An Empirical Loss Model for an Additively Manufactured Luneburg Lens Antenna

Authors

  • Brian F. LaRocca Department of the Army Aberdeen Proving Ground, Aberdeen, MD 21005, USA
  • Mark S. Mirotznik Electrical Engineering Department University of Delaware, Newark, DE 19716, USA

DOI:

https://doi.org/10.13052/2022.ACES.J.370505

Keywords:

Additive Manufacturing, Dielectric Loss, Effective Medium Theory, Lens Antenna, Luneburg Lens

Abstract

This research applies Effective Medium Theory and 3D Finite Element Analysis to model the transmissive loss through a waveguide fed additively manufactured Luneburg lens. New results are presented that provide rational function approximations for accurately modeling the aperture, beam, and radiation loss factors of the antenna. It introduces a normalized loss tangent and shows that the loss factors are dependent on the product of this parameter and the lens radius. Applying the constraint that the main beam of the radiation pattern contains 50% of accepted power, a maximum useful radius is tabulated for common polymers used in additive manufacturing.

Downloads

Download data is not yet available.

Author Biography

Brian F. LaRocca, Department of the Army Aberdeen Proving Ground, Aberdeen, MD 21005, USA

Brian F. LaRocca received the B.S.E.E and M.S.E.E degrees from New Jersey Institute of Technology, Newark, NJ, USA in 1985 and 2000 respectively. From 1985 to 1996 he worked in industry, 1996 to 2004 as a government contractor, and 2004 to present as a civilian engineer with the Dept. of the Army at Ft. Monmouth, NJ, USA and Aberdeen Proving Ground, MD, USA. He received the Ph.D. degree in electrical engineering from the University of Delaware, Newark, DE, USA in the summer of 2022.Mark S. Mirotznik image38(S’87–M’92–SM’11) received the B.S.E.E. degree from Bradley University, Peoria, IL, USA, in 1988, and the M.S.E.E. and the Ph.D. degrees from the University of Pennsylvania, Philadelphia, PA, USA, in 1991 and 1992, respectively. From 1992 to 2009, he was a Faculty Member with the Department of Electrical Engineering, The Catholic University of America, Washington, DC, USA. Since 2009, he has been a Professor and an Associate Chair for Undergraduate Programs with the Department of Electrical and Computer Engineering, University of Delaware, Newark, DE, USA. He holds the position of Senior Research Engineer with the Naval Surface Warfare Center, Carderock Division. His current research interests include applied electromagnetics and photonics, computational electromagnetics, multifunctional engineered materials, and additive manufacturing.

References

R. K. Luneburg, Mathematical Theory of Optics. Brown University Press, Providence, RI, USA, 1944.

P. S. Hall and S. J. Vetterlein, “Review of radio frequency beamforming techniques for scanned and multiple beam antennas,” IEEE Proc. Microwaves, Antennas Propag., vol. 137, no. 5, pp. 293-303, 1990.

Y. Li, Lei G. M. Chen, Z. Zhang, Z. Li, and J. Wang, “Multibeam 3-D-printed Luneburg lens fed by magnetoelectric dipole antennas for millimeter-wave MIMO applications,” IEEE Trans. Antennas Propag., vol. 67, no. 5, pp. 2923-2933,May 2019.

J. Deroba, A. Good, K. Sobczak, Z. Larimore, and M. S. Mirotznik, “Additively manufactured Luneburg retroreflector,” IEEE Trans. Aerospace Electronic Syst., Sep. 2019.

M. Liang, W.-R. Ng, K. Chang, K. Gbele, M. E. Gehm, and H. Xin, “A 3-D Luneburg lens antenna fabricated by polymer jetting rapid prototyping,” IEEE Trans. Antennas Propag., vol. 62, no. 4, pp. 1799-1807, 2014.

Z. Larimore, S. Jensen, P. Parsons, B. Good, K. Smith, and M. S. Mirotznik, “Use of space-filling curves for additive manufacturing of three dimensionally varying graded dielectric structures using fused deposition modeling,” Additive Manuf., vol. 15, pp. 48-56, 2017.

Z. Larimore, S. Jensen, A. Good, J. Suarez, and M. S. Mirotznik, “Additive manufacturing of Luneburg lens antennas using space-filling curves and fused filament fabrication,” IEEE Trans. Antennas Propag., vol. 66, no. 6, pp. 2818-2827,2018.

S. Biswas, A. Lu, Z. Larimore, P. Parsons, A. Good, N. Hudak, B. Garrett, J. Suarez, and M. S. Mirotznik, “Realization of modified Luneburg lens antenna using quasi-conformal transformation optics and additive manufacturing,” Microwave Optical Technol. Lett., vol. 61, no. 4, pp. 1022-1029, 2019.

S. Biswas and M. S. Mirotznik, “High gain, wide-angle QCTO-enabled modified Luneburg lens antenna with broadband anti-reflective layer,” Nature: Sci. Rep., vol. 10, no. 1, pp. 1-13, 2020.

O. Bjorkqvist, O. Zetterstron, and O. Quevedo-Teruel, “Additive manufactured dielectric Gutman lens,” Electronic Lett., vol. 55, no. 25, pp. 1318-1320, 2019.

J. Poyanco, F. Pizarro, and E. Rajo-Iglesias, “3D-printing for transformation optics in electromagnetic high-frequency lens applications,” Materials, vol. 13, pp. 1-11, 2020.

P. Liu, X. Zhu, Y. Zhang, J. Li, and Z. Jiang, “3D-printed cylindrical Luneburg lens antenna for millimeter wave applications,” Int. J. RF Microwave Comput.-Aided Eng., vol. 30, pp. 1-8, 2019.

C. Wang, J. Wu, and Y. Guo, “A 3-D printed multibeam dual circularly polarized Luneburg lens antenna based on quasi-icosahedron models for Ka-band wireless applications,” IEEE Trans. Antennas Propag., vol. 68, no. 8, pp. 5807-5815, 2020.

K. Hoel, S. Kristoffersen, M. Ignatenko, and D. Filipovic, “Half ellipsoid Luneburg GRIN dielectric lens loaded double ridged horn antenna,” in Proc. IET 12th Eur. Conf. Antennas Propag., London, UK, 2018.

P. I. Deffenbaugh, R. C. Rumpf, and K. H. Church, “Broadband microwave frequency characterization of 3-D printed materials,” IEEE Trans. Compon. Packaging Manuf. Technol., vol. 3, no. 12, pp. 2147-2155, 2013.

J. Monkevich and G. Le Sage, “Design and fabrication of a custom-dielectric Fresnel multi-zone plate lens antenna using additive manufacturing techniques,” IEEE Access, vol. 7, 2019.

J. Zechmeister and J. Lacik, “Complex relative permittivity measurement of selected 3D-printed materials up to 10 GHz,” in Proc. IEEE Conf. Microwave Techn., Pardubice, Czech Republic, 2019.

Y. Li and Q. Zhu, “Luneburg lens with extended flat focal surface for electronic scan applications,” Optics Express, vol. 24, no. 7, 2016.

J. Krupka, “Measurements of the complex permittivity of low loss polymers at frequency range from 5 GHz to 50 GHz,” IEEE Microwave Wireless Compon. Lett., vol. 26, no. 6, pp. 464-466, 2016.

J. K, Pakkathillam, B. T. Sivaprakasam, J. Poojali, C. V. Krishnamurthy, and K. Arunachalam, “Tailoring antenna focal plane characteristics for a compact free-space microwave complex dielectric permittivity measurement setup,” IEEE Trans. Instrum. Meas., vol. 70, 2021.

A. Sihvola, Electromagnetic Mixing Formulas and Applications. London, U.K.: The Institution of Engineering and Technology, 2008.

R. C. Johnson, Antenna Engineering Handbook. McGraw-Hill, New York, NY, USA, 1993.

COMSOL Multiphysics§v. 5.6. Stockholm, Sweden: COMSOL AB. Available: www.comsol.com.

MATLAB, ver. 2021a. Natick, MA, USA: The Mathworks Inc., 2021.

E. Burden, Y. Oh, B. Mummareddy, D. Negro, P. Cortes, A. Du Plessis, E. MacDonald, J. Adams, F. Li, and R. Rojas, “Unit cell estimation of volumetrically-varying permittivity in additively manufactured ceramic lattices with X-ray computed tomography,” Mater. Des., vol. 210, Nov. 15, 2021.

G. Guo, Y. Xia, C. Wang, M. Nasir, and Q. Zhu, “Optimal radiation pattern of feed of Luneburg lens for high-gain application,” IEEE Trans. Antennas Propag., vol. 68, no. 12, pp. 8139-8143, Dec. 2020.

C. A. Balanis, Antenna Theory - Analysis and Design. Hoboken, NJ, USA: John Wiley & Sons Inc., 2005.

M. Dourado, J. Meireles, and A. Rocha, “A global optimization approach applied to structural dynamic updating,” in Proc. 14th Int. Conf. Comput. Sci. Its Appl. (ICCSA), vol. 8580, pp. 195-210, 2014.

Downloads

Published

2022-05-31

How to Cite

[1]
B. F. . LaRocca and M. S. . Mirotznik, “An Empirical Loss Model for an Additively Manufactured Luneburg Lens Antenna”, ACES Journal, vol. 37, no. 05, pp. 554–567, May 2022.

Issue

2022: Vol 37 Iss 5

Section

General Submission

Categories