A 3-D Printed Ultra-Wideband Achromatic Metalens Antenna

Lens antennas, which can transform the incident spherical wavefronts to planar above the radiating aperture, have attracted increasing attention due to their simple structure and high gain performance. Nevertheless, conventional lens antennas face with the problem of dispersion effects, which hinders their applications in large bandwidth and multi-channel communications. In this article, we propose a millimeter-wave achromatic metalens antenna using three-dimensional (3D) printing technology to reduce the dispersion effect and enlarge its bandwidth. The proposed ultra-wideband achromatic metalens antenna consists of a convex-liked metalens (VLM) and a concave-liked metalens (CLM) integrated as a metalens group. The VLM is designed on the basis of dielectric posts with different heights. The calculated transmission phase (from 0 to $2\pi$ ) of VLM can be realized by changing the height of dielectric posts. The CLM consists of discrete variable-width dielectric posts with two different heights to achieve desired transmission phase. Measured results demonstrate that the maximum realized gain is 23.27 dBi, and the return loss is smaller than −15 dB within the whole operating bandwidth. More importantly, a broad 3-dB gain bandwidth of more than 68.4% has been achieved to cover nearly the entire V and W bands, ranging from 50 to 102 GHz.

a dual-band Fresnel metalens antenna working at 75 GHz and 120 GHz is realized by merging two single-band Fresnel zone plate metalens antennas [8]. The measured peak gains are 20.3 and 21.9 dBi, the gain bandwidths are 20.7% and 8.3% in the two bands, respectively. Both of these lens antennas feature high-gain characteristics, but their bandwidths are limited.
Several dipole and monopole antennas are designed in mm-wave regions to achieve wideband properties. The series-fed angled eight-dipole array antenna could realize 3-dB gain bandwidth of 66.7% ranging from 22 to 44 GHz with a maximum gain of 10.8 dBi [9]. A low-profile polarized magneto-electric monopole antenna realizes a wide bandwidth of 60.7% (from 23.5 to 44 GHz), and the measured gain of this antenna is around 7 dBi in working frequencies [10]. Although the dipole and monopole antennas have a large bandwidth, their gain cannot reach the same level as the lens antenna.
To realize a high-gain and wideband lens antenna, researchers have utilized the synthesis approach to calculate the phase delay of elements and then match the desired phase at different operating frequencies to minimize the discrepancy between them, resulting in 3-dB gain bandwidth of 13.5% [11]. Broadband lens antenna using Huygens' principle and wideband element is also reported in [12], and it realizes a 3-dB gain bandwidth of 16.7%. Dispersion is the main factor that inevitably affecting the operating bandwidth of dielectric metalenses [13]. In a broad frequency range, the incident wave will produce several different focal positions after phase compensation from the dielectric lens, and resulting in chromatic aberrations [14]. Therefore, the bandwidth of conventional lens antennas is difficult to be larger than 50%.
Compared with the conventional stereo lens, the flat metalens employs the arbitrary designed unit array to freely control the amplitude, phase and polarization of electromagnetic (EM) waves. To overcome the optical dispersion, a dual-layer achromatic metalens is reported in [15] to realize a small focal length difference across the visible frequency range. It requires two different materials namely Al 2 O 3 and GaN to provide different refractive indices for each layer of the metalens. In [16], an achromatic metasurface-based binary phase Fresnel zone plate using TiO 2 material with high refractive indices to obtains an averaged focal distance deviation of 8%, showing a great achromatic capacity. However, the TiO 2 material has a low transmission efficiency in mm-wave region, and the fabrication of Al 2 O 3 , GaN, and TiO 2 films are normally deposited by semiconductor processing with thicknesses on the order of tens to a few hundred nanometers. For mm-wave and terahertz frequency bands, the dimensions of antennas are typically comparable to or larger than the operating wavelength. This presents a challenge for the use of Al 2 O 3 , GaN, and TiO 2 materials as alternative candidates for mm-wave metalenses, because hundred micrometers thick of these materials are difficult to be deposited by semiconductor process. Although they have inspired the design of broadband antennas in the mm-wave field, their material selection, complex and costly fabrication methods have posed challenges to the design of mm-wave antennas.
To solve the above issues, this paper presents a novel and innovative approach to design an achromatic dielectric metalens antenna with high gain and ultra-wideband. The proposed achromatic dielectric metalens antenna consists of a convex-liked metalens (VLM) and a concave-liked metalens (CLM). The VLM is a Fresnel phase compensation metalens antenna with a high-gain performance. The CLM can defocus the incident wave to reduce the chromatic aberration. To the best of our knowledge, this is the first study of ultra-wideband achromatic metalens antenna fabricated by 3D printing technology with low cost and high accuracy, realizing a 3-dB gain bandwidth larger than 68.4% from 50 to 102 GHz due to the opposing dispersion properties of VLM and CLM integration. The element units of metalens could be designed arbitrarily without considering their phase dispersion.

II. CONVEX LIKED METALENS DESIGN
The VLM is a phase compensated Fresnel zone plate lens with various advantages, e.g., low dielectric loss, ease of manufacturing, low profile and high-gain properties [17]. In Fig. 1, a schematic of the VLM design with a positive focal length is shown. It consists of a series of transparent and opaque concentric rings, as shown in Fig. 1(b), and the materials in the transparent and opaque rings are air and homogenous dielectric, respectively. The radius of concentric rings can be obtained in equation (1) [7].
where λ 0 is the designed free-space wavelength at 60 GHz, F 1 is focal length of VLM, N is the total number of rings, which is 5 in this design, and D is the maximum diameter of the whole metalens. F 1 /D is the ratio between the focal length and maximum diameter of metalens. Small  F 1 /D will cause low sidelobe level and antenna gain. On the contrary, large F 1 /D will reduce the phase errors in the phase compensation process, but it deteriorates the efficiencies of antenna [18]. To make a tradeoff between higher loss and spillover efficiencies, the optimized value of F 1 /D is set as 0.4 [11], [19]. Then, the radius of concentric rings is calculated and listed in Table 1. Phase compensation solution is utilized to enhance the high-gain performance of Fresnel zone plate antenna [20]. The dielectric posts are fabricated by 3D printer, i.e., Form3, with a relative dielectric constant ε r = 2.66 and loss tangent tanδ = 0.03 [21]. The element of VLM is simulated using the commercial software HFSS with periodic boundary conditions. The simulated transmission phase versus the post's height is shown in Fig. 2, and a full phase cycle of 2π is obtained by tuning H_VLM from 0.5 to 8 mm. In order to enhance the capability of phase correction and convert the incident spherical wave from the primary feed to the plane wave with high efficiency, the Fresnel metalens with subwavelength dielectric opaque concentric rings are proposed. The desired phase compensation at each post is calculated according to [20]. The profile of the desired phase for each post across the lens aperture is shown in Fig. 3(a). The optimal height of the dielectric post for each lens element can be determined by matching the desired phase to the phase shift obtained by reference to the transmission phase curve in Fig. 2. The profile heights across the lens aperture are shown in Fig. 3(b). Smaller height of the metalens can help to reduce the dielectric loss.
The proposed VLM is simulated in ANSYS HFSS and fed by two different horns, with the operational frequencies ranging from 50 to 75 GHz and 75 GHz to 110 GHz, respectively. While the use of standard gain horns are valid design options, however, the gain of standard horn is quite high (∼24 dBi) and the using of a standard gain horn will result in large F/D for achieving a relatively high aperture efficiency [29]. The designed feed horn with a gain of ∼15 dBi will help to keep the low profile of the whole antenna compared to using a standard gain horn. In this design, the F/D of the lens antennas is set as 0.4 to keep a balance between illumination efficiency and spillover efficiency [29].
The simulated radiation performance of the VLM at 60 GHz and 85GHz is shown in Fig. 4(a)-(b). It can be observed that the sidelobe level of VLM remains below −25 dB in the xz-plane and the yz-plane, respectively. The simulated gains of VLM at different frequencies are shown in Fig. 4(c). The results show that the gain exhibits a steep rise as the frequency increase, making it difficult to identify a stable bandwidth within this range, hence, the bandwidth of the VLM needs to be boosted. In particular, the bandwidth should be increased without changing the focal point position at different frequencies to keep the high gain property of the metalens antenna. To achieve this, we proposed an achromatic dielectric metalens group with VLM and CLM together.

A. ELEMENT DESIGN
In this section, we used a unit structure that differs from VLM to achieve higher transmittance, although it comes at the cost of a larger period. The primary reason for this is that the design of VLM follows the principles of Fresnel lens, which requires smaller unit structures to bring each concentric ring closer to a standard circle and thereby enhance performance. On the other hand, CLM's design does not require smaller unit structures but focuses on achieving greater transmission efficiency. Therefore, CLM and VLM employ different unit structures to achieve their respective design goals.
The elements of CLM are fabricated using the same 3D printer with accuracy of 0.025 mm in horizontal plane and layer accuracy of 0.05 mm. The CLM element is shown in Fig. 5, which is a cross type dielectric post. The height of the central square post is set as 4.5 mm or 6.5 mm. The width W_CLM varies from 0.4 mm to 2.3 mm with a step size of 0.05 mm. Periodic boundary conditions are employed with a periodicity of P in both x and y directions. The corresponding transmission phase is shown in Fig. 6, where the total transmission phase can cover 0-2π , and overall transmission amplitudes remain above 0.84 at 60 GHz. Hence, the transmission phase can be modified by tuning the element's width and height of the central post. The transmission amplitude of 4.5 mm height central square post is larger than that of 6.5 mm because increasing the height will increase the  dielectric loss. Therefore, the dielectric post elements with two different heights are selected to cover 0-2π phase range with high transmission amplitude.

B. CLM DESIGN
As shown in formula (1), a lens with specific R i will demonstrate different focal lengths at different working frequencies.
This phenomenon is well known as the dispersion effect. Because of this, the feeding position of the lens antenna needs to be tuned for different operating frequencies, otherwise, the gains will be affected. However, once the feeding position is fixed, only the corresponding operating frequency will result in a high gain, while the others will be adversely affected and subsequently lower the bandwidth. In this study, an achromatic metalens group is proposed to achieve achromatic function with ultra-wideband, and the configuration of this achromatic metalens group is shown in Fig. 7.  and exhibit the focusing property to enhance the gain bandwidth. The VLM and CLM is directly fabricated together by the 3D printing technology without air gap.
In Fig. 8, the elucidation of the operational mechanisms of VLM and CLM is presented, the solid lines within the diagram depict the path of light transmission, while the dashed lines symbolize their extensions. By examining the Fig. 8(a), it becomes apparent that a convex lens has the ability to converge light rays into a real focal point. However, in the Fig. 8(b), the focal point depicted therein is the convergence point of the extended reverse trajectory of the outgoing rays. That means, the CLM manifests the property of dispersing parallel light, and this particular focal point is non-existent in reality, leading to the definition of the CLM focal length as a negative value. These two metalens constitute an achromatic metalens antenna with the same material and fabrication process. This approach also reduces the assembly error in which no alignment is needed for the two metalenses. For the lens group with a small or no gap between the two lenses, the optical focus of each lens is obtained by using the equation of achromatic condition [22] where φ 1 and φ 2 are the diopter of each lens, φ=1/F. From equation (2), it is known that the focal length of the metalens group should keep positive to have focusing property, and this requires the absolute focal length value of the CLM greater than that of the VLM. In the field of optics, the conventional approach for correcting chromatic aberration is through the use of a lens group consisting of a convex lens and a concave lens made of distinct materials with varying focal lengths. As light travels through a convex lens, the different frequencies of light will converge at different focal points due to chromatic dispersion as shown in Fig. 9(a). Subsequently, as the light passes through a concave lens, the diverse frequencies of light will diverge and separate into different positions as shown in Fig. 8(b). In the Fig. 9(b), by integrating these two lenses, chromatic aberration can be compensated, resulting in the convergence of light with specific frequency ranges at the same focal point. If two lenses are fabricated using the same material and diopter, a non-diopter optical lens group is obtained, which means this lens group does not possess focus capacity. In this study, we use the same material of high-temperature resin to fabricate VLM and CLM with different diopter. For a CLM with a focal length of F 2 , the required phase profile is defined as [15] Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply. where D is 50 mm, which is the diameter of the CLM, (x F , y F ) is an arbitrary point in the lens plane, (x n , y n ) is the central point of the lens, and λ 0 is the wavelength at 60 GHz. The profile of the desired phase for each post across the lens aperture is shown in Fig. 10(a). The simulation model is demonstrated in Fig. 7(b) and Fig. 10(b). In contrast to the VLM, the focal length of the CLM cannot be acquired directly from the simulation software since it cannot find a real focal spot for the CLM. The CLM is taken into the overall metalens group consideration that the focal length of the metalens group F 3 and focal length of the CLM F 2 are input parameters, according to the various performance, e.g., the maximum gain and bandwidth of this lens antenna to obtain the optimal parameters of F 3 and F 2 . And the total focal length of lens group can be calculated using the Abbe formula as where d is the distance between the VLM and CLM, which is equal to the maximum height of the element of CLM (6.5mm). From equation (4), it shows that F 3 can be derived by F 1 and F 2 , where F 1 is 20 mm, F 2 is unknown. Thus, the design process is transformed into an independent parameter optimization problem. In order to better obtain the solution of the optimization problem, it is necessary to take equation (2) as the boundary condition and find the appropriate F 2 to satisfy the equation (4). Optimizing the achromatic metalens antenna using bandwidth as a performance metric can lead to determining the optimal solution. It is worth noting that according to (2), the absolute value of F 2 must be greater than F 1 , but not excessively so. This is because if the absolute value of F 2 is much larger than F 1 , the total focal length F 3 will be very small, leading to low levels of edge radiation of the metalens group antenna, and negatively affecting the radiation efficiency. Through a series of simulation, the performance characteristics of an achromatic metalens group at different values of F 2 was studied, as shown in Fig. 11. The gain-frequency curve of the metalens group was simulated and analyzed to evaluate its gain performance across different frequency ranges. The results showed that the metalens group exhibited optimal broadband characteristics when the value of |F2| was approximately three times of F 1 . This can be attributed to the optimal interaction between the physical structure and optical performance of the metalens group when F 2 is close to three times of F 1 , which result in the best chromatic aberration correction effect. The simulated gain-frequency curves at different values of F 2 with value of −75 mm demonstrated the highest maximum gain among these curves. However, we also observed that the performance of the metalens group at low frequencies deteriorated when F 2 was set to −75 mm. Therefore, a balance between gain and bandwidth is necessary when selecting the value of F 2 for the metalens group. After weighing the options, we ultimately chose a value of −65 mm for F 2 , which could provide appropriate gain and bandwidth.

A. METALENS GROUP FABRICATION
Our proposed achromatic metalens antenna is fabricated using the 3D printing technology with Low Force Stereolithography (LFS) to drastically reduce the forces exerted on parts during the print process and laser spot size is 0.085 mm [23]. In mm-wave fields, a substantial amount of antennas have also been fabricated using the 3D printing technique as reported in [21], [24], [25], [26]. The achromatic metalens group is printed horizontally, layer-bylayer from the CLM to the VLM, and the CLM is directly in contact with thin struts that can support the weight of the metalens group, as shown in Fig. 12(a). Since the CLM elements have different widths W_CLM, this leads to different across-section areas. The contact points between the thin struts and the elements cannot be made with a minimum diameter, especially for elements with a large width. A support strut with a small diameter is not strong enough to hold the elements up and will cause the printed dielectric posts to appear tapered. Considering that the removal of the struts will also leave a vestige on the surface of the element, as shown in Fig. 12(b). The large diameter contact points of struts would severely increase diffuse reflection, which is undesirable. With the help of Formlabs' printing software, the contact point diameter can be manually set from 0.2 to 1 mm. The contact point diameter can also be minimized on the premise of accurately printing the element. In this study, the lens layer's height is set to 0.05 mm along the z-axis to ensure that all the element heights in Fig. 2 can be accurately fabricated.

B. MEASUREMENT DEMONSTRATION
The achromatic metalens antenna was measured by a mmwave measurement setup in the State Key Laboratory of Terahertz and Millimeter Waves at City University of Hong Kong, as shown in Fig. 13. This measurement setup is built to measure the radiation performance of antennas at mm-wave region. The center of Fig. 13 is the proposed achromatic metalens antenna with a fixture to support the antenna and keep the feed horn at the focal point. The signal from the frequency extender modules covers the frequency ranges from 50 to 110 GHz, and two different standard waveguides WR-15 and WR-10, with the frequency ranges of 50 to 75 GHz and 75 to 110 GHz are needed, respectively. Thus, we designed two different feed horns to match the WR-15 and WR-10 waveguides. The gain of the lens antenna was measured by the gain comparison method [27]. The performance of the proposed achromatic metalens group antenna has been experimentally verified. The simulated and measured radiation patterns in the xz-plane and yz-plane are given in Fig. 14 and Fig. 15, respectively. The results show that a good agreement between the measured and simulated radiation patterns. As shown in Fig. 14, the sidelobe levels of achromatic metalens antenna at 50 GHz, 60 GHz, and 70 GHz are less than −20 dB in both xz and yz planes. From Fig. 15, the sidelobe levels of the achromatic lens antenna are less than −18 dB in the xz plane, and −15 dB in the yz plane at 75 GHz, 85 GHz, and 95 GHz, respectively. The measured and simulated reflection coefficients of achromatic lens antenna are demonstrated in Fig. 16(a), and the results show that the S 11 of our proposed achromatic metalens antenna was smaller than −16 dB ranging from 50 GHz to 110 GHz. The measured and simulated gains of achromatic metalens antenna in the frequency band of interest are plotted in Fig. 16(b). The measured maximum gain is 23.27 dBi at 68 GHz, corresponding to an aperture efficiency of 16.75%. The measured cross polarization levels are better than 30 dB below the main beam. The measured 3-dB gain bandwidth of the achromatic lens antenna is larger than 68.4% from 50 to 102 GHz, and the gain at 60 GHz is 22.27 dBi. Compared with the VLM, the measured gain of achromatic metalens group is reduced by 2.13 dB due to the addition of the CLM, which increases the dielectric loss (tanδ = 0.03) while expanding the bandwidth. Unlike the low-frequency range from 50 GHz to 75 GHz, the gain at the high-frequency range from 75 GHz to 102 GHz has fluctuations and a descending tendency. This is mainly because our proposed antenna needs to use two different horns as feed. The horn working at the higher frequency (smaller wavelength) is more sensitive for fabrication accuracy. The other reason is that the change in the main beam width in the horn will change the antenna edge taper at the frequency range from 75 GHz to 102 GHz [29]. Despite the fluctuations, the overall gain of the achromatic metalens antenna is stable within 3 dB at a wide frequency range from 50 to 102 GHz.
While achromatic can increase the bandwidth, it also has limitation. As shown in the Fig. 16(b), the gain starts to decrease at high frequencies, and the difference between the gain and the feed horn antenna gain becomes smaller. This indicates a decrease of the achromatic ability. The aperture efficiency is relatively low, primarily attributed to the generally lower aperture efficiency of the dielectric lens. In additional to the common spillover loss, taper loss, polarization loss, and feed loss for reflectarray/transmitarray antennas, the dielectric lens antennas generally have a lower aperture efficiency  due to the increased dielectric loss. As shown in the comparison Table 2, the aperture efficiency of most millimeter-wave dielectric lens antennas is below 30%, while planar reflectarray/transmitarray can achieve a relatively higher aperture efficiency. In particular, the use of a dual-layer structure in this design introduces increased dielectric losses resulting in diminished aperture efficiency. Nevertheless, these results demonstrate that our proposed achromatic metalens antenna could achieve high gain and ultra-wideband properties at mm-wave frequencies, opening avenues for further ultrahigh-speed wireless communications.
Finally, we summarize the overall performance characteristics of the proposed design and compare it with other wideband lens antennas listed in Table 2. The comparison shows that the design presented here offers the largest gain bandwidth. Compared with the-state-of-the-art 3D printed transmissive lenses and reflectarrays shown in [20], [30] and [28] utilizing the single-layer lens approach, this design realizes ultra-wide bandwidth by using achromatic metalens group to eliminate the dispersion effects. Especially in comparison to [30] with nearly the same aperture area, our proposed achromatic metalens antenna can reach the same gain with twice the bandwidth, proving that our design is suitable for high-gain and wideband applications. Using achromatic theory can simplify the element design instead of looking for a wideband element. The reflectarray in [28] uses wideband element to realize the 3-dB gain bandwidth of 30%, which is smaller than our proposed achromatic metalens group antenna. Additionally, in comparison to other designs [11], [12], which employ the microstrip elements, this work uses a rapid, low cost and straightforward fabricate technology based on 3D printing to achieve a considerable wide bandwidth, spanning over almost the total V and W bands.

V. CONCLUSION
In this paper, we propose a novel 3D-printed high gain and ultra-wideband achromatic metalens antenna operating at mm-wave frequency. The achromatic metalens antenna is composed of a phase compensation Fresnel lens as VLM with high gain performance and a CLM behind the VLM to reduce the chromatic effects and extend the working bandwidth. This achromatic metalens antenna group is fabricated in one piece using a laser curing 3D printer with fast prototyping and low cost. The simulated and measured results agree well, and the 3-dB gain bandwidth of our proposed achromatic metalens antenna is over 68.4% from 50 to 102 GHz. The measured maximum gain is 23.27 dBi at 68 GHz. The wideband antenna under consideration owns its potential applications in various areas, including ultrawideband proximal communication, specific frequency band research, indoor communication, etc.