A Novel Logarithmic-Spiral-Shaped 3-D-Printed Dielectric Polarizer for Dual-Circularly Polarized Conical-Beam Radiation Patterns in the Ka-Band

In this contribution, the design of a novel logarithmic-spiral-shaped (LSS) anisotropic dielectric polarizer is presented for millimeter-wave applications within the Ka-band (28–30 GHz). The proposed antenna is composed of a conical horn fed by a waveguide dual-mode converter (DMC), where the TE01 and TM01 modes are independently excited to generate linearly azimuthal polarized and linearly radial polarized conical beam radiation patterns, respectively. The horn antenna is loaded with the novel LSS dielectric polarizer, which converts the linearly azimuthal polarized wave generated by the excitation of the TE01 mode into a right-handed circularly polarized (RHCP) wave and the linearly radial polarized wave generated by the excitation of the TM01 mode into a left-handed circularly polarized (LHCP) wave. In order to experimentally validate the proposed design, both the DMC along with the conical horn antenna and the novel LSS dielectric polarizer are manufactured by means of distinct 3-D printing techniques. An excellent agreement between simulations and measurements is achieved.


I. INTRODUCTION
C ONICAL-BEAM (CB) antennas have garnered signifi- cant attention due to their unique characteristics, making them highly suitable for meeting the escalating demands of enhanced communication systems.These antennas are extensively utilized in the Ka-band for applications, such as indoor 5G NR communications [1] and the burgeoning field of drone applications [2], [3].Furthermore, they are widely employed in establishing connectivity between terrestrial vehicles in motion and geostationary satellites [4].In many of these applications, moreover, the feature of circular polarization (CP) proves highly advantageous, as it demonstrates robustness against multipath effects, and it further ensures stability in instances of misalignment between transmitter and receiver.Consequently, recent numerous attempts of achieving CP-CB radiation can be found in the literature.Some designs are based on geometrical solutions [5] and other realizations rely on planar solutions, for instance, by employing printed microstrip antennas while exciting higher order electromagnetic modes.Exciting two orthogonal TM 21 modes in a circular patch antenna has been proven as an efficient method to generate a CP-CB pattern [6], [7].Other realizations based on planar patch antennas involve the modification of the patch structure by adding curved conducting branches.By feeding a circular patch at its geometric center with its TM 01 and TM 02 modes and optimizing the conducting branches, it is possible to generate electric fields polarized in both radial and azimuthal directions, respectively, with a 90 • phase offset, resulting in the generation of a CP-CB pattern [8], [9].
As can be seen, antenna designs presented in the literature that enable the generation of CP-CB radiation patterns predominantly consist of flat printed low-gain antennas operating in low-frequency bands.With the prevailing trend of expanding the frequency spectrum to accommodate emerging applications that demand increased bandwidth capabilities, there is an imperative to propose novel designs of high-gain CP-CB antennas capable of operating in the Ka-band and higher frequencies.Some high-gain linearly polarized (LP) CB antenna designs have recently been proposed to operate within Ka-band frequency spectrum [2], [10].However, there is still a need for a high-gain CP-CB solution.The generation of high-gain CB radiation can be straightforwardly accomplished employing waveguide technology.By exciting the TE 01 and TM 01 modes of a circular waveguide and employing a suitable conical horn antenna, it is possible to achieve two high-gain LP-CB radiation patterns.However, there is a need to convert these dual-LP CB radiation patterns into dual-CP CB radiation patterns.All the presented designs capable of generating CP-CB radiation share the characteristic of addressing the CP generation at the antenna element level, which, in many cases, tends to increase the complexity of the design.As additive manufacturing technologies continue to gain widespread popularity, opportunities arise for designing intricate structures that were traditionally challenging to produce using conventional manufacturing methods [11].Consequently, the prospect of liberating the antenna element of the task of generating CP in order to simplify its design can be contemplated.Currently, an established method to achieve linear to CP conversion involves the utilization of an anisotropic planar dielectric polarizer comprised of parallel dielectric slabs [12], which enables the conversion of an LP wave into a CP wave.Due to its simplicity and straightforward manufacturability, several antenna designs have adopted this polarization conversion technique for millimeter-wave band applications [13], [14], [15].This polarizer can be utilized either by placing it away from the feed, where it is illuminated by a radiated electromagnetic field, as implemented in design [13], or by positioning it at the feed aperture, where it is illuminated by an extended electromagnetic mode, as performed in [12].The latter method allows for the realization of a more compact antenna with the drawback that the electromagnetic field illuminating the polarizer deviates from being a transverse electromagnetic wave, which is the optimal case for achieving the highest polarization purity.
In pursuit of optimal illumination while considering form factor, an alternative method has been proposed, which entails the placement of a dielectric lens between the feed and the polarizer, with the purpose of illuminating the latter with a plane or quasi-plane wave, thus seeking to emulate the TEM wave ideal excitation condition [14], [15].However, the introduction of a dielectric lens inevitably entails a slight increase in the overall size of the design, along with other undesired effects, such as reflections at the dielectric-air interfaces as well as an increase in overall dielectric losses.Regarding the polarization conversion capability of the planar anisotropic dielectric polarizer, due to the shape and geometric arrangement of the dielectric slabs, the polarizer only exhibits the desired anisotropy to achieve polarization conversion when its excitation is performed with an LP wave with its electric field vectors rectilinearly oriented.In general, electromagnetic modes that enable the generation of CB radiation patterns exhibit electric and magnetic field distributions that do not properly align with the geometry of the traditional dielectric polarizer, as instead of rectilinearly oriented electric field vectors, these modes usually feature radial or azimuthal electric field polarizations, as can be observed in [6], [7], [8], and [9] or in the already mentioned TE 01 and TM 01 modes of a circular waveguide.Thus, the traditional dielectric polarizer geometry proves to be inefficient in the conversion of radial or azimuthal polarized electric fields into CP electric fields, as the misalignment of its geometry with the geometry of the field radiated by these higher order modes impedes the generation of the necessary anisotropy for CP conversion.Hence, there is a current need for an innovative polarizer structure capable of converting radial and azimuthal polarized electric fields into CP electric fields, thus achieving a CP-CB radiation pattern from an LP feed.
Acknowledging this necessity, in this contribution, a novel cylindrical dielectric polarizer capable of generating dual-CP CB radiation patterns from a dual-LP antenna feeder is presented for millimeter-wave applications in the Ka-band.As already outlined, the aim is to generate high-gain CB farfield radiation featuring dual-CP.The generation of two CB radiation patterns becomes achievable through the distinctive electromagnetic properties of the TM 01 and TE 01 modes of a circular waveguide.These modes exhibit electric field nulls at their center and maxima in the central circular crown of the waveguide.Thus, radiating these modes through a conical horn results in the generation of two far-field CB radiation patterns featuring orthogonal linear polarizations, one radial (TM 01 ) and one azimuthal (TE 01 ).To attain CP in both CB radiation patterns, as previously indicated, the design of a novel dielectric polarizer demonstrating anisotropy in the polarization directions of both modes, radial and azimuthal, is imperative.
This article is organized as follows: Section II is dedicated to detailing the operation of the novel LSS anisotropic dielectric polarizer.A review of the background theory of the traditional dielectric polarizer is conducted, followed by a comprehensive explanation of the operation and design of the new proposed LSS polarizer.In Section III, an experimental design of the proposed LSS polarizer is carried out to validate its operation.TM 01 and TE 01 modes are generated by means of a dual-mode converter (DMC), which feeds a conical horn that integrates the proposed LSS dielectric polarizer at its aperture.This experimental design, shown in Fig. 1, is intended to operate in the 28-30-GHz frequency spectrum, although the polarizer may cover a much wider frequency band, as demonstrated in Section II-C.As stated, the DMC enables the excitation of the TE 01 mode, featuring azimuthal ( φ-) polarization, and the TM 01 mode, featuring radial ( ρ-) polarization, in the conical horn.Conversely, the novel LSS dielectric polarizer ensures the LP-CP conversion of the electric field for both modes, thereby generating two CB far-field radiation patterns featuring dual-CP, RHCP, and left-handed circularly polarized (LHCP), respectively.Section IV is dedicated to review the manufacturing techniques employed to realize the antenna design developed in Section III, alongside validating its performance through measurements in anechoic chamber.Finally, Section V presents the article conclusions.

II. LSS ANISOTROPIC DIELECTRIC POLARIZER
In this section, the proposed novel LSS dielectric polarizer is detailed.Initially, before delving into its operation and design intricacies, a section is dedicated to review the operation of the traditional dielectric polarizer [12], aiming to enhance comprehension regarding the functionality of the newly proposed LSS polarizer.
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A. Traditional Dielectric Polarizer
Fig. 2(a) illustrates the configuration of the traditional dielectric polarizer design [12], which consists of a series of dielectric slabs with a thickness of w 1 , arranged in parallel, and separated by a distance of w 2 , having each slab a height of h.The polarizer is tilted 45 • , so if a horizontally or vertically polarized wave is decomposed in its two orthogonal components ⃗ E x || / ⃗ E x ⊥ and ⃗ E y || / ⃗ E y ⊥ , respectively, due to the anisotropy that the polarizer exhibits, each of them is affected differently by the dielectric slabs, as the effective dielectric permittivities in each direction, ε || and ε ⊥ , are different.These dielectric permittivities can be calculated as [16] where m, the content ratio, is defined as a ratio between variables w 1 and w 2 [m = w 1 /(w 1 + w 2 )].The variables ε 1 and ε 0 are the relative dielectric permittivities of the dielectric material and air, respectively.This difference in the value of the effective dielectric constants ε || and ε ⊥ results in a different propagation constant for each component, leading to a different transmission phase across the polarizer.The transmission phase difference between both components can be calculated as a function of h as follows: Thus, adjusting the polarizer parameters, it is possible to generate a 90 • phase shift between both orthogonal electric field components, achieving LP to CP conversion.As shown in Fig. 2(b) and (c), if a conical horn excited with the degenerate and orthogonal TE 11x and TE 11y modes illuminates the traditional dielectric polarizer, RHCP and LHCP pencil-beam radiation patterns can be achieved, respectively.

B. Logarithmic-Spiral-Shaped (LSS) Dielectric Polarizer Design
Based on the traditional dielectric polarizer, a novel structure is proposed, as shown in Fig. 2(d).The novel dielectric polarizer consists in LSS dielectric slabs, each having a height of h and a thickness denoted by w 1 (ρ).The slabs are azimuthally separated from each other by an arc distance w 2 (ρ).As can be seen, both the thickness and separation between dielectric slabs are dependent with ρ, being ρ the radial distance from the origin in a standard cylindrical coordinate system.This dependence arises from the fact that the content ratio, m, must be kept constant for any radial distance.Therefore, both the thickness of the dielectric slabs and their separation increase as the radial distance grows.These parameters can be expressed as a function of the content ratio, m, the radial distance, ρ, and the number of dielectric slabs, N slabs The polarizer can convert incident φ-and ρ-LP waves, achieved by the excitation of the φ-polarized TE 01 mode and the ρ-polarized TM 01 mode in the conical horn antenna, into RHCP and LHCP waves, respectively.This innovative design extends the traditional polarizer concept by ensuring that the rotating slab trajectory forms a local angle of 45 • with φ and ρ directions, thus ensuring local anisotropy for incident φ-and ρ-polarized e-field modes.As linearly φ-( ⃗ E ϕ ) and ρ-( ⃗ E ρ ) polarized waves impinge on the anisotropic polarizer, if they are decomposed in their respective orthogonal electric field components, ⃗ , each component will exhibit a different propagation constant, as the local effective dielectric permittivities, ε || and ε ⊥ , are different.This will lead to different propagation constants for each component and, consequently, to different transmission phases.Thus, by tuning the polarizer dimensions, it is possible to generate a 90 • phase shift between both electric field components, achieving linear φ-and ρ-polarization to CP conversion, RHCP and LHCP, respectively.It should be noted again, that in order to maintain a constant value for m, the filling factor, along the whole radius of the polarizer (ρ-direction), the dielectric slabs progressively increase their width and the separation between them radially.When the TE 01 mode is excited in the conical horn antenna, a linearly φ-polarized electric field ( ⃗ E ϕ ) impinges on the polarizer.The ⃗ E ϕ field is decomposed in a • phase difference between these two orthogonal components will give rise to an LHCP wave from a linearly ρ-polarized one [Fig.2(f)].
Concerning the design of the LSS dielectric polarizer, it has been crafted as follows.As depicted in Fig. 2(d), it features two primary components: a central dielectric hub and several dielectric slabs emanating from it.The primary role of the central hub is to provide structural rigidity.Its placement has been precisely positioned at the geometric center of the polarizer, coinciding with the nulls of the electric and magnetic fields of both TM 01 and TE 01 modes at the aperture of the conical horn antenna.This strategic placement ensures the robustness of the polarizer without compromising the propagation of these modes.On the other hand, the polarizing dielectric slabs are designed in accordance with the aforementioned considerations to generate the necessary anisotropy for LP to CP conversion.At each point, the polarizing slab should be tilted 45 • to the incident φ-and ρ-polarized electric fields.The analytical expression that enables the depiction of the profile that satisfies the condition of maintaining a constant angle with Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.the unit vectors φ-and ρ-throughout its entire trajectory is that of a logarithmic spiral.This expression can be presented in polar coordinates as follows [17]: being ρ slab the ρ coordinates of the dielectric slab's profile, r ap the radius of the conical horn aperture, ϕ the azimuthal angle, and α the angle between the trajectory of the spiral profile at any point, denoted as r slab , and the unit vector ρ-at that same point.Thus, the profile that the dielectric slab should have to generate the necessary anisotropy for the transformation of the incident LP φ-and ρ-polarized electric fields into CP fields, shown in Fig. 3(a), is determined using (6) with r ap = 20 mm and α = 45 • , as selecting this value for α ensures that the logarithmic spiral trajectory forms a 45 • angle with both φ-and ρ-directions at all points of its profile.An infinitesimal close-up view of the dielectric slab profile is shown in Fig. 3(b).As can be seen, at every generic angle ϕ i , the trajectory of the dielectric slab, r slab (ϕ i ), is tilted 45 • to the orientation of the incident electric fields, φ(ϕ i ) and ρ(ϕ i ).Following (4) and fixing values for N slabs and m, a second profile can be outlined to comply with the calculated dielectric slab's width [Fig.3(c)].Subsequently, following (5) with the same previously fixed values for N slabs and m, the separation between dielectric slabs can be computed, leading to the final LSS polarizer observed in Fig. 3(d).

C. LSS Polarizer Bandwidth Analysis
This section is dedicated to analyze the bandwidth within the Ka-band (26)(27)(28)(29)(30)(31)(32)(33)(34)(35)(36)(37)(38)(39)(40), in which the LSS polarizer exhibits robust operation, allowing for polarization conversion in its two operating modes simultaneously, TE 01 -RHCP and TM 01 -LHCP.Fig. 4 illustrates the simultaneous dual-mode operation of the LSS polarizer in the Ka-band, with axial ratio simulated results extracted from CST Microwave Studio software.The simulation method consisted in directly exciting the TE 01 and TM 01 modes on a conical horn with the integrated LSS dielectric polarizer at its aperture.A parametric variation of the variable h is performed for a fixed value of m = 0.5 and a high value for N slabs , which ensures the LSS polarizer to exhibit a homogeneous anisotropy along its entire aperture, thus guaranteeing optimal polarization conversion capabilities.As seen, by adjusting the value of h, the height of the LSS polarizer, it is straightforward to select the subband within the Ka-band, wherein the LSS polarizer can operate robustly in its dual-mode configuration.The relative bandwidth in terms of axial ratio (AR < 3 dB) is about 35% for TE 01 mode and 30% for TM 01 mode.It can be observed that for higher values of h, the LSS polarizer operates in the lower part of the Ka-band, whereas reducing the value of h enables operation in the upper part of the Ka-band.

III. EXPERIMENTAL DESIGN: DMC AND CONICAL HORN WITH INTEGRATED LSS POLARIZER
This section is dedicated to develop a fully functional antenna within the 28-30-GHz frequency band, previously depicted in Fig. 1.As mentioned, the experimental antenna proposal consists of a DMC and the novel LSS dielectric polarizer.The DMC enables the excitation of the TE 01 mode, featuring azimuthal ( φ-) polarization, and the TM 01 mode, featuring radial ( ρ-) polarization, in a conical horn.The novel LSS dielectric polarizer is integrated into the conical horn aperture to ensure the LP-CP conversion of the electric field for both modes, achieving dual-CP CB radiation.For this purpose, a first parametric analysis of all the LSS polarizer geometric parameters is conducted in Section III-A to optimize its dual-mode performance in the specified frequency range, followed by the DMC and conical horn design in Section III-B, which is also optimized to operate in the 28-30-GHz frequency band.It is important to note that, as will be shown in this section, the DMC limits the operational bandwidth of the complete antenna in terms of impedance matching, yet as stated in Section II-C, the novel LSS polarizer exhibits a wider operational frequency range in terms of polarization conversion capabilities.

A. LSS Polarizer Simulated Parametric Analysis
Regarding the variables defining the optimal dimensions of the dielectric LSS polarizer, a parametric analysis is conducted through electromagnetic simulation using CST Microwave Studio as the electromagnetic simulation tool.The simulation method involved directly exciting the TE 01 and TM 01 modes on the circular waveguide that feeds the conical horn with the integrated LSS dielectric polarizer at its aperture.The parametric analysis of the LSS polarizer variables is depicted in Fig. 5. Initially, an in-depth examination of the variations in parameters h and m is conducted across three specified frequencies within the band, namely, 28, 29, and 30 GHz, while maintaining N slabs at a constant value of 12.Both parameters, h and m, are instrumental in achieving maximal polarization purity within our designated frequency range.Concurrently, the variable N slabs assumes a critical role in homogenizing the anisotropy exhibited by the LSS polarizer at its aperture, allowing for a better polarization conversion of the electric field distributions of the TM 01 and TE 01 modes.Thus, Fig. 5(a)-(c) delineates the axial ratio variations for distinct combinations of h and m at the aforementioned frequencies.Notably, optimal axial ratio values manifest at medium values of m, ranging between 0.4 and 0.5.Conversely, parameter h assumes greater influence in positioning the minimum axial ratio within the desired frequency band.Thus, for lowest in-band axial ratio, h = 19.15mm and m = 0.5 are selected as optimal values.Following this, the axial ratio for these h and m optimal values is examined for different values of N slabs within the operational frequency range [Fig.5(d)].As can be observed, by increasing the value of N slabs while maintaining the optimal values of h and m, the polarizer exhibits a more homogeneous anisotropy along its aperture, resulting in an improved in-band axial ratio.The lowest number of slabs that allows the achievement of the optimal anisotropy homogeneity and, therefore, the optimal axial ratio in the design frequency band, is N slabs = 12.Although a higher value of N slabs also enables achieving adequate dual-mode polarization conversion, this result is set as optimal as it also ensures the manufacturability of the LSS polarizer.Thus, the optimal parameter configuration for the LSS polarizer is found for h = 19.15mm, m = 0.5, and N slabs = 12.It is worth mentioning that, while the optimal polarizer height obtained through electromagnetic simulation is h = 19.15mm, if the calculation is performed making use of the analytical expressions ( 1)-( 3), a discrepancy is observed in the obtained results.With the selected optimal value m = 0.5 and considering that ε 1 = 2.7 for gray resin, which is the material used for the LSS polarizer manufacture, and ε 0 = 1 for air, the calculated values for ε || (1) and ε ⊥ (2) are 1.85 and 1.46, respectively.Thus, an analytical height value of h = 17 mm is calculated with (3) for the polarizer to generate a 90 • phase shift between orthogonal electric field components at the central frequency of the band, 29 GHz, achieving LP-CP conversion.This result slightly deviates from the electromagnetically simulated optimal value of h = 19.15mm, as the electromagnetic simulation considers effects omitted in the theoretical calculation.These include dielectric losses and edge effects in the dielectric slabs as well as reflections at the dielectric-air interfaces.Moreover, the electromagnetic field distributions given by the TM 01 and TE 01 modes that impinge on the polarizer differ from being TEM waves, as assumed in the analytical approach and considered as the optimal scenario in terms of polarization conversion efficiency.This is, indeed, one of the notable advantages of the design.The polarizer is designed to be integrated at the conical horn aperture, ensuring a good polarization purity, even in the absence of optimal feeding by a radiated TEM or quasi-TEM wave.

B. Feed Antenna: DMC and Integrated Conical Horn
Regarding the DMC used to feed the conical horn antenna, as previously mentioned, it is designed based on works [18] and [19], integrating these single-mode converters (SMC) into a single-piece DMC used to feed a conical horn antenna [Fig.6(a)].Since this does not constitute a novel contribution, a detailed explanation of its operation is not provided, as it is already covered in the original works.However, to demonstrate the proper functioning of the conical horn antenna [Fig.6(b)] and the successful excitation of TE 01 [Fig.6(c)] and TM 01 [Fig.6(d)] modes, its simulated radiation properties are analyzed with the commercial electromagnetic software CST Microwave Studio.The DMC features two input ports, which are standard WR28 rectangular waveguides.As can be seen from Fig. 6(c), TE 10 mode is excited at port 1 to generate the TE 01 mode inside the output circular waveguide, which exhibits a φ-polarized electric field.Conversely, as seen in Fig. 6(d), TE 10 mode is excited at port 2 to generate the TM 01 mode inside the output circular waveguide, which exhibits a ρ-polarized electric field.As observed in Fig. 6(e), both modes are adequately excited within the operational bandwidth, as their reflection coefficient remains below −15 dB throughout most of the frequency band.Concerning the radiation properties of the conical horn antenna, TE 01 [Fig.6(f)] and TM 01 [Fig.6(g)] directivity patterns are shown at the central frequency of the band, 29 GHz.As can be seen, the antenna successfully achieves the generation of two CB radiation patterns featuring orthogonal LP.It is worth noting that the radiation pattern generated by the TM 01 mode demonstrates higher directivity than the radiation pattern generated by the TE 01 mode.The TM 01 mode exhibits a more uniform field distribution at the horn aperture than that of the TE 01 mode, which presents a tapered field distribution with nulls both at the center and edges of the horn aperture.Consequently, the CB pattern radiated by the excitation of the TM 01 mode in the conical horn antenna features higher directivity, along with slightly higher secondary lobes, typical of uniformly illuminated aperture antennas.
The antenna, comprised by the DMC with the integrated conical horn and the LSS polarizer, exhibits a total relative bandwidth of dual-mode operation that is limited by the relative bandwidth of the DMC in terms of impedance matching.Defining a maximum reflection coefficient of −10 dB, the TE 10 -TE 01 mode converter exhibits a relative bandwidth of 10.1%, whereas the one for the TM 10 -TE 01 is slightly higher, specifically of 13.7%.Furthermore, as demonstrated in this section, both mode converters exhibit a reflection coefficient below −14 dB across the entire operating band, from 28 to 30 GHz, which corresponds to an operational bandwidth of 6.9%.However, it is crucial to emphasize that, even though the operational bandwidth of the entire antenna system is constrained by the relative bandwidth in terms of impedance matching of the DMC, the novel LSS polarizer, as shown in Section II-C, can provide a wider dual-mode relative bandwidth in terms of axial ratio (AR < 3 dB) of about 35% and 30% for TE 01 and TM 01 modes, respectively.

IV. MANUFACTURING AND EXPERIMENTAL RESULTS
In this section, an overview of the manufacturing process for the two integral components of the antenna, namely, the DMC and the integrated LSS dielectric polarizer, is provided.Furthermore, a comparative analysis is presented between the experimental results of the antenna and the outcomes of the electromagnetic simulations.
Regarding the manufacturing process, the DMC and the conical horn antenna are produced as a single piece using AlSi10Mg alloy through selective laser melting (SLM) technology.SLM represents a state-of-the-art additive manufacturing method, in which fine layers of metal powder are selectively melted and fused using a high-powered laser.This method, operating in a layer-by-layer fashion, allows for the construction of intricate microwave components tailored for millimeter-wave band applications [20], [21], [22].Conversely, the LSS dielectric polarizer is additively manufactured using photopolymer resin.Specifically, the stereolithography (SLA) 3-D printing technique is employed, which utilizes a high-precision laser to selectively solidify a liquid photopolymer resin, layer by layer, thereby enabling the fabrication of complex dielectric structures [11], [13], [14].The polarizer is printed with the Form 3 3-D printer using gray resin material, both supplied by Formlabs.Thus, the characterization of gray resin dielectric properties is carried out employing waveguide measurement techniques.The results yield values for its relative permittivity (ε r ) of 2.7 and a loss tangent (tanδ) of 0.02.These findings closely align with the values reported in existing [23], [24].In Fig. 7(a), the complete antenna assembly is shown, consisting in the DCM alongside the conical horn and the integrated LSS dielectric polarizer.Besides, the DMC and the integrated conical horn antenna, manufactured as a single piece by means of SLM, are shown in [Fig.7(b)].Additionally, the novel LSS dielectric polarizer, produced through SLA with optimal parameters of N slabs = 12, h = 19.15mm, and m = 0.5, is shown in Fig. 7(c).
Regarding the experimental results of the prototype, first, the reflection coefficient is shown in Fig. 8.As observed, the measured values are in accordance with the simulated results.The measured reflection coefficients are kept below −10 dB for both modes of operation across the entire operating bandwidth.A resonance in the measured reflection coefficient of the TE 01 mode at the frequency of 29.4 GHz is observable.This resonance, not present in the simulation, is attributed to minor errors in the DMC's manufacturing process, aspect that is further detailed later in this section.The prototype has also been measured in anechoic chamber to validate its radiation performance.The normalized radiation pattern and the axial ratio are depicted in Fig. 9 for both operating modes, TE 01 (RHCP) and TM 01 (LHCP), at the frequencies of 28, Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.symmetry of the dual-CP-CB radiation patterns, both in terms of directivity and axial ratio.First, regarding the normalized radiation pattern, as observed, there is a notable agreement between simulations and measurements.The radiation pattern exhibits its maximum for the TE 01 (RHCP) configuration at θ = 11 • for 28 and 29 GHz and at θ = 10 • for 30 GHz.Conversely, for the TM 01 (LHCP) configuration, the maximum value of the radiation pattern is located at θ = 11 • for 28 GHz, θ = 10 • for 29 GHz, and θ = 9 • for 30 GHz.On the other hand, regarding the CP purity, a significant agreement between simulated and measured results is also observed.The measured axial ratio for both cases remains below 3 dB across the entire operating frequency band in most of the BW −3dB .The measured axial ratio at the maximum value of the main lobe is below 2.5 dB for the TE 01 mode and below 2 dB for the TM 01 mode throughout the entire operating band.It is worth mentioning that, while the simulated results for axial ratio and normalized radiation patterns exhibit nearly revolution symmetry, slight asymmetries are observed in the measured results.This discrepancy is attributed to manufacturing errors in the DCM.SLM requires orienting the part to be manufactured in a specific manner to ensure proper fabrication, which can potentially result in asymmetries in the manufactured prototype.
These asymmetries, consequently, may lead to resonances at certain frequencies that asymmetrically affect the radiation of the manufactured antenna.
Finally, the directivity and realized gain are depicted in Fig. 10 for both operating modes of the antenna.As observed, there is a strong correspondence between simulations and measurements.It can be noticed that the directivity and gain of the TM 01 mode (LHCP) are slightly higher than those of the TE 01 mode (RHCP).As mentioned in Section III-B, the TM 01 mode exhibits a more uniform field distribution at the horn aperture than that of the TE 01 mode.Consequently, the CB radiation pattern generated by the TM 01 mode excitation exhibits higher directivity, as well as higher secondary lobes.The measured in-band directivity ranges from 14.65 to 15.3 dBi for the TE 01 mode, whereas for the TM 01 mode, the in-band directivity values are in between 15.7 and 16.1 dBi.Total losses range between 1.7 and 2.1 dB for both Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.TE 01 and configurations, values that are in accordance with other experimental studies conducted using gray resin as the manufacturing material [25].In simulations, the loss tangent for gray resin is set to 0.02 for the whole frequency band, as mentioned earlier, while the conductivity set for the AlSi10Mg alloy is 3 MS/m, value that coincides with other studies where the same alloy is employed [26], [27].
To conclude, Table I provides a comparison between the CP-CB antenna presented in this study and other state-of-theart CP-CB antenna designs.Some of them are characterized by geometrical solutions, such as the truncated cone slot array presented in [5] or by their planar printed structure, such as works presented in [6] and [8], although all of them yield modest gains in low-frequency bands.Conversely, there are proposals for high-gain antennas intended for operation in the Ka-band, as seen in [10], though featuring LP radiation.The presented design incorporates the appealing features of high-gain and a dual CP-CB radiation pattern, highly desirable for addressing the demands of emerging Ka-band applications.Furthermore, by externalizing the polarization conversion task to a 3-D-printed polarizer instead of implementing it at the element level, the design complexity is significantly reduced.

V. CONCLUSION
A novel LSS dielectric polarizer is presented to achieve dual-CP-CB radiation in the Ka-band.The proposed antenna is composed of a waveguide DMC that excites the TE 01 and TM 01 modes in a circular waveguide that feeds a conical horn antenna when exciting the TE 10 mode at its input ports 1 and 2, respectively.The conical horn antenna is loaded with the proposed novel LSS dielectric polarizer.The polarizer, positioned at the conical horn aperture, turns the linearly φ-polarized wave of the extended TE 01 mode into an RHCP wave and the linearly ρ-polarized wave of the extended TM 01 mode into an LHCP wave.Thus, when exciting TE 10 at port 1, a high-gain RHCP-CB radiation pattern is generated, whereas if the TE 10 mode is excited at port 2, a high-gain LHCP-CB radiation pattern is generated.The relative bandwidth achieved by the LSS polarizer in terms of axial ratio (AR < 3 dB) is about 35% for TE 01 mode and 30% for TM 01 mode.
locally parallel to the dielectric slabs, and a −45 • tilted component ( ⃗ E ϕ ⊥ ), locally orthogonal to the dielectric slabs [Fig.2(d)].The polarizer will delay the ⃗ E ϕ || component with respect to the ⃗ E ϕ ⊥ component.Thus, adjusting the height of the polarizer, a 90 • phase difference between these two components can be achieved, obtaining an RHCP wave from a φ-LP one [Fig.2(e)].Likewise, when the TM 01 is excited in the conical horn antenna, a linearly ρpolarized electric field ( ⃗ E ρ ) impinges on the polarizer.The ⃗ E ρ field is decomposed in a −45 • tilted component ( ⃗ E ρ || ), locally parallel to the dielectric slabs, and a +45 • tilted component ( ⃗ E ρ ⊥ ), locally orthogonal to the dielectric slabs [Fig.2(d)].The polarizer Swill delays the ⃗ E ρ || component with respect to the ⃗ E ρ ⊥ component.Achieving a 90

Fig. 4 .
Fig. 4. Wideband operation of the LSS polarizer within the Ka-band.Dual-mode axial ratio for different values of h.

Fig. 5 .
Fig. 5. Simulated parametric analysis of the variables h, m, and N slabs conducted on the conical horn model with the integrated novel LSS dielectric polarizer, directly exciting TE 01 and TM 01 modes on the circular waveguide.h and m variation effect on axial ratio for TE 01 mode (up) and TM 01 mode (down) for fixed N slabs = 12 at (a) 28 GHz, (b) 29 GHz, (c) 30 GHz, and (d) N slabs variation effect on TE 01 and TM 01 modes axial ratio for fixed optimal h = 19.15mm and m = 0.5.

TABLE I COMPARISON
BETWEEN CP-CB ANTENNAS FOUND IN THE STATE OF THE ART