T. Zentgraf, Y. Liu, M. H. Mikkelsen, J. Valentine, and X. Zhang, “Plasmonic Luneburg and Eaton lenses,” Nat. Nanotechnology 6, 151–155 (2011).

A. Di Falco, S. C. Kehr, and U. Leonhardt, “Luneburg lens in silicon photonics,” Opt. Express 19, 5156–5162 (2011).

[PubMed]

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332, 1291–1294 (2011).

[PubMed]

A. J. Danner, T. Tyc, and U. Leonhardt, “Controlling birefringence in dielectrics,” Nat. Photonics 5, 357–359 (2011).

Y. Zeng, J. Liu, and D. H. Werner, “General properties of two-dimensional conformal transformations in electrostatics,” Opt. Express 19, 20035–20047 (2011).

[PubMed]

Y. Zeng, Q. Wu, and D. H. Werner, “Electrostatic theory for designing lossless negative permittivity metamaterials,” Opt. Lett. 35, 1431–1433 (2010).

[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. Materials 9, 387–396 (2010).

N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Materials 9, 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. Express 18, 21238–21251 (2010).

[PubMed]

U. Leonhardt, “Perfect imaging without negative refraction,” New J. Phys. 11, 093040 (2009).

U. Leonhardt and T. G. Philbin, “Transformation optics and the geometry of light,” Prog. Opt. 53, 69–152 (2009).

Y. G. Ma, C. K. Ong, T. Tyc, and U. Leonhardt, “An omnidirectional retroreflector based on the transmutation of dielectric singularities,” Nat. Materials 8, 639–642 (2009).

J. C. Miñano, “Perfect imaging in a homogeneous three-dimensional region,” Opt. Express 14, 9627–9635 (2006).

[PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).

[PubMed]

U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006).

[PubMed]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).

[PubMed]

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]

B. Durand and L. Durand, “Improved WKB radial wave functions in several bases,” Phys. Rev. A 33, 2887–2898 (1986).

[PubMed]

R. H. Good, “The generalization of the WKB method to radial wave equations,” Phys. Rev. 90, 131–137 (1953).

J. E. Eaton, “On spherically symmetric lenses,” Trans. IRE Antennas Propag. 4, 66–71 (1952).

R. E. Langer, “On the connection formulas and the solutions of the wave equation,” Phys. Rev. 51, 669–676 (1937).

J. C. Maxwell, “Solutions of problems,” Camb. Dublin Math. J. 8, 188 (1854).

C. Gomez-Reino, M. V. Perez, and C. Bao, Gradient-Index Optics: Fundamentals and Applications (Springer, 2002).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, 1998).

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Materials 9, 387–396 (2010).

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Materials 9, 387–396 (2010).

W. C. Chew, Waves and Fields in Inhomogeneous Media (IEEE Press, 1995).

A. J. Danner, T. Tyc, and U. Leonhardt, “Controlling birefringence in dielectrics,” Nat. Photonics 5, 357–359 (2011).

B. Durand and L. Durand, “Improved WKB radial wave functions in several bases,” Phys. Rev. A 33, 2887–2898 (1986).

[PubMed]

B. Durand and L. Durand, “Improved WKB radial wave functions in several bases,” Phys. Rev. A 33, 2887–2898 (1986).

[PubMed]

J. E. Eaton, “On spherically symmetric lenses,” Trans. IRE Antennas Propag. 4, 66–71 (1952).

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332, 1291–1294 (2011).

[PubMed]

C. Gomez-Reino, M. V. Perez, and C. Bao, Gradient-Index Optics: Fundamentals and Applications (Springer, 2002).

R. H. Good, “The generalization of the WKB method to radial wave equations,” Phys. Rev. 90, 131–137 (1953).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, 1998).

J. D. Jackson, Classical Electrodynamics, 3rd ed. (John Wiley & Sons, 2004).

N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Materials 9, 129–132 (2010).

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).

R. E. Langer, “On the connection formulas and the solutions of the wave equation,” Phys. Rev. 51, 669–676 (1937).

A. J. Danner, T. Tyc, and U. Leonhardt, “Controlling birefringence in dielectrics,” Nat. Photonics 5, 357–359 (2011).

A. Di Falco, S. C. Kehr, and U. Leonhardt, “Luneburg lens in silicon photonics,” Opt. Express 19, 5156–5162 (2011).

[PubMed]

U. Leonhardt, “Perfect imaging without negative refraction,” New J. Phys. 11, 093040 (2009).

Y. G. Ma, C. K. Ong, T. Tyc, and U. Leonhardt, “An omnidirectional retroreflector based on the transmutation of dielectric singularities,” Nat. Materials 8, 639–642 (2009).

U. Leonhardt and T. G. Philbin, “Transformation optics and the geometry of light,” Prog. Opt. 53, 69–152 (2009).

U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006).

[PubMed]

U. Leonhardt and T. G. Philbin, Geometry and Light: The Science of Invisibility (Dover Publications, 2010).

T. Zentgraf, Y. Liu, M. H. Mikkelsen, J. Valentine, and X. Zhang, “Plasmonic Luneburg and Eaton lenses,” Nat. Nanotechnology 6, 151–155 (2011).

R. K. Luneburg, Mathematical Theory of Optics (University of California Press, 1964).

Y. G. Ma, C. K. Ong, T. Tyc, and U. Leonhardt, “An omnidirectional retroreflector based on the transmutation of dielectric singularities,” Nat. Materials 8, 639–642 (2009).

J. C. Maxwell, “Solutions of problems,” Camb. Dublin Math. J. 8, 188 (1854).

T. Zentgraf, Y. Liu, M. H. Mikkelsen, J. Valentine, and X. Zhang, “Plasmonic Luneburg and Eaton lenses,” Nat. Nanotechnology 6, 151–155 (2011).

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]

Y. G. Ma, C. K. Ong, T. Tyc, and U. Leonhardt, “An omnidirectional retroreflector based on the transmutation of dielectric singularities,” Nat. Materials 8, 639–642 (2009).

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]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).

[PubMed]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).

[PubMed]

C. Gomez-Reino, M. V. Perez, and C. Bao, Gradient-Index Optics: Fundamentals and Applications (Springer, 2002).

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. J. Sakurai, Modern Quantum Mechanics, Revised ed. (Addison-Wesley, 1994).

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]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).

[PubMed]

L. Solymar and E. Shamonina, Waves in Metamaterials (Oxford University, 2009).

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Materials 9, 387–396 (2010).

D. R. Smith, Y. Urzhumov, N. B. Kundtz, and N. I. Landy, “Enhancing imaging systems using transformation optics,” Opt. Express 18, 21238–21251 (2010).

[PubMed]

N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Materials 9, 129–132 (2010).

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).

[PubMed]

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]

L. Solymar and E. Shamonina, Waves in Metamaterials (Oxford University, 2009).

A. J. Danner, T. Tyc, and U. Leonhardt, “Controlling birefringence in dielectrics,” Nat. Photonics 5, 357–359 (2011).

Y. G. Ma, C. K. Ong, T. Tyc, and U. Leonhardt, “An omnidirectional retroreflector based on the transmutation of dielectric singularities,” Nat. Materials 8, 639–642 (2009).

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332, 1291–1294 (2011).

[PubMed]

T. Zentgraf, Y. Liu, M. H. Mikkelsen, J. Valentine, and X. Zhang, “Plasmonic Luneburg and Eaton lenses,” Nat. Nanotechnology 6, 151–155 (2011).

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]

Y. Zeng, J. Liu, and D. H. Werner, “General properties of two-dimensional conformal transformations in electrostatics,” Opt. Express 19, 20035–20047 (2011).

[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).

Y. Zeng, Q. Wu, and D. H. Werner, “Electrostatic theory for designing lossless negative permittivity metamaterials,” Opt. Lett. 35, 1431–1433 (2010).

[PubMed]

Y. Zeng, J. Liu, and D. H. Werner, “General properties of two-dimensional conformal transformations in electrostatics,” Opt. Express 19, 20035–20047 (2011).

[PubMed]

Y. Zeng, Q. Wu, and D. H. Werner, “Electrostatic theory for designing lossless negative permittivity metamaterials,” Opt. Lett. 35, 1431–1433 (2010).

[PubMed]

T. Zentgraf, Y. Liu, M. H. Mikkelsen, J. Valentine, and X. Zhang, “Plasmonic Luneburg and Eaton lenses,” Nat. Nanotechnology 6, 151–155 (2011).

T. Zentgraf, Y. Liu, M. H. Mikkelsen, J. Valentine, and X. Zhang, “Plasmonic Luneburg and Eaton lenses,” Nat. Nanotechnology 6, 151–155 (2011).

J. C. Maxwell, “Solutions of problems,” Camb. Dublin Math. J. 8, 188 (1854).

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).

Y. G. Ma, C. K. Ong, T. Tyc, and U. Leonhardt, “An omnidirectional retroreflector based on the transmutation of dielectric singularities,” Nat. Materials 8, 639–642 (2009).

N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Materials 9, 129–132 (2010).

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Materials 9, 387–396 (2010).

T. Zentgraf, Y. Liu, M. H. Mikkelsen, J. Valentine, and X. Zhang, “Plasmonic Luneburg and Eaton lenses,” Nat. Nanotechnology 6, 151–155 (2011).

A. J. Danner, T. Tyc, and U. Leonhardt, “Controlling birefringence in dielectrics,” Nat. Photonics 5, 357–359 (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. Express 19, 5156–5162 (2011).

[PubMed]

J. C. Miñano, “Perfect imaging in a homogeneous three-dimensional region,” Opt. Express 14, 9627–9635 (2006).

[PubMed]

D. R. Smith, Y. Urzhumov, N. B. Kundtz, and N. I. Landy, “Enhancing imaging systems using transformation optics,” Opt. Express 18, 21238–21251 (2010).

[PubMed]

Y. Zeng, J. Liu, and D. H. Werner, “General properties of two-dimensional conformal transformations in electrostatics,” Opt. Express 19, 20035–20047 (2011).

[PubMed]

Y. Zeng, Q. Wu, and D. H. Werner, “Electrostatic theory for designing lossless negative permittivity metamaterials,” Opt. Lett. 35, 1431–1433 (2010).

[PubMed]

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]

R. E. Langer, “On the connection formulas and the solutions of the wave equation,” Phys. Rev. 51, 669–676 (1937).

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. A 33, 2887–2898 (1986).

[PubMed]

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]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).

[PubMed]

U. Leonhardt and T. G. Philbin, “Transformation optics and the geometry of light,” Prog. Opt. 53, 69–152 (2009).

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332, 1291–1294 (2011).

[PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).

[PubMed]

U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006).

[PubMed]

J. E. Eaton, “On spherically symmetric lenses,” Trans. IRE Antennas Propag. 4, 66–71 (1952).

C. Gomez-Reino, M. V. Perez, and C. Bao, Gradient-Index Optics: Fundamentals and Applications (Springer, 2002).

R. K. Luneburg, Mathematical Theory of Optics (University of California Press, 1964).

U. Leonhardt and T. G. Philbin, Geometry and Light: The Science of Invisibility (Dover Publications, 2010).

L. Solymar and E. Shamonina, Waves in Metamaterials (Oxford University, 2009).

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).

COMSOL, www.comsol.com .

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, 1998).