• Journal of electromagnetic engineering and science
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• v.1 no.1
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• pp.11-17
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• 2001

In this paper, spherical Luneburg lens antennas have been systematically analyzed using the Eigenfunction Expansion Method (EEM), The developed technique has capability of performing a complete 3-D analysis to characterize the multi-layered dielectric spherical lens with arbitrary permittivity and permeability. This paper describes the analysis technique, and presents the results of the parametric study of Luneburg lens antennas by varying design parameters suoh as the diameter of the lens antenna (up to 80 wavelength), number of spherical shells (up to 30 shells), air-gaps between spherical shells, and dielectric loss of the material. Many representative engineering design curves including the far-field patterns, wide-angle sidelobe characterizations, antenna efficiency have been presented.

• Current Optics and Photonics
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• v.4 no.4
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• pp.326-329
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• 2020

The Eaton lens, with spherical symmetry to its refractive index, was described by Eaton in 1952 and was found recently in the design of an invisible sphere for cloaking. In this paper, an Eaton lens for rotating 90° was designed using Luneburg theory, by which we found it was a fourth-order equation in the refractive index n. Therefore, the refractive index n has four roots. The equation in n was solved and studied using mathematical technology. The unsuitable complex roots of the equation should be dropped; consequently, only one of the four roots remained. To verify the refractive-index profile, the only root was solved for, before a simulation using finite-element analysis (FEA) was performed. The simulation showed that all rays will bend 90° to the right. The result of the simulation is identical to our expectation. This treatment provides a possible method for rotating light at many other angles.