting in enhanced gain.Lens antennas provide a more compact alternative to standard high-gain quasi-optical systems, like reflectors, as the source is in direct contact with the lens substrate.They offer advantages such as ease of manufacture, cost-effectiveness, and seamless integration capabilities.At THz frequencies, two prominent types of lens antennas are metallic [8] and dielectric lenses [9].While both types have their merits, dielectric lenses have gathered significant interest for THz applications due to their advantageous properties, including being easy to shape into desired structures, low loss characteristics, ease of fabrication and integration, and high gain [10].However, implementing dielectric lenses in practice has posed challenges.3-D printing, for instance, offers versatility but has inherent limitations regarding material options and feature sizes needed for THz frequencies [11], [12].In contrast, silicon micromachining provides precise dimensional control down to micrometers, smooth surface morphology down to nanometers, compatibility with siliconbased integrated circuit (IC) fabrication technology, and is thus high-volume manufacturable [13].While silicon micromachining has been widely explored for microwave devices at THz frequencies [13], [14], [15], there is limited research on its application for high-gain and wideband antennas [16].
Recently, there have been a number of studies showcasing silicon lens antennas, particularly those utilizing a hemispherical lens shape [3], [17].However, these designs often involve intricate fabrication processes and suffer from limitations in aperture efficiency and limited bandwidth.Another approach in recent literature involved Fresnel lens antennas with multistep phase compensation components [18], but these faced challenges related to restricted bandwidth and gain.These existing studies emphasize the need for a new solution that simplifies fabrication, improves aperture efficiency, and expands the operational bandwidth and gain of silicon lens antennas.Furthermore, most reported high-gain THz antennas utilize linear polarization (LP).However, circular polarization (CP) is preferred in many applications due to its resistance to external interference, its capacity for multipath mitigation, as well as its advantageous potential for polarimetric imaging and facilitating polarization diversity access [19].Unfortunately, there has been limited progress in realizing high-gain CP antennas operating at THz frequencies.To the best of our knowledge, this represents the first high-gain and wideband circularly polarized (CP) THz antenna.Previous works, such as those [11] and [20], have demonstrated CP antennas but are constrained by limited fractional bandwidth, typically up to 19%, and operation up to 320 GHz.These limitations arise from their fabrication using 3-D printing technology, which hinders achieving higher frequencies due to constraints in fabrication accuracy.
The novelty of this work lies in utilizing a combination of a silicon polarizer and an elliptical Fresnel lens antenna to enable a wideband, circularly polarized, high-gain antenna in a compact planner structure in the 500-to 750-GHz frequency band.Notably, this unique approach achieves wideband characteristics in return loss and for circularly polarized radiation without requiring any additional phase compensation components, solely relying on the novel elliptical Fresnel zone structure.The validity of this novel concept has been confirmed by fabricating and characterizing a siliconmicromachined antenna prototype.

A. Elliptical Fresnel Lens
The phase-correcting fresnel zone planner lens (FZPL) antenna offers several advantages for high-gain applications, such as a low profile, simple fabrication process, and low loss, in particular for THz frequencies since only utilizing dielectric and no metallic materials [21], [22], [23].Fig. 1(a) illustrates the concept of the proposed phase-correcting FZPL, which comprises a set of concentric annular sections known as Fresnel zones.These zones consist of alternating materials, with odd-numbered zones made of a homogeneous dielectric material and even-numbered air-filled zones.The boundaries of the elliptical Fresnel zones, represented by the radii r nx and r ny , for n = 1, 2, . . ., N , can be calculated using the formulas provided in [21] and [22] (1) (2) where λ 0 represents the free-space wavelength corresponding to the frequency of operation, which in our case is 625 GHz, F is the focal length, N is the total number of elliptical zones, and D x , D y are the diameters of the length in xand y-direction.In this work, an innovative approach to implementing a wideband Fresnel lens antenna is proposed.In contrast to the conventional method [11], which involves circular zones and the utilization of external phase correction components to attain high gain and wide bandwidth, the concept of elliptical zones controlled by an ellipticity factor (e n ) is explored in our novel approach.This factor enables a gradual transition from elliptical to circular shapes, allowing for precise phase correction within each zone and obviating the necessity for supplementary phase correction components.Through systematic analysis, optimized values of e n for different zones are determined, exerting a significant influence on phase correction, and realized gain.As an example, the specific impact of the e n factor on the realized gain of a N = 9 zone lens, i.e., the optimization for the outermost zone, is demonstrated in Fig. 2 In this work, the feed is a standard open waveguide (WR-1.5)with a gain of 7.3 dBi.To balance between aperture efficiency and spillover loss, the focus-to-diameter ratios (F/D x and F/D y ) are chosen so that the equal beamwidth in the E-and H-planes after focusing is optimized.Also, the required phase correction is determined by the height of the zone layers (h) and can be expressed as where ε r = 11.9 is the relative dielectric constant of silicon used as the lens material, with a specified resistivity of more than 2000 -cm.A gain of 27 dBi is targeted for the nine-zone (N = 9) FZPL, and the antenna optimization is based on (1)-( 3).As the optimum F value, 4.2 mm is considered to have the highest achievable gain, which means that the F/D x and F/D y ratios are equal to 0.51 and 0.55, respectively.To assess the effectiveness of the proposed elliptical shape, a comparison with the conventional circular Fresnel lens antenna is conducted as is shown in Fig. 3.
It is crucial to highlight that both designs have identical aperture sizes and feeding configurations, differing solely in the shape of the Fresnel zones.This comparative analysis aims to evaluate the performance enhancements achieved by the novel elliptical configuration.The results of this comparison reveal a substantial enhancement in return loss and bandwidth for the elliptical configuration.Additionally, the improvement in reflection loss is observed, leading to an approximately 1 dB increase in realized gain.These findings underscore the effectiveness of the proposed lens structure, showcasing simultaneous improvements in bandwidth and gain without the need for extra phase components, solely relying on the ellipticity factor.Fig. 4 illustrates the distribution of the electric field phase in the transmitted beam with x-polarization for both circular and elliptical Fresnel lenses, simulated at 625 GHz.While some nonuniformity in phase remains present in the zones of the elliptical lens, it is notably reduced compared to the circular counterpart.This reduction in phase variation indicates that the elliptical shape better controls the phase of propagating waves, leading to lower variations in impedance and improved reflection loss through this phase compensation approach.The antenna structure and alignment pin mounted on a standard waveguide is shown in Fig. 5.

B. Circular Polarizer
The incident spherical waves from the primary feed propagate through the different Fresnel zones, forming a quasiplanar wave with LP.A circular polarizer is added to convert the incident linear to CP, as illustrated in Fig. 1(b).The incident wave from the antenna exhibits a polarization with a 45 • clockwise rotation relative to the x-axis.This polarization can be decomposed into two orthogonal LP electric field components, denoted as E x and E y .Due to the disparate relative dielectric constants ε x and ε y , these two electric field components will propagate through the polarizer at distinct velocities.Consequently, a phase difference between E x and E y emerges, reflecting the influence of the differing dielectric constants on the wave propagation characteristics within the medium.This circular polarizer consists of a layer of alternating dielectric and air bars along the y-axis and thus exhibits anisotropic characteristics.For the x-axis polarization (x-pol) incident field, this periodic structure can be represented as two capacitors connected in parallel.On the other hand, for the y-axis polarization (y-pol) incident field, the layers can be seen as two-series capacitors.Consequently, we can calculate the equivalent effective dielectric constants along the x and y axes (ε x and ε y ) using the following equations: (5) where ε 0 and ε d represent the permittivity of air and respectively, and q 0 and q d refer to the volume fraction of the air and the dielectric, The transmission coefficient of the resulting equivalent anisotropic dielectric material, considering multiple-reflection theory according to [24], can be calculated using the following equation: where h p is the thickness of dielectric material, and k x/y are the equivalent wavenumbers of the dielectric polarizer along the xand y-axes, respectively.Incident linear polarized waves from the feed can be decomposed into two vectors with equal amplitude in the xand y-axes and phase shift differences between the two vectors.To have a circularly polarized wave, a 90 • phase difference is essential between T x and T y , so the dimension of the dielectric polarizer should be optimized to satisfy the desired phase shift.Furthermore, the transmission coefficient should have the highest value to ensure the lowest transmission loss.Thus, the optimization criteria for h p and q d can be summarized as follows: resulting in q d and h p are chosen as 0.42 and 430 µm, respectively, for the center frequency of 625 GHz.So, the width of air and dielectric bars are chosen 144 µm, and 108 µm, respectively.The optimization is performed numerically within MATLAB, ensuring precise and tailored values for the given frequency.The transmission phase differences between the xand y-axes are shown in Fig. 6, showing that the phase error is less than 6.5 • for the entire waveguide band from 500 to 750 GHz.The phase error can be further minimized for specific parts of the waveguide band used, by optimizing for a different center frequency.Thus, this type of dielectric polarizer can be added to the elliptical Fresnel Lens to realize CP.All the full-wave electromagnetic simulations were conducted by CST Microwave Studio Suite.

III. FABRICATION
The fabrication process is performed on a silicon on isolator (SOI) wafer that contains two separate silicon layers, a device layer, and a handle wafer, 96 and 430 µm thick, respectively, separated by a 1 µm thick buried oxide layer (BOX) layer.The Fresnel lens is etched into the device layer, and the dielectric polarizer into the handle wafer.The resistivity of the SIO wafer is specified to 2000 -cm, which is sufficient to minimize dielectric loss [25], [26].For our simulation and fabrication, we derived a loss tangent value of 0.000118 at the center frequency, based on the reported resistivity of the wafer.The fabrication process, in contrast to a corporate-fed antenna array Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.  of similar aperture requiring a complex embedded waveguide distribution network [4], is very simple as it requires only two deep-silicon etching steps, and as no metallization and no wafer bonding processes are needed.Fig. 7 summarizes the fabrication process flow.Fig. 8 shows scanning electron microscopy (SEM) photographs of the front side (lens) of the manufactured elliptical FZPL antenna.Also, the fabricated lens antenna is shown in Fig. 9.

IV. MEASUREMENT
The antenna prototype characterization is performed in the THz anechoic chamber at KTH Royal Institute of Technology, Sweden.The schematic of the far-field measurement setup is   shown in Fig. 10.The antenna under test (AUT) is mounted on the standard WR-1.5 waveguide flange of a 500-750 GHz frequency extender, and a fully automated 3-D robot controls the antenna's position.
As transmitter and receiver of the measurement setup, a pair of Virginia Diodes (VDI) frequency extenders WR-1.5 is used, connected to a Rohde and Schwarz ZVA-24 vector network analyzer (VNA).A standard-gain horn antenna manufactured by Anteral is used as the transmitting antenna.The distance between the antennas is chosen to be 1 m, to ensure optimal direct illumination in the far-field and not compromise with the dynamic range of the setup.Fig. 11 illustrates implementing a circularly polarized antenna measurement setup by employing the frequency extenders and VNA.For circularly polarized characterization, the rotating source method, as outlined in [27], is employed in this study to evaluate the performance of the CP of the antenna.The transmitting and receiving antennas can rotate at 0 • and 90 • , enabling the measurement of vector responses in two orthogonal orientations to determine the axial ratio, realized gain, and circularly polarized radiation patterns.furthermore, post-processing, following the acquisition of calibration and measurement data, is performed to calculate these parameters, as outlined in [27].Control of the measurement setup is executed through MATLAB code, managing robot movements, data storage, and post-processing.The rotation accuracy is maintained at 0.1 • in all directions, with a rotation speed of 2.2 s per step, encompassing the time for moving to the next step, saving data, and the sweeping time of the VNA.
The lens antenna must be accurately mounted onto the WR-1.5 waveguide flange.For this, A custom 3-D-printed alignment pin is designed and integrated to maintain the ideal distance between the waveguide's feeding port and the intricate lens structure.This innovative component significantly enhances the accuracy of alignment and desired length to Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.

TABLE I COMPARISON OF THE THZ AND SUB-THZ HIGH GAIN LENS ANTENNAS
ensure that the F/D ratio is equal to the expected value.The alignment pins employed in this study exhibit cylindrical geometry, featuring variable radii at different heights.This design facilitates a controlled distance between the fabricated chip and the feed, particularly at specific locations such as 4.2 mm from the open waveguide position.The pins' radii increase at these designated points, effectively constraining the chip from moving closer to the feed.Consequently, to ensure the consistent maintenance of the distance between the lens and the feed, the chip is gently pressed against the alignment pin.The fabrication precision of these alignment pins is maintained at 100 µm.Simulation results substantiate that this level of accuracy ensures negligible errors in antenna performance.Specifically, the expected change in gain is less than 0.1 dB with this finely tuned accuracy.This demonstrates the robustness of the alignment pin fabrication process and its capability to uphold antenna performance within tight tolerances.
The S11 of the elliptical FZPL antenna is below −15 dB all over the whole waveguide band of 500 to 750 GHz, matching excellently the simulated data, as depicted in Fig. 12.
The realized gain and radiation efficiency, over frequency, are illustrated in Fig. 13.The determined realized gain of the antenna is 24.3-25.7 dBi in the 250 GHz frequency band through measurements using two calibrated standard horn antennas.Notably, there is excellent agreement with the simulated gain, exhibiting only a minor deviation of 0.5 dB.
Radiation efficiency, representing the effectiveness of the antenna in converting input power into radiated power, is a crucial parameter.In the simulation, the average radiation efficiency is found to be −0.67 dB, while the measured radiation efficiency is −0.85 dB.Also, Aperture efficiency is determined by comparing the effective area of the aperture to its actual physical area, expressed as the ratio (A e /A).In the simulation, the average aperture efficiency is 41.98%, showing a slight better compared to the measured value of 37.84%.The interplay between aperture efficiency and other factors like spillover and illumination losses is crucial for understanding the overall antenna performance.While spillover efficiency and illumination losses are parameters derived from simulation and not directly measurable, their consideration provides valuable insights into the antenna's behavior in operational scenarios.The simulation reports estimated average spillover loss and illumination loss as −0.65 and −2.45 dB, respectively.These values, although not directly comparable with experimental measurements, contribute to the comprehensive understanding of the antenna's efficiency.The consistent behavior observed in simulation and measurement results emphasizes the antenna's commendable radiation and aperture efficiency, supporting its overall performance.Moreover, these values exceed that of conventional Fresnel lens antennas [11] and align with the performance observed in other high-gain antennas operating in the terahertz range [5].
Fig. 14 displays the circularly polarized radiation patterns of the elliptical FZPL antenna at three frequency points (500, 625, and 750 GHz) in the xz and yz planes.Despite the very high frequencies, there is an almost perfect agreement with the simulated data, which proves the quality of the THz antenna chamber.Furthermore, the axial ratio has been derived from the measurements to verify the CP performance of the antenna and is shown in Fig. 15.The measured axial ratio, also shown in the figure, ranges from 1.5 to 2.4 and compares very well to the simulated ratio ranging from 1.0 to 2.45.The measured axial ratio for the antenna aligns well with other circularly polarized THz antennas.Despite operating at a higher frequency and wider bandwidth, the elliptical Fresnel lens antenna's axial ratio remains comparable to those reported in [11] and [20].Table I provides a comparison of previously reported lens antennas at sub-THz and THz frequencies.Only very few high-gain lens antennas have been demonstrated above 100 GHz.The lens antenna in this article is the first lens antenna with CP above 320 GHz, and the only so far published antenna that achieves full-band performance, and, with the exception of [28], the only one above 600 GHz.
V. CONCLUSION This article introduced an innovative 500-750-GHz elliptical FZPL antenna design to ensure a wide bandwidth in the sub-THz region.The silicon-micromachined lowprofile antenna represents a remarkable advancement, boasting exceptional performance features such as high gain, CP, and compact size.It is the first full-band lens antenna at THz and sub-THz frequencies, and the first circularly polarized lens antenna above 320 GHz.The outstanding agreement between the measurements of the fabricated prototypes, in particular the radiation patterns, with simulation data proves the excellent suitability of silicon-micromachining for high-performance THz antennas.

Fig. 1 .
Fig. 1.Configuration of the elliptical fresnel planner lens antenna and dielectric polarizer.(a) Top and bottom view of the proposed lens and dielectric polarizer.(b) CP and gain enhancement schematic for the modified elliptical FZPL antenna.
(a) and (b) shows the dependency of the overall antenna gain on different distributions of the e n factors for the nine-zone lens.

Fig. 2 .
Fig. 2. (a) Evaluating the relation between e factor and realized gain for elliptical fresnel lens antenna with N = 9 zones for the largest zone.(b) Variation in maximum achievable gain with ellipticity factors (e) for different zones.each curve represents a distinct e factor setting for individual zones, showcasing the impact of e on the antenna's maximum gain across multiple configurations.

Fig. 3 .Fig. 4 .
Fig. 3. Comparison of simulation results of reflection and realized gain between conventional circular Fresnel lens and elliptical Fresnel lens.

Fig. 6 .
Fig.6.Computed transmission phase difference of the anisotropic dielectric polarizer under xand y-polarized incidences across the waveguide band, when minimized for the center frequency.

Fig. 7 .
Fig. 7. Schematic fabrication process flow.(a) SOI wafer, (b) oxide layers grew on both sides, (c) lithography (it is performed on one side, and after etching, the oxide is applied on the other side), (d) oxide dry etching, (e) DRIE of device layer and handle layer (first one side then another side), and (f) oxide dry etching both sides.

Fig. 8 .
Fig. 8. SEM images of the manufactured elliptical FZPL antenna, top view of zones, and polarizer at the back.

Fig. 10 .
Fig. 10.Radiation pattern measurement setup at THz Lab, KTH with three-axis azimuth, elevation, and polarization rotation stage, overall configuration, and a close-up view of the waveguide flange and the 3-D printed alignment pin to ensure the optimal distance between the feed and the lens.

Fig. 11 .
Fig. 11.Schematic block diagram of the measurement setup used for characterizing the circularly polarized radiation patterns, axial ratio, and realized gain of the elliptical lens antenna.

Fig.Fig. 13 .
Fig. Comparison of measured and simulated reflection for the elliptical FZPL antenna.
Alireza Madannejad (Student Member, IEEE) was born in Iran, in 1992.He received the M.Sc.degree in electrical engineering from the University of Tehran, Tehran, Iran, in 2017.He is currently pursuing the Ph.D. degree with the Division of Micro and Nano Systems, KTH Royal Institute of Technology, Stockholm, Sweden.In 2017, he started working as a Technical Staff and Researcher at the Antenna Type Approval Laboratory, University of Tehran.He has worked in applied electromagnetics, antenna and component measurement, telecommunications systems, and radar systems.Since 2021, he has been working on the THz communication system and passive component design.Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.