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Reflecting Luneburg Lenses

Abstract : This paper presents the exact closed-form solution for a new planar lens, hereinafter referred to as Reflecting Luneburg Lens (RLL). The proposed structure consists of two stacked parallel plate waveguides of circular shape. The rays generated by a point source located at the periphery of the bottom waveguide propagate along curvilinear paths, whose trajectories result from a variable refractive index profile with azimuthal symmetry. Then, these rays encounter a reflecting boundary and emerge all parallel in the upper uniform waveguide. The behavior of this lens resembles that of a flat Luneburg lens, with the fundamental difference that it works in reflection. The exact refractive index profile is found by solving the non-linear integral equation of ray-congruence trough a truncated Abel transform method. The concept is numerically verified through different implementations of the effective refractive index profile, including a metasurface-based implementation. The proposed lens triggers new possibilities that the normal flat Luneburg lens does not offer, and it is applicable in a large variety of microwave, terahertz and optical devices.
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https://hal-univ-rennes1.archives-ouvertes.fr/hal-03137418
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Submitted on : Wednesday, February 10, 2021 - 5:08:20 PM
Last modification on : Friday, October 22, 2021 - 3:04:11 AM
Long-term archiving on: : Tuesday, May 11, 2021 - 8:58:11 PM

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Jorge Ruiz-Garcia, Enrica Martini, Cristian Della Giovampaola, David González-Ovejero, Stefano Maci. Reflecting Luneburg Lenses. IEEE Transactions on Antennas and Propagation, Institute of Electrical and Electronics Engineers, 2020, pp.1-1. ⟨10.1109/TAP.2020.3044668⟩. ⟨hal-03137418⟩

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