https://orcid.org/0000-0002-7122-4824
Figures
Abstract
This study presents the design and development of a truncated spherical dielectric lens antenna. The primary goal of this research is to significantly improve and optimize the directivity and beamwidth characteristics of the feed antenna by adjusting the feed position around the focal point of the lens. Polytetrafluoroethylene (PTFE), with a dielectric constant of 2.1, is chosen as the lens medium. Simulations are carried out using the CST-Studio Suite across the span of 8 to 12 GHz. Vector Network Analyzer (VNA) and an anechoic chamber are utilized for experimental validation. Directivity of 21.9 dBi and a beamwidth of 13.1° have been achieved by optimizing the dimensions of 24.34 mm thickness, 55 mm center of curvature and 110 mm aperture of the lens. By utilizing its simple geometrical shape, compact size, and ease of design and construction, this dielectric lens antenna is ideal for RF applications, particularly when energy concentration is necessary.
Citation: Ali SZ, Ahsan K, ul Khairi D, Akhter Raza S, Alhalabi W, Kazem LH, et al. (2025) Optimal dimensions and performance evaluation of a truncated spherical dielectric lens antenna at X-band frequencies. PLoS ONE 20(3): e0318547. https://doi.org/10.1371/journal.pone.0318547
Editor: Sachin Kumar, Galgotias College of Engineering and Technology, Greater Noida, INDIA
Received: October 19, 2024; Accepted: January 17, 2025; Published: March 17, 2025
Copyright: © 2025 Ali et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Data Availability: All relevant data are within the article and its Supporting Information files.
Funding: This project was funded by the Deanship of Scientific Research (DSR) at King Abdulaziz University, Jeddah, under Grant No. (RG-6-611-43). The authors gratefully acknowledge the technical and financial support provided by DSR.
Competing interests: The authors have declared that no competing interests exist.
1 Introduction
High-frequency communication systems employ lenses to send and receive electromagnetic waves (EM). These lenses are evaluated as critical components that provide enhanced efficiency and directivity [1]. In applications such as millimeter (30–300 GHz) and terahertz (0.3–10 THz), dielectric lens antennas are primarily applicable due to their curved surfaces [2]. Initially, the use of dielectric lens antennas, which had been prominent in microwave applications, gradually declined as smaller reflector antennas evolved to become more applicable to microwave configurations [3]. Modern developments in millimeter-wave and submillimeter-wave technologies have reignited interest in antenna design. Due to the essential features of these high-frequency bands, compact and extremely effective antenna solutions are necessary to meet the needs of new applications [4].
Dielectric lenses are frequently used in a variety of applications, such as microwave imaging, broadband communication systems, and radiation pattern optimization employing beam-shaping techniques [5–7]. In contrast with reflectors, dielectric lenses provide a different advantage by enabling beam shaping without blocking the antenna aperture. This characteristic is particularly useful in applications that require high gain while reducing hardware complexity [8]. Integrated lens antennas (ILAs), which feature a direct coupling between the lens base and the feed, are widely used in systems that require high gain and narrow beamwidths. These applications encompass radar, communication, and energy-focusing technologies [9]. Lens antenna subarrays (LAS) are a recent invention in millimeter wave beam guiding technology that significantly reduces hardware complexity [10]. comparebly, horn antenna arrays combined with dielectric lenses, while efficient for multi-beam operation and polarization control, show significant size and enhanced system complexity [11].
state-of-the-art developments have resulted in the fabrication of small, high-performance antennas for X-band and Ku-band applications. A specialized S-shaped slotted micros-trip patch antenna obtains dual-band operation at 10 GHz and 17.65 GHz with a peak gain of 6.3 dB. This antenna’s tiny dimensions (24 × 16 × 0.8 mm³) and enhanced current dispersion are achieved by adding slits and slots. This design demonstrates outstanding performance, utilizing it appropriate for satellite communication and radar systems [12].
The advent of 5G connectivity has drastically increased the need for compact and high-performance antenna designs. A new finding developed a hairpin-shaped micros-trip patch antenna for 5G mobile, operating at 60 GHz and compliant with the IEEE 802.11ad standard. This design was tested on three substrates—FR4, Rogers RO4350B, and Arlon AD255C—This antenna exhibits good bandwidth of 3.8 GHz and a return loss of –34.5 dB when fabricated on a 1.2 mm thick Rogers RO4350B, allowing that it is appropriate for high-frequency applications [13].
To overcome the low directivity of microstrip patch antennas, a novel approach was developed that uses inverse refraction metamaterials (IRMM) as a flat lens. This work proposes an omega-shaped metamaterial (OSM) lens layer specifically designed for Ku-band operation at 12 GHz. The experimental results showed a significant increase in antenna directivity, with a single layer of the OSM lens achieving a 2.74 dB improvement and a double-layer configuration achieving a 4.08 dB improvement. Notably, the metamaterial layers employed in this study have dimensions equivalent to the patch size, indicating that it can be used for compact implementation while getting a considerable performance benefit [14].
Metasurfaces are a promising technology for regulating electromagnetic waves, with features like beam focusing, polarization control, and multi-beam creation [15–17]. Despite these advances, many contemporary designs are hampered by difficulties like as structural complexity, high fabrication costs, and poor adaptation to small hardware systems. Metamaterial-based lenses [18–22] and metasurfaces [23–26] perform well in gain enhancement and beamforming, but require complex geometries and parameter tuning.
For directivity optimization, a truncated PTFE-based spherical lens is significantly more effective than materials including glass or acrylic. PTFE’s low dielectric value and minimum signal loss enhance the high-frequency utilization, while glass’s larger dielectric constant leads to significant signal degradation [27]. Moreover, PTFE is more durable than glass and acrylic because to its greater thermal stability and resistance to environmental conditions such as moisture and UV radiation [28]. Lightweight and flexible, it is perfect for small antenna systems [29]. PTFE lenses are more efficient and adaptable than acrylic, making them promising choice for use in high-frequency antenna systems [30]. With these attributes, PTFE lenses are ideal options for applications that demands precision beam shaping and adaptive radiation patterns.
Part I includes a brief overview of the research aims and essential background information. Part II looks into the lens design process, using the CST Studio Suite software and according to recognized lens optics principles. Key characteristics such as lens thickness (T), radius of curvature (R), lens aperture (L), and focal length (f) were computed methodically. Iterative simulations were run, with parameter tweaks made to attain optimal performance. Part III describes the experimental setup and methodology used for practical demonstrations. Finally, Part IV provides a full analysis of the experimental data, verifying the design and evaluating its performance characteristics.
2 The design, optimization, and fabrication of feed and lens antennas
In this section, feed and lens antennas are designed, optimized, and fabricated. Design is guided by feed selection, electromagnetic simulations, and optimizations, followed by fabrication methods that turn the optimized design into a physical structure. Fig 1 illustrates the experimental process.
2.1 Designing feed antenna
To feed the lens, a pyramidal horn antenna with an operating frequency of 11 GHz was chosen. The design parameters of the horn antenna are shown in Fig 2.
The voltage standing wave ratio of the horn antenna is not good for the entire band of 0 GHz to 15 GHz, However, acceptable performance (VSWR < 2) is observed from 8 GHz onwards, as depicted in Fig 3. The simulation range will be refined to 8–12 GHz to ensure optimal feed antenna performance.
The horn antenna was simulated within the CST Studio Suite over the frequency range of 8 GHz to 12 GHz. As depicted in Fig 4, the designed horn antenna exhibits favorable performance with S11 below –10 dB, indicating good impedance matching.
2.2 Design and calculation of semi-circular dielectric lens
Taking into consideration of lens shape, it would be based on the refractive index. The refractive index of dielectric materials can be calculated as in Eq 1 [26].
From an optical formula, the relation between focal length and the radius of curvature R of the two lens surfaces can be written as in Eq 2.
where a concave surface is indicated by a negative radius. The radius of curvature R of the surface of a single lens is determined using an optical formula, as shown in Eq 3.
Material made of PTFE has a dielectric constant of 2.1 Therefore, Eq 3 may be summed up in Eq 4
We first fixed the radius of curvature of the lens sphere to R = 100 mm and cut the sphere with a different-sized plane to capture and obtain lenses of different thicknesses and apertures. Fig 5 depicts the entire procedure.
By using Eq 4, the Focal length, f = 222.6 mm was calculated at R = 100 mm, and then the feed antenna was placed 222.6 mm away from the lens as shown in Fig 6.
A simulation-based approach was used to investigate the influence of lens thickness on directivity and angular beam width. Fig 7(a) and 7(b) graphically present the simulation results, offering valuable insights into design optimization. Compared to tabular data, these visual representations effectively convey complex relationships, facilitating the identification of trends and patterns. This approach improves both the efficiency of data analysis and the presentation of research outcomes.
A dual-axis plot in Fig 7(a) shows that as thickness increases, directivity increases steadily, reaching a maximum of 24 dBi at 40 mm. Directivity is observed to diminish with increasing thickness, with a marginal increase observed between T = 25 mm and T = 40 mm (22.7 dBi). With increasing thickness, the angular beam width also narrows, reaching a minimum of 8.4 degrees at T = 60 mm. It is clear, however, that the beam width is 9.1 degrees, demonstrating a reasonable compromise between beam sharpness and thickness at T = 40 mm.these observations indicate that although greater thickness typically enhances directivity and beam focus, the performance gains diminish significantly beyond T = 25 mm, accompanied by increased design complexity and aperture size.
Fig 7(b) confirms these trends, with directivity peaking at T = 40 mm and minimal gains beyond T = 25 mm. Beam width narrows to a minimum at T = 60 mm, remaining adequate at T = 40 mm. T = 25 mm optimizes directivity (22.7 dBi) and beam width (11.4 degrees) while requiring a 132 mm aperture compared to 160 mm at T = 40 mm. The presented data identifies T = 25 mm as the optimal lens thickness, maximizing directivity and beam focus while minimizing aperture size and design complexity. This selection provides a more efficient and cost-effective solution for applications requiring high performance.
Finally, further optimization of the lens was performed with different feed position values around the calculated actual focal length (f = 165.5 mm) as shown in Table 1.
In comparison to alternative feed sites, the data shown in Table 1 shows that placing the feed at f = 165.5 mm results in better directivity and beam width. By increasing the system’s capacity to concentrate radiated energy and reducing the beam width, this result implies that f = 165.5 mm is the best feed site. By positioning the feed in this manner, the system may increase the focus and direction of the energy it radiates, producing a smaller and more focused beam.
The relationship between the position of the feed, the directivity, and the angular width of a lens is also shown in Fig 8. The bars show the directivity and angular width values for various feed positions, demonstrating how these characteristics vary when the lens’ feed position is changed.
Hence at f = 165.5 mm, the proposed design geometry and necessary final design values have been shown in Fig 9.
In Table 2, which includes a list of the particular lens parameters, you can see the optimized values for each lens parameter that were found through simulation and optimization. Based on the intended result or performance requirements, these optimized values show the optimal or most efficient configuration for the lens.
The lens is simulated with optimized values to check the return loss and impedance matching. it is showing good performance with S11 < –10 dB which indicates that the optimized lens is effectively reducing reflections and improving impedance matching as shown in Fig 10.
The value of the voltage standing wave ratio of the lens is below 2 for the entire band of interest, as shown in Fig 11.
The CNC machine was used to manufacture the pair of lenses. In order to physically align the lens center and feed center on a straight line, lens support frames (custom and non-custom) were made to hold the antenna. Further, the lens mount provides a convenient way to move the lens to a different position from the feed point. The lenses in the frames are shown in Fig 12.
3 Results and discussion
A return loss graph for both the feed and the lens is shown simultaneously in Fig 13. Below S11 < –10 dB, the graphs of the simulated return loss from 8 to 12 GHz show good performance. A resonance frequency below S11 < –10 dB is shown by the S11 findings without a lens; however, many resonance frequencies below S11 < –10 dB are shown by the S11 results with a lens.
The far-field results show that the directivity of the horn antenna at 11 GHz is 16.8 dBi and the angular width of the beam is 27.50. ∘ as shown in Fig 14(a) and 14(b).
we set our horn antenna to the focal distance of the lens antenna and chose a band between 10GHz to 12GHz. the findings indicate that the horn antenna’s directivity at 11 GHz has been enhanced to 21.9 dBi and the beam’s angular width has been decreased by 13.1 ∘ . As shown in Fig 15(a) and 15(b),
The simulated results, which are depicted in Fig 16, illustrate that the energy concentrates in a certain direction that corresponds to the focal point or peak. At this focal point, when energy intensity is at its peak, the lens has successfully focused and converged energy. In addition, the graph shows the existence of side lobes, which are smaller peaks or secondary maxima seen at angles distant from the focal point. The lens has concentrated some energy in the side lobes, although it was less intense than it was in the focal center. Side lobes may be the consequence of diffraction or flaws in the lens’s construction.
An anechoic chamber has been utilized to verify the directivity measurement result. The proposed hardware has been placed in the chamber and used a range of 10 GHz to 12 GHz signal by a vector network analyzer. A comparison of the measured response change in directivity with and without the lens has been shown in Fig 17(a), 17(b) and 17(c).
According to 17(a), 17(b), and 17(c), there is a high-intensity focal point or peak as a result of the lens’s effective convergence of the horn antenna energy in a particular direction. As the angular location travels away from the focal point, the energy constricts in this direction as the intensity weakens. The graphs also appear to reveal a primary lobe that is rather narrow and exhibits a marked decrease in energy intensity when the angle is moved away from the focal point. This indicates that the lens has successfully focused and concentrated the energy, resulting in narrow beam width and great directivity.
In Fig 18, the integrated results of the far-field directivity (phi = 90 ∘ ) have been shown, and the significant change in directivity and beam-width with and without lens can be observed. it appears that the inclusion of a lens has caused a significant change in the directivity and beamwidth of the antenna in the (phi = 90 ∘ ) plane.
4 Conclusion
It is not uncommon for the inclusion of a lens to significantly alter the directivity and beamwidth of an antenna, as lenses can be used to focus or defocus the radiated energy in different directions. The specific impact on the directivity and beamwidth will depend on the design and properties of the lens, the antenna, and the operating frequency of the system. The present works have succeeded in designing the dielectric lens antenna
The results of this study demonstrate the usefulness of the truncated directed lens antenna for X-band and Ku-band applications. The design strategy and analytical methods used in this study enhance antenna technology in these frequency bands. The antenna displayed better directivity, allowing it to concentrate and focus the energy radiated in a particular direction, hence boosting signal intensity and coverage in the intended locations. The smaller beamwidth also assured improved spatial resolution and reduced interference from nearby sources. As summarized in Table 3, this lens design achieves superior performance with a simplified structure, wide bandwidth, and enhanced gain, suitable for compact and efficient communication systems.
Acknowledgments
I would like to express my special thanks of gratitude to my supervisor Dr Kamran Ahsan as well as all authors who gave me the golden opportunity to do this wonderful project on the topic “Optimal Dimensions and Performance Evaluation of a Truncated Spherical Dielectric Lens Antenna at X-Band Frequencies,” which also helped me in doing a lot of Research and I came to know about so many new things. I am really thankful to them. Secondly, I would also like to thank my parents and friends who helped me a lot in finalizing this project within the limited time frame.
References
- 1. Datta S, Tamburrino A, Udpa L. Gradient index metasurface lens for microwave imaging. Sensors. 2022:22(21);8319.
- 2. Kadera P, Sanchez-Pastor J, Eskandari H, Tyc T, Sakaki M, Schüßler M, et al. Wide-angle ceramic retroreflective luneburg lens based on quasi-conformal transformation optics for mm-wave indoor localization. IEEE Access. 2022;10:41097–111.
- 3. Milligan TA. Modern antenna design. McGraw-Hill; 1985.
- 4. Zetterstrom O, Fonseca NJG, Quevedo-Teruel O. Compact half-luneburg lens antenna based on a glide-symmetric dielectric structure. IEEE Antennas Wirel Propagat Lett 2022;21(11):2283–7.
- 5. Xue C, Lou Q, Chen ZN. Broadband double-layered huygens’ metasurface lens antenna for 5G millimeter-wave systems. IEEE Trans Antennas Propagat 2019;68(3):1468–76.
- 6. Golovachev Y, Etinger A, Pinhasi GA, Pinhasi Y. Propagation properties of sub-millimeter waves in foggy conditions. J Appl Phys. 2019:125(15);151612.
- 7. dos Santos RA, Lobao da Silva Fre G, da Silva LG, Paiva MC, Spadoti DH. Ultra-wideband dielectric lens antennas for beamsteering systems. Int J Antennas Propagat. 2019;2019.
- 8. Thornton J, Huang K. Modern lens antennas for communications engineering. Wiley; 2013.
- 9. Saleem MK, Xie M, Alkanhal MAS, Saadi M. Effect of dielectric materials on integrated lens antenna for millimeter wave applications. Microwave Optic Technol Lett. 2019;61(4):1079–83.
- 10. Shila KA, Mumcu G. A millimeter-wave 2D beam steering antenna using extended hemispherical dielectric lens antenna subarrays. IEEE Access. 2022;10:103065–73.
- 11. Ding Y, Zou Z, Luo Y, Yang G. A lens antenna with reconfigurable beams for mmWave wind profile radar. Sensors. 2022:22(9);3148.
- 12. Imeci ST, Tütüncü B, Herceg L. Performance-enhanced S-shaped slotted patch antenna for X band/Ku band applications. Wirel Personal Commun. 2023;129(2):1069–82.
- 13.
Tütücü B. Microstrip antenna for 5G communication: design and performance analysis. In: 2020 International Congress on Human-Computer Interaction, Optimization and Robotic Applications (HORA). IEEE; 2020.
- 14. Tütücü B, Torpi H, I˙meci ST. Directivity improvement of microstrip antenna by inverse refraction metamaterial. J Eng Res. 2019;7(4).
- 15. Pendry JB, Holden AJ, Robbins DJ, Stewart WJ. Magnetism from conductors and enhanced nonlinear phenomena. IEEE Trans Microw Theory Techniq 1999;47(11):2075–84.
- 16. Smith DR, Padilla WJ, Vier DC, Nemat-Nasser SC, Schultz S. Composite medium with simultaneously negative permeability and permittivity. Phys Rev Lett. 2000;84(18):4184–7 doi: https://doi.org/10.1103/PhysRevLett.84.4184 PMID: 10990641
- 17. Liu J, Cheng Y, Nie Y, Gong R. Metamaterial extends microstrip antenna. Microwaves RF. 2013:52(12);69.
- 18. Pors A, Nielsen MG, Eriksen RL, Bozhevolnyi SI. Broadband focusing flat mirrors based on plasmonic gradient metasurfaces. Nano Lett 2013;13(2):829–34.
- 19. Xu HX, Tang S, Wang GM, Cai T, Huang W, He Q, et al. Multifunctional microstrip array combining a linear polarizer and focusing metasurface. IEEE Trans Antennas Propagat 2016;64(8):3676–82.
- 20. Li X, Xiao S, Cai B, He Q, Cui TJ, Zhou L. Flat metasurfaces to focus electromagnetic waves in reflection geometry. Optics Lett 2012;37(23):4940–2.
- 21. Aieta F, Genevet P, Kats MA, Yu N, Blanchard R, Gaburro Z, et al. Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces. Nano Letters 2012;12(9):4932–6.
- 22. Li H, Wang G, Liang J, Gao X, Hou H, Jia X. Single-layer focusing gradient metasurface for ultrathin planar lens antenna application. IEEE Trans Antennas Propagat 2016;65(3):1452–7.
- 23. Wu C, Cheng Y, Wang W, He B, Gong R. Ultra-thin and polarization-independent phase gradient metasurface for high-efficiency spoof surface-plasmon-polariton coupling. Appl Phys Exp. 2015:8(12);122001.
- 24. Yang Y, Wang W, Moitra P, Kravchenko II, Briggs DP, Valentine J. Dielectric meta-reflectarray for broadband linear polarization conversion and optical vortex generation. Nano Lett 2014;14(3):1394–9.
- 25. Chen J, Cheng Q, Zhao J, Dong D, Cui TJ. Reduction of radar cross section based on a metasurface. Prog Electromagnet Res. 2014;146:71–6.
- 26. Zhang K, Ding X, Wo D, Meng F, Wu Q. Experimental validation of ultra-thin metalenses for N-beam emissions based on transformation optics. Appl Phys Lett. 2016:108(5);053508.
- 27. Chen Y, et al. PTFE lenses for antenna directivity enhancement in high-frequency applications. IEEE Trans Antennas Propagat. 2020;68(5):3523–31.
- 28. Zhao X, et al. Environmental stability of PTFE in antenna applications: a review. Mater Sci Eng: B. 2021;271:115458.
- 29. Zhang L, et al. Design and application of flexible antennas using PTFE. Int J Antennas Propagat. 2022;2022:8361205.
- 30. Guan W, et al. Comparative analysis of PTFE and acrylic lenses in antenna systems. Prog Electromagnet Res. 2023;173:57–68.
- 31. Moderate W. Cylindrical dielectric lens with graded refractive index for wideband applications. Wideband Appl J. 2024;22:12–21.
- 32. High X. Dual-layer metasurface lens with a tunable focal point. X-band Appl. 2023;21(5):14.0–20.8.
- 33. Moderate X. Hemispherical dielectric lens optimized for X-band frequencies. X-band Appl. 2023;20(8):14.2–20.4.
- 34. Low X. Flat dielectric lens using hybrid materials for compact integration. X-band Appl. 2022;19(8):15.5–19.2.