## Two-dimensional inside-out Eaton Lens: Design technique and TM-polarized wave properties |

Optics Express, Vol. 20, Issue 3, pp. 2335-2345 (2012)

http://dx.doi.org/10.1364/OE.20.002335

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### Abstract

In this paper we perform a theoretical and numerical study of two-dimensional inside-out Eaton lenses under transverse-magnetic-polarized excitation. We present one example design and test its performance by utilizing full-wave Maxwell solvers. With the help of the WKB approximation, we further investigate the finite-wavelength effect analytically and demonstrate one necessary condition for perfect imaging at the level of wave optics, i.e. imaging with unlimited resolution, by the lens.

© 2012 OSA

**OCIS Codes**

(000.3860) General : Mathematical methods in physics

(250.5403) Optoelectronics : Plasmonics

**ToC Category:**

Physical Optics

**History**

Original Manuscript: November 9, 2011

Revised Manuscript: December 5, 2011

Manuscript Accepted: January 3, 2012

Published: January 18, 2012

**Citation**

Yong Zeng and Douglas H. Werner, "Two-dimensional inside-out Eaton Lens: Design technique and TM-polarized wave properties," Opt. Express **20**, 2335-2345 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-3-2335

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### References

- C. Gomez-Reino, M. V. Perez, and C. Bao, Gradient-Index Optics: Fundamentals and Applications (Springer, 2002).
- J. C. Maxwell, “Solutions of problems,” Camb. Dublin Math. J.8, 188 (1854).
- R. K. Luneburg, Mathematical Theory of Optics (University of California Press, 1964).
- J. E. Eaton, “On spherically symmetric lenses,” Trans. IRE Antennas Propag.4, 66–71 (1952).
- U. Leonhardt and T. G. Philbin, “Transformation optics and the geometry of light,” Prog. Opt.53, 69–152 (2009).
- U. Leonhardt and T. G. Philbin, Geometry and Light: The Science of Invisibility (Dover Publications, 2010).
- J. C. Miñano, “Perfect imaging in a homogeneous three-dimensional region,” Opt. Express14, 9627–9635 (2006). [PubMed]
- Y. G. Ma, C. K. Ong, T. Tyc, and U. Leonhardt, “An omnidirectional retroreflector based on the transmutation of dielectric singularities,” Nat. Materials8, 639–642 (2009).
- N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Materials9, 129–132 (2010).
- V. N. Smolyaninova, I. I. Smolyaninov, A. V. Kildishev, and V. M. Shalaev, “Maxwell fish-eye and Eaton lenses emulated by microdroplets,” Opt. Lett.35, 3396–3398 (2010). [PubMed]
- D. R. Smith, Y. Urzhumov, N. B. Kundtz, and N. I. Landy, “Enhancing imaging systems using transformation optics,” Opt. Express18, 21238–21251 (2010). [PubMed]
- T. Zentgraf, Y. Liu, M. H. Mikkelsen, J. Valentine, and X. Zhang, “Plasmonic Luneburg and Eaton lenses,” Nat. Nanotechnology6, 151–155 (2011).
- U. Leonhardt, “Perfect imaging without negative refraction,” New J. Phys.11, 093040 (2009).
- A. Di Falco, S. C. Kehr, and U. Leonhardt, “Luneburg lens in silicon photonics,” Opt. Express19, 5156–5162 (2011). [PubMed]
- A. Vakil and N. Engheta, “Transformation optics using graphene,” Science332, 1291–1294 (2011). [PubMed]
- A. J. Danner, T. Tyc, and U. Leonhardt, “Controlling birefringence in dielectrics,” Nat. Photonics5, 357–359 (2011).
- J. A. Lock, “Scattering of an electromagnetic plane wave by a Luneburg lens. II. Wave theory,” J. Opt. Soc. Am. A25, 2980–2990 (2008).
- J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett.85, 3966–3969 (2000). [PubMed]
- L. Solymar and E. Shamonina, Waves in Metamaterials (Oxford University, 2009).
- J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312, 1780–1782 (2006). [PubMed]
- U. Leonhardt, “Optical conformal mapping,” Science312, 1777–1780 (2006). [PubMed]
- D.-H. Kwon and D. H. Werner, “Transformation electromagnetics: An overview of the theory and its application,” IEEE Antennas Prop. Mag.52, 24–45 (2010).
- H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Materials9, 387–396 (2010).
- D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett.84, 4184–4187 (2000). [PubMed]
- W. C. Chew, Waves and Fields in Inhomogeneous Media (IEEE Press, 1995).
- J. J. Sakurai, Modern Quantum Mechanics, Revised ed. (Addison-Wesley, 1994).
- J. D. Jackson, Classical Electrodynamics, 3rd ed. (John Wiley & Sons, 2004).
- R. H. Good, “The generalization of the WKB method to radial wave equations,” Phys. Rev.90, 131–137 (1953).
- B. Durand and L. Durand, “Improved WKB radial wave functions in several bases,” Phys. Rev. A33, 2887–2898 (1986). [PubMed]
- R. E. Langer, “On the connection formulas and the solutions of the wave equation,” Phys. Rev.51, 669–676 (1937).
- Y. Zeng, Q. Wu, and D. H. Werner, “Electrostatic theory for designing lossless negative permittivity metamaterials,” Opt. Lett.35, 1431–1433 (2010). [PubMed]
- COMSOL, www.comsol.com .
- C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, 1998).
- Y. Zeng, J. Liu, and D. H. Werner, “General properties of two-dimensional conformal transformations in electrostatics,” Opt. Express19, 20035–20047 (2011). [PubMed]

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