Conformal transformation optics is employed to enhance an H-plane horn's directivity by designing a graded-index all-dielectric lens. The transformation is applied so that the phase error at the aperture is gradually eliminated inside the lens, leading to a low-profile high-gain lens antenna. The physical space shape is modified such that singular index values are avoided, and the optical path inside the lens is rescaled to eliminate superluminal regions. A prototype of the lens is fabricated using three-dimensional printing. The measurement results show that the realized gain of an H-plane horn antenna can be improved by 1.5-2.4 dB compared to a reference H-plane horn.

Department of Electrical Engineering Ferdowsi University of Mashhad Mashhad Iran

Department of Theoretical Physics and Astrophysics Faculty of Science Masaryk University Kotlár̆ská 2 61137 Brno Czechia

Division of Electromagnetic Engineering KTH Royal Institute of Technology Stockholm Sweden

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Pendry JB. Controlling electromagnetic fields. Science. 2006;312:1780–1782. doi: 10.1126/science.1125907. PubMed DOI

Leonhardt U. Optical conformal mapping. Science. 2006;312:1777–1780. doi: 10.1126/science.1126493. PubMed DOI

Li J, Pendry JB. Hiding under the carpet: A new strategy for cloaking. Physical Review Letters. 2008;101:203901. doi: 10.1103/physrevlett.101.203901. PubMed DOI

Chang Z, Zhou X, Hu J, Hu G. Design method for quasi-isotropic transformation materials based on inverse Laplace’s equation with sliding boundaries. Optics Express. 2010;18:6089–6096. doi: 10.1364/oe.18.006089. PubMed DOI

Ma HF, Cui TJ. Three-dimensional broadband ground-plane cloak made of metamaterials. Nature Communications. 2010;1:21. doi: 10.1038/ncomms1023. PubMed DOI PMC

Kwon D-H, Werner DH. Polarization splitter and polarization rotator designs based on transformation optics. Optics Express. 2008;16:18731–18738. doi: 10.1364/oe.16.018731. PubMed DOI

Eskandari H, Majedi MS, Attari AR. Design of reflectionless non-magnetic homogeneous polarization splitters with minimum anisotropy based on transformation electromagnetics. Journal of the Optical Society of America B. 2017;34:1191–1198. doi: 10.1364/josab.34.001191. DOI

Mousavi SSS, Majedi MS, Eskandari H. Design and simulation of polarization transformers using transformation electromagnetics. Optik. 2017;130:1099–1106. doi: 10.1016/j.ijleo.2016.11.129. DOI

Eskandari H, Majedi MS, Attari AR. Non-reflecting non-magnetic homogeneous polarization splitter and polarization deflector design based on transformation electromagnetics. Optik. 2017;135:407–416. doi: 10.1016/j.ijleo.2017.01.080. DOI

Eskandari H, Attari AR, Majedi MS. Design of polarization splitting devices with ideal transmission and anisotropy considerations. Journal of the Optical Society of America B. 2018;35:1585–1595. doi: 10.1364/josab.35.001585. DOI

Landy NI, Padilla WJ. Guiding light with conformal transformations. Optics Express. 2009;17:14872–14879. doi: 10.1364/oe.17.014872. PubMed DOI

García-Meca C, et al. Squeezing and expanding light without reflections via transformation optics. Optics Express. 2011;19:3562–3575. doi: 10.1364/oe.19.003562. PubMed DOI

Eskandari H, Majedi MS, Attari AR. Reflectionless compact nonmagnetic optical waveguide coupler design based on transformation optics. Applied Optics. 2017;56:5599–5606. doi: 10.1364/ao.56.005599. PubMed DOI

Eskandari H, Attari AR, Majedi MS. Reflectionless design of a nonmagnetic homogeneous optical waveguide coupler based on transformation optics. Journal of the Optical Society of America B. 2017;35:54–60. doi: 10.1364/josab.35.000054. PubMed DOI

Eskandari H, Quevedo-Teruel O, Attari AR, Majedi MS. Transformation optics for perfect two-dimensional non-magnetic all-mode waveguide couplers. Optical Materials Express. 2019;9:1320–1332. doi: 10.1364/ome.9.001320. DOI

Eskandari, H., Quevedo-Teruel, O., Attari, A. R. & Majedi, M. S. Design of nonmagnetic all-mode waveguide coupler with perfect transmission using transformation optics. In 2019 13th European Conference on Antennas and Propagation (EuCAP), 1–4 (2019).

Eskandari, H., Attari, A. R., Majedi, M. S. & Tyc, T. Waveguide tapering using conformal transformation optics for ideal transmission. In 2019 Thirteenth International Congress on Artificial Materials for Novel Wave Phenomena (Metamaterials), X–116–X–118. 10.1109/MetaMaterials.2019.8900947 (2019).

Quevedo-Teruel, O. et al. Transformation optics for antennas: why limit the bandwidth with metamaterials?. Sci. Rep.3, 10.1038/srep01903 (2013). PubMed PMC

Eskandari H, Majedi MS, Attari AR, Quevedo-Teruel O. Elliptical generalized Maxwell fish-eye lens using conformal mapping. New Journal of Physics. 2019;21:063010. doi: 10.1088/1367-2630/ab2471. DOI

Ebrahimpouri M, Quevedo-Teruel O. Ultrawideband anisotropic glide-symmetric metasurfaces. IEEE Antennas and Wireless Propagation Letters. 2019;18:1547–1551. doi: 10.1109/lawp.2019.2922238. DOI

Chen Q, Giusti F, Valerio G, Mesa F, Quevedo-Teruel O. Anisotropic glide-symmetric substrate-integrated-holey metasurface for a compressed ultrawideband Luneburg lens. Applied Physics Letters. 2021;118:084102. doi: 10.1063/5.0041586. DOI

Hunt J, et al. Planar, flattened luneburg lens at infrared wavelengths. Optics Express. 2012;20:1706–1713. doi: 10.1364/oe.20.001706. PubMed DOI

Driscoll T, et al. Performance of a three dimensional transformation-optical-flattened lüneburg lens. Optics Express. 2012;20:13262–13273. doi: 10.1364/oe.20.013262. PubMed DOI

Zhou F, et al. Additive manufacturing of a 3D terahertz gradient-refractive index lens. Advanced Optical Materials. 2016;4:1034–1040. doi: 10.1002/adom.201600033. DOI

Yao K, Jiang X. Designing feasible optical devices via conformal mapping. Journal of the Optical Society of America B. 2011;28:1037–1042. doi: 10.1364/josab.28.001037. DOI

Schmiele M, Varma VS, Rockstuhl C, Lederer F. Designing optical elements from isotropic materials by using transformation optics. Physical Review A. 2010;81:033837. doi: 10.1103/physreva.81.033837. DOI

Aghanejad I, Abiri H, Yahaghi A. Design of high-gain lens antenna by gradient-index metamaterials using transformation optics. IEEE Transactions on Antennas and Propagation. 2012;60:4074–4081. doi: 10.1109/tap.2012.2207051. DOI

Ebrahimpouri M, Quevedo-Teruel O. Bespoke lenses based on quasi-conformal transformation optics technique. IEEE Transactions on Antennas and Propagation. 2017;65:2256–2264. doi: 10.1109/tap.2017.2679494. DOI

Ding T, Yi J, Li H, Zhang H, Burokur SN. 3D field-shaping lens using all-dielectric gradient refractive index materials. Scientific Reports. 2017;7:782. doi: 10.1038/s41598-017-00681-z. PubMed DOI PMC

Ebrahimpouri M, Zetterstrom O, Quevedo-Teruel O. Experimental validation of a bespoke lens for a slot log-spiral feed. IEEE Antennas and Wireless Propagation Letters. 2020;19:557–560. doi: 10.1109/LAWP.2020.2971852. DOI

Eskandari, H., Saviz, S. & Tyc, T. Directivity enhancement of a cylindrical wire antenna by a graded index dielectric shell designed using strictly conformal transformation optics. Sci. Rep.11, 10.1038/s41598-021-92200-4 (2021). PubMed PMC

Xu, Y., Fu, Y. & Chen, H. Planar gradient metamaterials. Nat. Rev. Mater. 1, 10.1038/natrevmats.2016.67 (2016).

Wang, H., Xu, Y., Genevet, P., Jiang, J.-H. & Chen, H. Broadband mode conversion via gradient index metamaterials. Sci. Rep.6, 10.1038/srep24529 (2016). PubMed PMC

Fu, Y., Xu, Y. & Chen, H. Applications of gradient index metamaterials in waveguides. Sci. Rep.5, 10.1038/srep18223 (2015). PubMed PMC

Gu, C. et al. A broadband polarization-insensitive cloak based on mode conversion. Sci. Rep.5, 10.1038/srep12106 (2015). PubMed PMC

Fu Y, et al. Compact acoustic retroreflector based on a mirrored luneburg lens. Physical Review Materials. 2018;2:105202. doi: 10.1103/physrevmaterials.2.105202. DOI

Xu, Y., Li, S., Hou, B. & Chen, H. Fano resonances from gradient-index metamaterials. Sci. Rep.6, 10.1038/srep19927 (2016). PubMed PMC

Clarricoats, P. J. B. & Olver, A. D. Corrugated Horns for Microwave Antennas. (IET, 1984).

Olver, A. D., Clarricoats, P., Shafai, L. & Kishk, A. Microwave Horns and Feeds. (IET, 1994).

Lier E. Hard waveguide feeds with circular symmetry for aperture efficiency enhancement. Electronics Letters. 1988;24:166–167. doi: 10.1049/el:19880110. DOI

Bhattacharyya A, Goyette G. Step-horn antenna with high aperture efficiency and low cross-polarisation. Electronics Letters. 2002;38:1495–1496. doi: 10.1049/el:20021081. DOI

Lier, E. & Matthews, J. Performance comparison of high-gain horn antennas. In 2005 IEEE Antennas and Propagation Society International Symposium, 3, 753–756. 10.1109/aps.2005.1552365 (IEEE, 2005).

Morgan KL, Brocker DE, Campbell SD, Werner DH, Werner PL. Transformation-optics-inspired anti-reflective coating design for gradient index lenses. Optics Letters. 2015;40:2521–2524. doi: 10.1364/ol.40.002521. PubMed DOI

Eskandari, H. & Tyc, T. Controlling refractive index of transformation-optics devices via optical path rescaling. Sci. Rep.9, 10.1038/s41598-019-54516-0 (2019). PubMed PMC

Papamichael, N. & Stylianopoulos, N. Numerical Conformal Mapping: Domain Decomposition and the Mapping of Quadrilaterals, chap. 2, 51–63 (World Scientific Pub Co Inc, 2010).

Rahm M, Cummer SA, Schurig D, Pendry JB, Smith DR. Optical design of reflectionless complex media by finite embedded coordinate transformations. Physical Review Letters. 2008;100:063903. doi: 10.1103/physrevlett.100.063903. PubMed DOI

Urzhumov YA, Kundtz NB, Smith DR, Pendry JB. Cross-section comparisons of cloaks designed by transformation optical and optical conformal mapping approaches. Journal of Optics. 2010;13:0242002. doi: 10.1088/2040-8978/13/2/024002. DOI

Shilov, G. E., Silverman, R. A. et al.Elementary Real and Complex Analysis (Courier Corporation, 1996).

Balanis, C. A. Antenna Theory: Analysis and Design (Wiley, 2016).

Ebrahimpouri M, Rajo-Iglesias E, Sipus Z, Quevedo-Teruel O. Cost-effective gap waveguide technology based on glide-symmetric holey EBG structures. IEEE Transactions on Microwave Theory and Techniques. 2018;66:927–934. doi: 10.1109/tmtt.2017.2764091. DOI

Ebrahimpouri, M., Algaba Brazalez, A., Manholm, L. & Quevedo-Teruel, O. Using glide-symmetric holes to reduce leakage between waveguide flanges. IEEE Microw. Wirel. Components Lett.28, 473–475. 10.1109/LMWC.2018.2824563 (2018).

Quevedo-Teruel O, et al. Glide-symmetric fully metallic luneburg lens for 5g communications at ka-band. IEEE Antennas and Wireless Propagation Letters. 2018;17:1588–1592. doi: 10.1109/LAWP.2018.2856371. DOI

Zetterstrom O, Hamarneh R, Quevedo-Teruel O. Experimental validation of a metasurface luneburg lens antenna implemented with glide-symmetric substrate-integrated holes. IEEE Antennas and Wireless Propagation Letters. 2021;20:698–702. doi: 10.1109/lawp.2021.3060283. DOI

Bjorkqvist O, Zetterstrom O, Quevedo-Teruel O. Additive manufactured dielectric gutman lens. Electronics Letters. 2019;55:1318–1320. doi: 10.1049/el.2019.2483. DOI