2021 8th NAFOSTED Conference on Information and Computer Science (NICS) Investigation on Radiation Characteristics of Dielectric Lens Antennas at Millimeter-Wave Phan Van Hung1, Nguyen Quoc Dinh1* Le Quy Don Technical University, Ha Noi-City, Viet Nam, E-mail: phanvanhung@tcu.edu.vn, dinhnq@lqdtu.edu.vn *Corresponding author: Nguyen Quoc Dinh Abstract - In 5G mobile communication, the antenna system for the base stations must be highly directional capable of generating multi-beam and wide-angle beam scanning The lens antenna is being selected as one of the highly efficient antennas used for base stations In this paper, the authors calculate, model, and simulate the dielectric lens antenna (LsA) structure of the elliptic shape, inner flat surface, and Abbe's sine condition, thereby comparing and evaluating radiation characteristics and wide-angle beam scanning capability among three lens antenna structures The results show the lens antenna's efficiency with Abbe's sine condition and inner flat surface when the wide-beam scanning angle is up to 900 while maintaining high directivity, lower side lobe level than elliptic shape lens antenna Keywords - lens antenna, wide-angle beam scanning, Abbe’s sine condition I INTRODUCTION In the 1880s, Hertz and Oliver Lodge investigated dielectric lenses as parts of an antenna in the electromagnetic wave field In 1888, the first dielectric lens antenna was tested and operated at a 1-meter wavelength [1] However, it was not until the Second World War that lens antennas were researched and developed more Dielectric lenses are used to transform the radiation pattern of feed into some forms of higher gain, capable of generating multiple fixed beams or scanning wide-angle beams In the past two decades, with remarkable advances in lens fabrication technology for the millimeter-wave range, researchers have been more interested and more in lens antennas The dielectric lens antenna's size is made more compact with new technology, meeting practical requirements and applications In 5G mobile communications, the antenna system for the base station must be able to generate multi-beam and wideangle beam scanning to accommodate multiple wireless connections at the same time in different locations [2]-[6] In the N257 band (26.50 GHz - 29.50 GHz), lens antennas are considered as a potential candidate [7]-[12] Because of its particular structure, the lens antenna is not affected by the blockage of the feeds, so setting up the off-focus feed allows the antenna to generate more beams and improve the wideangle beam scanning Lens structure and feed trajectories are essential factors which determine the beam scanning angle In the research of Y Yamada and colleagues, they performed calculations and built lens structures based on the power conservation law and Abbe's sine conditions By a ray-tracing method, the caustic points and their trajectories are determined When setting up feed on the trajectories, the lens antenna can create multi-beams and a wide-angle beam 978-1-6654-1001-4/21/$31.00 ©2021 IEEE scanning [9]–[13] However, the comparison and evaluation of the efficiency of wide-angle beam scanning ability of three types of lens antenna structures with elliptic shape, inner flat surface, and Abbe's sine condition have not been clarified Therefore, in this paper, the authors modeled these lens antenna structures and used ANSYS HFSS electromagnetic field calculation software to simulate the structure to make evaluations and comparisons on the effectiveness of each structure in terms of wide-angle beam scanning based on the radiation characteristics of the lens antenna The paper is structured into four sections Section presents models of the lens antenna structures with the widebeam angle scanning The simulation results and evaluations are presented in section Section is a conclusion II ANTENNA STRUCTURE MODLE A Lens Antenna Structure with Elliptic Shape The lens antenna with elliptic shape is structured by two main components: a feed and an elliptic shape lens, as shown in Figure The lens has a circular structure that rotates around the Oz axis The inner surface (S1) is a spherical surface with a radius of r1 The outer surface (S2) is an elliptic shape with a focal length FT r1 T , where T is the lens thickness at the lens center (on the Oz axis) The lens's outer surface structure is calculated in the polar coordinate system based on the electrical and physical length of wave rays to satisfy Snell's law The wave rays from the feed to the aperture plane are equal path length The electrical path length of every ray is given by the equation [14] r1 nl1 s1 r1 nT (1) and the following physical length condition: (r1 l1 )cos s1 r1 T (2) The setting r2 r1 l1 , from equations (1) and (2), the elliptic surface equation for the outer lens surface S2 is: (r1 T )(n 1) FT (n 1) (3) n cos n cos where n is the refractive index of the lens dielectric The lens thickness at the lens center is given by equation (4), and D is the lens diameter 317 r2 T r1 4r12 D 2( n 1) (4) 2021 8th NAFOSTED Conference on Information and Computer Science (NICS) Lens x l1 Feed horn Aperture plane Aperture plane s1 Lens x r1 l3 l2 Feed horn l1 z z D s1 r2 D s2 Fig Lens antenna structure with elliptic shape Fig Lens antenna structure with an inner flat surface The elliptic shape lens is a single refracting surface All the inner surface points of the lens are at the same distance from the feed and are illuminated with identical amplitude The refraction occurs only on the elliptic outer lens surface dr rn sin( ) d n cos( ) B Lens Antenna with an inner flat surface The lens antenna structure with the inner flat surface (S1), is shown in Figure By setting a fixed value of z1 (z1=F), the slope on S1 is equal to infinity For the rays coming out from the outer curve surface S1 to be collimated (planar waves inphase), the wave rays are parallel to the radiation axis Oz Suppose that the electrical path length of every ray is the same at the aperture plane, it is required that l1 nl2 l3 F nT (5) and the following physical length condition: l1 cos l2 cos r l3 F T (6) where θ is incident angle and θr is refracted angle These angles satisfy the Snell’s law sin n sin r The outer surface structure is determined by the equation: dz n sin dx n cos [(n-1)T- F x12 ] ( n 1) x12 n F n F F x12 n F x12 ( n 1) x12 n F z r cos (14) Lt r n z0 z cos To satisfy Abbe's sine condition, the radiated rays from the feed and the wave rays coming out from the outer surface of the lens have their intersections on a circle with radius fc, as shown in Figure The circle on the xOz plane is determined by the equation: x fc sin( d ) (7) (8) z2 F (9) x2 x1 1 (n 1) x12 n F where, (z1, x1) is points on S1 surface; (z2, x2) indicates points on S2 lens surface T (15) when d is very small then (15) becomes x fc sin( ) (16) and dx f c cos (17) d By solving three differential equations (11), (13), and (17) simultaneously, the structure of the inner and outer surfaces of the lens can be determined The radiating rays from the feed passing through the lens satisfy Snell's law, the wave rays coming out from the lens aperture plane are collimated rays The wave rays are parallel and in phase with each other In this case the central thickness is 4F D2 2F 2( n 1) (12) dz n sin dx (13) d n cos d The condition for the total length of radiated rays from the feed to the aperture plane of the lens antenna is given by: Based on equations (5) and (6), the structure of the outer surface of the lens is determined as follows: z2 (11) (10) Lens x Aperture plane Feed horn The lens antenna with an inner flat surface is a tworefracting surface lens The radiation rays from the feed horn are refracted at both the inner flat surface and outer surface C Lens Antenna with Abbe’s Sine Condition The lens structure with the Abbe' sine condition is determined based on the ray-tracing method and the three differential equations [14]-[17] The equation that gives the inner surface structure of the lens is as follows: 318 z0 z D F Fig Lens antenna structure with Abbe’s sine condition 2021 8th NAFOSTED Conference on Information and Computer Science (NICS) by the radiating ray from the convergence point to the lens center and the Oz axis The angle α shifts between 00 and 400 with a step of 100 The convergence point of the lens is at the phase center of the conical horn antenna The antenna radiates in the Oz axis direction Figure shows the lens antenna structure with the feed horn set up on the R trajectory φ = 00 φ = 900 Normalize Gain (dBi) -5 -10 Lens area R F cos -15 (18) III SIMULATION RESULTS ANALYSIS -20 -25 -60 -40 -20 20 Radiation angle (deg.) 40 A Simulation Parameters The structural and simulation parameters of the lens antenna are presented in Table The electromagnetic field calculation software ANSYS HFSS is used to calculate the electromagnetic field distribution on the planes and the radiation characteristics of the lens antenna based on the proposed structure The hybrid finite element boundary integral (FEBI) technique is used FEBI is a numerical method that uses the MoM solution as a truncation boundary for the FEM solution and hence combines the best of FEM and MoM methods increasing the simulation speed and reducing computational effort [22] The lens uses a Teflon dielectric material with relative permeability μr=1, and relative permittivity εr = 2.1, which corresponds to the refractive index is 𝑛 = √2.1 60 (a) Radiation pattern on the xOz and yOz planes TABLE I f D (b) Reflection coefficient S11 Fig Radiation parameters of conical horn antenna D Feed Horn The conical horn antenna, which is employed as the wideangle radiator element for the lens antenna, is designed to operate in the N257 band, 26.50 GHz - 29.50 GHz for 5G mobile communications The conical horn antenna has a peak gain of 17.84 dBi and can focus more than 90% of radiating power into the lens when the horn antenna's phase center is placed at the focal point of the lens Figure shows the radiation pattern in xOz, yOz planes and the reflection coefficient S11 of the conical horn antenna E Lens Antenna Structure with Wide-Angle Beam Scanning x R F cos Lens α z F Feed trajectory Fig Lens antenna structure with wide-angle beam scanning Based on the ray-tracing method performed in studies [12], [18]-[21], the convergence points and their trajectory have been determined when changing the incident angles Therefore, in this study, the authors set up the feed horn on the trajectory given by equation (18), with α being the angle made THE STRUCTURAL LENS PARAMETERS Parameters Frequency Lens diameter F Distance from the focal point to the lens vertex n Refractive index fc Radius of circle T Lens thickness at the center Value 28 100 Unit GHz mm 100 mm 2.1 117.21 Abbe’s Sine and Elliptic 29.83 Inner flat surface 26.28 mm mm B Simulation Results Analysis 1) The radiation characteristics changes of the LsA When the feed horn is placed on the R-trajectory, the change in the value of the maximum gain (G) and the side lobe level (SLL) of the three lens antenna structures with the radiation angle shift from 00 - 400 is determined, as shown in Figure Accordingly, it can be seen that the lens antenna has the highest maximum gain and lowest side lobe level when the feed horn is set up at the focal point of the lens The simulation results are detailed in Table Accordingly, when α = 00, the lens antenna with elliptic shape has the maximum gain of 28.32 dBi, while the maximum gain of the lens antenna with a flat inner surface and Abbe's sine conditions are 28.00 dBi and 28.05 dBi, respectively The maximum gain gradually decreases as the feed horn is shifted off-axis and on the R-trajectory The maximum gain attenuation of the lens antenna with elliptic shape occurs more than that of the lens antenna with the flat inner surface and Abbe's sine condition when the radiation angle α > 200 In particular, the maximum gain of lens antenna with elliptic shape is attenuated 2.91 dB at 400 compared to 00, while the figures for a lens antenna with the inner flat surface and the lens antenna with Abbe's sine condition are 1.85 dB and 1.55 dB, respectively 319 30 -15 29 -18 28 -21 27 -24 Gain Ellipse Gain Abbe' sine Gain S1 flat SLL Ellipse SLL Abbe's sine SLL S1 flat 26 25 10 20 2) Radiation pattern and field distribution of the LsA The radiation patterns of the conical horn antenna and the three types of lens antennas are shown in Figure From the radiation patterns, we can observe the effectiveness of using dielectric lenses in improving the radiation capacity of the lens antenna As described in Section II (D), the conical horn antenna reaches a maximum gain of 17.84 dBi when operated independently However, when the horn antenna is combined with the dielectric lens, the maximum gain of the lens antenna increases by more than 10 dB, which is close to the theoretical value of the aperture antenna given by equation (20) [23] Figure (b) shows the similar radiation patterns of two types of lens antennas (Abbe's sine and inner flat surface) with tworefracting surface lenses for wide-beam scanning angle applications Side lobe level (dB) Gain (dBi) 2021 8th NAFOSTED Conference on Information and Computer Science (NICS) -27 30 40 -30 Incident angle α (deg.) Fig The variation in the gain and side lobe level values D Gmax In addition, the side lobe level of the lens antenna with elliptic shape increases rapidly from -23.37 dB to -15.00 dB, while the lens antenna with Abbe's sine condition and the flat inner surface maintains the side lobe level at -21.55 dB and 22.09 dB, respectively ( θB_Ellipse shape) ( θB_Abbe's sine) ( θB_S1 Flat surface) ( Δ_Ellipse shape) ( Δ_Abbe's sine) ( Δ_S1 Flat surface) 7.5 7.0 6.5 6.0 40 10 20 30 Gain (dBi) 10 -5 -80 -60 -40 -20 20 40 60 80 Radiation angle_α (deg.) (a) Horn antenna, Elliptic shape, and Abbe’s sine lens antenna 30 Abbe's sine S1 Flat 25 α = 00 α = 100 α = 200 α = 300 α = 400 Horn antenna 20 Gain (dBi) 8.0 15 12 10 α = 00 α = 100 α = 200 α = 300 α = 400 Horn antenna 20 Deviation angle (deg.) HPBW (deg.) 8.5 Elliptic shape Abbe's sine 25 14 9.0 (20) 30 (19) L The radiation angle deviation from the feed setting angle (Δ) is given by equation (19), where θL is the radiation angle of rays going out the outer lens surface to the radiation axis Oz Figure shows the change in the half-power beamwidth (HPBW) and the radiation angle deviation values when the feed horn is moved on the R trajectory Accordingly, we can see that the HPBW (𝜃 ) of lens antennas with Abbe's sine condition is always smaller than the other two types of antennas However, the radiation angle deviations of the lens antennas with elliptic shape and inner flat surface are almost the same and less than those under Abbe's sine condition 9.5 15 10 -5 Incident angle α (deg.) -80 -60 -40 -20 20 40 60 80 Radiation angle_α (deg.) Fig The variation in the HPBW and deviation angle values Thus, for applications with beam scanning angle α < 200, we can use an elliptic lens antenna structure and apply lens antenna structures with Abbe's sine condition and the inner flat surface lens for applications requiring wider-angle beam scanning From equations (4), (10), and simulation parameters as shown in Table 1, it can be seen that the thickness of the lens with the flat inner surface at the lens center is thinner than that of two types of lenses with Abbe's sine condition and elliptic shape The unique construction of the lens with an inner flat surface makes it easier to fabricate than lenses with Abbe's sine condition and elliptic shape while maintaining the maximum gain of 26.15 dBi and the side lobe level lower -22.09 dB when the feed horn is placed at the wide radiation angle of 400 (b) Horn antenna, S1 flat surface, and Abbe’s sine lens antenna Fig The radiation pattern of horn antenna and LsAs The electric field distribution on the xOz plane of the elliptic lens antenna and the Abbe's sine condition at angle α = 300 are shown in Figure The radiating wave from the feed horn has a spherical waveform, the wave coming out from the outer surface of the lens is converted into the in-phase planar waveform The elliptic lens structure concaves in the direction of the feed horn, so the reflected rays from the inner surface of the elliptic lens tend to bounce back feed, leading to wave interference, making the side lobe level of the elliptic lens antenna higher Meanwhile, the lens structures with Abbe's sine condition and inner flat surface are convex and planar, 320 2021 8th NAFOSTED Conference on Information and Computer Science (NICS) respectively, so the reflected rays tend to go towards the edge of the lens Thus, interference and diffraction between the incident wave from the feed horn and the reflected ray from the lens surface are less, so the side lobe level tends to be lower The solution to reducing the reflection wave on the lens surface and the multi-reflection occurring inside the dielectric lens is to use a quarter-wavelength matching layer, presented in the literature [8] (a) Lens antenna with elliptic shape (b) Lens antenna with an inner flat surface (c) Lens antenna with Abbe’s sine condition Fig Electric field distribution on xOz plane TABLE II Radiation angle ( ) 00 100 200 300 400 Lens antenna with an elliptic shape G [dBi] SLL [dB] 28.32 28.25 28.00 27.17 25.41 -23.37 -19.10 -17.23 -16.72 -15.00 B L [0] 6.86 7.00 7.51 8.18 9.34 [0 ] 0.0 8.8 17.3 25.2 32.3 SIMULATION RESULTS Lens antenna with an inner flat surface Lens antenna with Abbe’s sine condition G [dBi] SLL [dB] G [dBi] SLL [dB] 28.00 27.78 27.69 27.28 26.15 -25.62 -23.84 -22.72 -22.65 -22.09 28.05 27.94 27.93 27.72 26.50 -25.40 -24.29 -22.65 -22.28 -21.55 B L [0 ] 7.12 7.22 7.64 8.19 8.94 [0] 0.0 8.8 17.3 25.4 32.3 B L [0] 6.80 6.85 7.14 7.72 8.64 [0] 0.0 8.6 16.8 24.4 31.0 Theoretical Gmax [dBi] 29.34 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conical horn antenna and the three types of lens antennas are shown in Figure From the radiation. .. L The radiation angle deviation from the feed setting angle (Δ) is given by equation (19), where θL is the radiation angle of rays going out the outer lens surface to the radiation axis Oz... that the thickness of the lens with the flat inner surface at the lens center is thinner than that of two types of lenses with Abbe''s sine condition and elliptic shape The unique construction of