Alumina 3-D Printed Wide-Angle Partial Maxwell Fish-Eye Lens Antenna

This letter presents a wide-angle partial Maxwell Fish-Eye (PMFE) lens antenna for W-band millimeter-wave communication, which is realized by alumina 3-D printing using lithography-based ceramic manufacturing. To achieve the targeted permittivity profile, in addition to structural measures, the solid-state porosity of alumina, and hence its material permittivity, is controlled by tuning the sintering temperature. The relative permittivity of bulk alumina was set at 5.13 with a sintering temperature of 1350 °C instead of being 9.2 with a sintering temperature of 1650 °C. The fabricated 3-D lens with a diameter of 33.7 mm achieves a peak realized gain of 25 dBi at a frequency of 109.5 GHz at the boresight, demonstrating a field-of-view of ±42° with a planar lens surface.

In our work, we focus on the partial Maxwell Fish-Eye (PMFE) lens, which uses gradient permittivity profiles close to those of the Gutman and Eaton lens types, thus combining their functionality [12], [13].Other examples of multifunctional lenses are bifunctional Luneburg/Eaton or Luneburg/ MFE lenses, whose functionality is dependent on the electromagnetic (EM) wave propagation direction, as discussed in [24], [25].The PMFE lenses presented in [12], [13] are functionally limited to the azimuthal plane, and their angular performance is strongly dependent on the dispersion characteristics of the used metallic structure geometry.Moreover, the practical realization of the wide-angle lenses operating in broadband frequency ranges and frequencies in the order of and over 100 GHz is often costly and highly demanding.
In this letter, we present an alternative PMFE lens approach based on exploiting lithography-based ceramic manufacturing (LCM) in combination with a specifically tuned sintering temperature (1350 °C).On the one hand, this allows us to design a 3-D broadband lens with large beam-steering capabilities in principal planes and with stable performance due to the use of a low-dispersive dielectric material [26].On the other hand, the decrease of the alumina sintering temperature from 1650 °C to 1350 °C leads to a decreased bulk relative permittivity (ε r ) from 9.2 to 5.13 [27], which is beneficial for the realization of lenses requiring an ε r in the order of 4 [10], [11], [12], [28], [29].A similar effect of the influence of sintering temperature on the material bulk permittivity was reported for zirconia in [30].Other benefits of employing alumina as the selected material are operational sustainability in high-temperature environments [31], strong chemical and radiation resistance demanded e.g., space applications [32], [33], low-loss and stable permittivity [26] over a very broadband frequency range limited only by the effective medium theory linearity [34], and fine porosity, which leads to the absence of a photonic crystal electromagnetic bandgap (EBG) in the considered frequency range [35].

II. 3-D PARTIAL MAXWELL FISH-EYE LENS
The MFE lens is a rotationally symmetric device that transforms a spherical wave at its focal point to the focal point located on the opposite side of the lens, acting as a mirror [36].The MFE lens can be compared to the Luneburg lens when it is cut in half [15].The MFE gradient permittivity profile (1) follows the distribution given by: (1 where ε r,eff is the effective relative permittivity, r is the radial position, and R is the lens radius.

A. MFE Lens Permittivity Profile Discretization
To realize the targeted MFE permittivity profile by 3-D printing using the LCM technique, a suitable discretization has to be applied.Based on our previous analysis of 3-D printed unit cells in [4], a cross-based unit cell with dimensions of 0.6475 × 0.6475 × 0.6475 mm 3 is selected for the lens discretization.The lens diameter is set to 33.7 mm.This value is limited by the maximum size of the printable green body, which is 64 × 40 × 100 mm 3 .The expected shrinkage is 7.5 % in the XYZ directions [27], so that means that the diameter of the printed green body, with the aforementioned value, will be 36.4mm, close to the maximum possible value.
The determined bulk relative permittivity of the alumina sintered at 1350 °C is 5.13, with a tangent loss of 3.65 × 10 −4 at 100 GHz [27].Then, the achievable effective relative permittivity (ε r,eff ) and effective tangent loss (tanδ eff ) for varying inner cross sizes of a cubic unit cell are obtained from the dispersion analysis described in [37] and [38].The resulting effective parameters and their corresponding frequencies are shown in Fig. 1.The minimum inner cross size of the green body is set to 0.2 mm, owing to the stability of the structure, resulting in 0.185 mm after sintering.To avoid an excessive ceramic/photopolymer resin residue in the fabricated lens structure, as reported in our previous works [4], [23], the maximum inner cross size of the green body is limited to 0.5 mm, resulting in 0.46 mm after sintering.The discretized ideal and 3-D printed ε r,eff profile of the MFE lens is depicted in Fig. 2.

B. Full-Wave Numerical Simulation
To verify the performance of the ideal MFE lens, a full-wave time-domain analysis in CST Studio Suite is performed at the W-band (75-110 GHz), with a WR-10 waveguide feed and the model discretized into rotational symmetric rings.In the next step, the lower part of the original MFE lens is cut away to create a planar surface for the feeding waveguide.The optimal position of the cut is found as a compromise between the maximization   of the lens antenna gain at its center and its edge positions, as depicted in Fig. 3.The works in [12] and [13] suggest cutting the lens at the position of 0.45R in the bed-of-nails and dielectric-filled PPW configurations, to achieve a maximum in beam-steering capabilities.However, such implementations are highly dispersive over frequency due to the use of metallic parts, which is in contrast to a low-dispersive dielectric unit cell design used in this work.
In our analysis, we sweep the lens cut position from 0.35R to 0.55R and evaluate the PMFE lens performance at the center, middle and edge positions (0, 6, and 13 mm) of the lens bottom to find an optimum between the maximum gain at the center and the edge positions.The achieved simulated realized gain and reflection coefficient are presented in Figs. 3 and 4. The electric field demonstrating EM wave propagation through the MFE and PMFE lenses is depicted in Fig. 5.The best results are achieved for the lens cut position at 0.45R, leading to the antenna realized gain of 25 dBi and 11.3 dBi at the lens center and edge positions, respectively, at the design frequency of 80 GHz.The reflection coefficient is better than −6.3 dB in the whole W-band.To improve the reflection coefficient of the PMFE lens antenna, the addition of an impedance matching layer (IML) [3], [4] is feasible.However, two important concerns have to be further addressed.First, adding an IML will change the optimal lens cut position, and the maximum gain and beam steering angle will be reduced.Second, to compensate for this effect, modification of the MFE lens permittivity distribution will be required to find a new optimum between the maximum gain at the center and the edge positions.
The simulated realized gain of the PMFE lens antenna created from cross-based unit cells at different waveguide feeding positions is shown in Fig. 6.It is noticeable that the maximum 90°beam steering is reached at the edge position.The expected antenna field-of-view (FoV), defined as −3 dB drop in gain, is ±42°.

C. Lens Fabrication and Characterization
The PMFE lens was fabricated via the LCM method using a Lithoz CeraFab-7500 printer and LithaLox360 photosensitive slurry, with a pixel size of 25 μm in X-, Y-, and Z-directions.After printing, the green PMFE lens was cleaned by LithaSol 20 cleaning solution to remove the excess of slurry.The sample was then slowly heated to remove the polymer from the system and to yield the alumina samples with the desired permittivity.In this study, the sintering temperature and dwell time were 1350 °C for 2 h.More details about this process can be found in our previous work [4].The structure of the fabricated lens is shown in Fig. 7.The lens antenna parameters and radiation patterns were measured employing the Vector Network Analyzer R&S ZVA67 with R&S ZVA-Z110E frequency convertors.The lens rotation was computer-controlled in 1°steps.Figs.8-11 show the measured and simulated results of cross-based PMFE lens antenna: radiation patterns with lens holder in H-plane, broadband realized gain at different waveguide feeding positions, aperture efficiency, and reflection coefficients.The measured antenna aperture efficiency is below 30%, mainly owing to the selected lens cut position, the directivity of the feeding waveguide, and nonideal impedance matching of the planar lens surface, also reported in [3] and [28], albeit for other types of lens.Further, the conductivity loss in the feeding waveguide and the dielectric loss in alumina have rather minor effects.Note that a part of   the beam energy misfocus for the waveguide feeding positions closer to the lens edge [Fig.5(c)].
The simulated maximum operational frequency of the PMFE lens antenna designed from the cross-based unit cells (Fig. 12) is characterized by the 1 dB gain drop at around 110 GHz.This is a 15 GHz improvement (caused by the decrease of alumina's bulk permittivity), when compared to the quasi-conformal transformation optics (QCTO) Luneburg lens discussed in a previous contribution, which was realized from conventionally sintered alumina, with an ε r of 9.52 and designed with the same unit cell constraints [4].The simulated maximum operational frequency for the given cross-based unit cell corresponds to the half-wavelength resonances in the effective medium (photonic crystal EBG).Nevertheless, the effect can differ depending on the unit cell shape [39].Even though nonideal lens alignment and a gap between the lens and the waveguide, the measured maximum operational frequency reaches 110 GHz for the PMFE lens, compared to the 98 GHz of the QCTO Luneburg lens.The  abrupt change of measured gain close to 110 GHz is caused by the window used for time-gating during signal post processing and does not represent the lens' response.The effect of a gap between the lens and excitation waveguide on the broadband antenna gain is documented in Fig. 12, where we can observe that the proper alignment between both parts is critical, since the gap between them influences the maximum gain due to the shift of the focal point and decreases the impedance matching.
A summary of achieved parameters is documented in Table I and a comparison to other related works is presented in Table II.The maximum operational frequency is defined by a reflection coefficient below −10 and 1 dB drop from the maximum gain at the broadside.

III. CONCLUSION
In this letter, we propose a 3-D partial MFE lens antenna realized in alumina by ceramic-based additive manufacturing.We demonstrate that a low sintering temperature of 1350 °C can be exploited to realize gradient index lenses with a maximum relative permittivity value close to 4, which is beneficial for modern wide-angle lens antenna designs.The fabricated lens exhibits a realized peak boresight gain of 25 dBi at 109.5 GHz and FoV of ±42°, with the possibility to steer the beam up to ±90°, although with a high scanning loss.This overcomes the achieved maximum operating frequency for current unit cell-based high-permittivity QCTO Luneburg lenses realized using LCM technology with standard processing.Moreover, compared with other lenses in literature in the W-band, it presents either a higher operating frequency, up to 110 GHz, or a wider FoV.

Fig. 1 .
Fig. 1.Effective relative permittivity and effective tangent loss of cross-based unit cell after sintering and the frequency at which they are obtained.

Fig. 5 .
Fig. 5. Electric field distribution of (a) MFE lens, PMFE lens cut at 0.45R at (b) the center, and (c) the edge position at 80 GHz.

Fig. 6 .
Fig. 6.Simulated radiation pattern of the PMFE lens antenna from cross-based unit cells at different waveguide feeding positions at 80 GHz (solid) and 110 GHz (dashed).

Fig. 8 .
Fig. 8. Measured (co-pol solid, x-pol dashed) and simulated (dotted) radiation patterns of the PMFE lens antenna at different waveguide feeding positions at 80 GHz.

Fig. 9 .
Fig. 9. Measured (co-pol solid, x-pol dashed) and simulated (dotted) radiation patterns of the PMFE lens antenna at different waveguide feeding positions at 110 GHz.

Fig. 10 .
Fig. 10.Measured (solid) and simulated (dashed) broadband realized gain and measured aperture efficiency (dotted) of the PMFE lens antenna at different waveguide feeding positions.

Fig. 12 .
Fig. 12. Measured and simulated broadband realized gain of the PMFE and QCTO Luneburg [4] lens antenna at boresight, including a gap effect.

TABLE I PARTIAL
MFE LENS PARAMETERS AT THE FREQUENCIES OF 80/110 GHZ

TABLE II COMPARISON
OF W-BAND BEAM SCANNING LENS ANTENNAS