Current Optics and Photonics

Optical Society of Korea (한국광학회)
권호 표지
DOI QR코드

DOI QR Code

Analytic Solution for an Eaton Lens for Rotating 90°

  • Zhao, Cun-Hua (College of Physics and Electronic Information, Luoyang Normal University)
  • Received : 2020.04.24
  • Accepted : 2020.06.17
  • Published : 2020.08.25
Download PDF
⟨ Previous Next ⟩

Abstract

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.

Keywords

References

  1. J. C. Maxwell, "Solution of problems," Cambridge and Dublin Math. J. 8, 188 (1854).
  2. R. K. Luneburg, Mathematical Theory of Optics (University of California Press, CA, USA, 1964).
  3. J. E. Eaton, "On spherically symmetric lenses," IEEE Trans. IRE Prof. Group. Antennas Propag. PGAP-4, 66-71 (1952). https://doi.org/10.1109/TPGAP.1952.237341
  4. U. Leonhardt and T. Philbin, Geometry and light: the Science of invisibility (Dover Publications, NY, USA, 2010).
  5. J. C. Minano, "Perfect imaging in a homogeneous threedimensional region," Opt. Express 14, 9627-9635 (2006). https://doi.org/10.1364/OE.14.009627
  6. S.-H. Kim, "Retroreflector approximation of a generalized Eaton lens," J. Mod. Opt. 59, 839-842 (2012). https://doi.org/10.1080/09500340.2012.675089
  7. D. Lee, C. Cho, J. Mun, N. Park, and J. Rho, "Demonstration of steering acoustic waves by generalized Eaton lens," Appl. Phys. Lett. 113, 161904 (2018). https://doi.org/10.1063/1.5051439
  8. J. Y. Li and M. N. M. Kehn, "The 90$^{\circ}$ rotating Eaton lens synthesized by metasurfaces," IEEE Antennas Wirel. Propag. Lett. 17, 1247-1251 (2018). https://doi.org/10.1109/LAWP.2018.2841187
  9. T. Zentgraf, Y. Liu, M. H. Mikkelsen, J. Valentine, and X. Zhang, "Plasmonic Luneburg and Eaton lenses," Nat. Nanotechnol. 6, 151-155 (2011). https://doi.org/10.1038/nnano.2010.282
  10. C. H. Zhao and C. L. Ding, Applied Optics (Publishing House of Electronics Industry, Beijing, China, 2017).