Abstract

Field solutions for a conventional Veselago-Pendry (VP) flat lens with $\epsilon =-\epsilon _0$ and $\mu =-\mu _0$ can be derived based on transformation optics (TO) principles. The TO viewpoint makes it clear that perfect imaging by a VP lens is a consequence of multivalued nature of the particular coordinate transformation involved. This transformation is equivalent to a “space folding” whereby one point in the transformed domain (source point) is mapped to three different points in the physical domain (the original source point plus two focal points). In theory, a VP lens would enable the recovery of the entire range of spectral components, i.e. both propagating and evanescent fields, thus characterizing a “perfect lens”. Such lens, if lossess, is indeed “perfect” for monochromatic waves; however, for any realistic wave packet the space folding interpretation provided by TO makes it clear that a VP lens violates primitive causality constraints, which precludes any practical realization. Here, we utilize complex transformation optics (CTO) to derive generalized Veselago-Pendry (GVP) lenses without requiring a multivalued transformation. Unlike the conventional VP lens, the proposed lenses can fully recover the evanescent spectra under more general conditions that include the presence of (anisotropic) material loss/gain.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Perfect lenses made with left-handed materials: Alice’s mirror?

Daniel Maystre and Stefan Enoch
J. Opt. Soc. Am. A 21(1) 122-131 (2004)

Dispersion engineering via nonlocal transformation optics

Massimo Moccia, Giuseppe Castaldi, Vincenzo Galdi, Andrea Alù, and Nader Engheta
Optica 3(2) 179-188 (2016)

Negative refraction without negative index in metallic photonic crystals

Chiyan Luo, Steven G. Johnson, J. D. Joannopoulos, and J. B. Pendry
Opt. Express 11(7) 746-754 (2003)

References

  • View by:
  • |
  • |
  • |

  1. V. G. Veselago, “The Electrodynamics of Substances with Simultaneously Negative Values of $\epsilon$ϵ and $\mu$μ,” Phys.-Usp. 10(4), 509–514 (1968).
    [Crossref]
  2. 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(18), 4184–4187 (2000).
    [Crossref]
  3. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
    [Crossref]
  4. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
    [Crossref]
  5. D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, “Limitations on subdiffraction imaging with a negative refractive index slab,” Appl. Phys. Lett. 82(10), 1506–1508 (2003).
    [Crossref]
  6. A. Grbic and G. V. Eleftheriades, “Overcoming the diffraction limit with a planar left-handed transmission-line lens,” Phys. Rev. Lett. 92(11), 117403 (2004).
    [Crossref]
  7. V. A. Podolskiy and E. E. Narimanov, “Near-sighted superlens,” Opt. Lett. 30(1), 75–77 (2005).
    [Crossref]
  8. W. C. Chew, “Some reflections on double negative materials,” Prog. Electromagn. Res. 51, 1–26 (2005).
    [Crossref]
  9. U. Leonhardt and T. Philbin, Geometry and Light: The Science of Invisibility (Dover Publications, 2010).
  10. R. W. Ziolkowski and E. Heyman, “Wave propagation in media having negative permittivity and permeability,” Phys. Rev. E 64(5), 056625 (2001).
    [Crossref]
  11. R. E. Collin, “Frequency dispersion limits resolution in veselago lens,” Prog. Electromagn. Res. 19, 233–261 (2010).
    [Crossref]
  12. Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical hyperlens: Far-field imaging beyond the diffraction limit,” Opt. Express 14(18), 8247–8256 (2006).
    [Crossref]
  13. A. V. Kildishev and E. E. Narimanov, “Impedance-matched hyperlens,” Opt. Lett. 32(23), 3432–3434 (2007).
    [Crossref]
  14. I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, “Magnifying superlens in the visible frequency range,” Science 315(5819), 1699–1701 (2007).
    [Crossref]
  15. M. Tsang and D. Psaltis, “Magnifying perfect lens and superlens design by coordinate transformation,” Phys. Rev. B 77(3), 035122 (2008).
    [Crossref]
  16. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
    [Crossref]
  17. U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
    [Crossref]
  18. W. X. Jiang, J. Y. Chin, and T. J. Cui, “Anisotropic metamaterial devices,” Mater. Today 12(12), 26–33 (2009).
    [Crossref]
  19. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
    [Crossref]
  20. E. E. Narimanov and A. V. Kildishev, “Optical black hole: Broadband omnidirectional light absorber,” Appl. Phys. Lett. 95(4), 041106 (2009).
    [Crossref]
  21. H. Chen, R.-X. Miao, and M. Li, “Transformation optics that mimics the system outside a schwarzschild black hole,” Opt. Express 18(14), 15183–15188 (2010).
    [Crossref]
  22. H. Odabasi, F. L. Teixeira, and W. C. Chew, “Impedance-matched absorbers and optical pseudo black holes,” J. Opt. Soc. Am. B 28(5), 1317–1323 (2011).
    [Crossref]
  23. F. Teixeira and W. Chew, “Differential forms, metrics, and the reflectionless absorption of electromagnetic waves,” J. Electromagn. Waves Appl. 13(5), 665–686 (1999).
    [Crossref]
  24. F. L. Teixeira and W. C. Chew, “Complex space approach to perfectly matched layers: a review and some new developments,” Int. J. Numer. Model. 13(5), 441–455 (2000).
    [Crossref]
  25. U. Leonhardt and T. G. Philbin, “General relativity in electrical engineering,” New J. Phys. 8(10), 247 (2006).
    [Crossref]
  26. M. Kuzuoglu, “Analysis of perfectly matched double negative layers via complex coordinate transformations,” IEEE Trans. Antennas Propag. 54(12), 3695–3699 (2006).
    [Crossref]
  27. H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9(5), 387–396 (2010).
    [Crossref]
  28. M. I. Stockman, “Criterion for negative refraction with low optical losses from a fundamental principle of causality,” Phys. Rev. Lett. 98(17), 177404 (2007).
    [Crossref]
  29. B.-I. Popa and S. A. Cummer, “Complex coordinates in transformation optics,” Phys. Rev. A 84(6), 063837 (2011).
    [Crossref]
  30. G. Castaldi, S. Savoia, V. Galdi, A. Alù, and N. Engheta, “$\mathcal {PT}$PT metamaterials via complex-coordinate transformation optics,” Phys. Rev. Lett. 110(17), 173901 (2013).
    [Crossref]
  31. S. Savoia, G. Castaldi, and V. Galdi, “Complex-coordinate non-hermitian transformation optics,” J. Opt. 18(4), 044027 (2016).
    [Crossref]
  32. H. Odabasi, K. Sainath, and F. L. Teixeira, “Launching and controlling gaussian beams from point sources via planar transformation media,” Phys. Rev. B 97(7), 075105 (2018).
    [Crossref]
  33. J.-P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114(2), 185–200 (1994).
    [Crossref]
  34. Z. S. Sacks, D. M. Kingsland, R. Lee, and J.-F. Lee, “A perfectly matched anisotropic absorber for use as an absorbing boundary condition,” IEEE Trans. Antennas Propag. 43(12), 1460–1463 (1995).
    [Crossref]
  35. W. C. Chew and W. H. Weedon, “A 3d perfectly matched medium from modified maxwell’s equations with stretched coordinates,” Microw. Opt. Technol. Lett. 7(13), 599–604 (1994).
    [Crossref]
  36. F. L. Teixeira, “On aspects of the physical realizability of perfectly matched absorbers for electromagnetic waves,” Radio Sci. 38(2), 15 (2003). 8014.
    [Crossref]
  37. J. B. Keller and W. Streifer, “Complex rays with an application to gaussian beams,” J. Opt. Soc. Am. 61(1), 40–43 (1971).
    [Crossref]
  38. G. A. Deschamps, “Gaussian beam as a bundle of complex rays,” Electron. Lett. 7(23), 684–685 (1971).
    [Crossref]
  39. L. B. Felsen, “Complex source point solution of the eld equations and their relation to the propagation and scattering of gaussian beams,” Symp. Matematica 18, 40–56 (1976).
  40. F. L. Teixeira and W. C. Chew, “On causality and dynamic stability of perfectly matched layers for fdtd simulations,” IEEE Trans. Microwave Theory Tech. 47(6), 775–785 (1999).
    [Crossref]
  41. K. Sainath and F. L. Teixeira, “Perfectly reflectionless omnidirectional absorbers and electromagnetic horizons,” J. Opt. Soc. Am. B 32(8), 1645–1650 (2015).
    [Crossref]
  42. R. F. Harrington, Time-Haarmonic Electromagnetic Fields (IEE Press, 2001).
  43. E. Heyman and L. B. Felsen, “Gaussian beam and pulsed-beam dynamics: complex-source and complex-spectrum formulations within and beyond paraxial asymptotics,” J. Opt. Soc. Am. A 18(7), 1588–1611 (2001).
    [Crossref]
  44. K. Tap, “Complex source point beam expansions for some electromagnetic radiation and scattering problems,” Ph.D. thesis, Ohio State University, The Ohio State University, Columbus, Ohio, USA (2007).
  45. T. Koschny, R. Moussa, and C. M. Soukoulis, “Limits on the amplification of evanescent waves of left-handed materials,” J. Opt. Soc. Am. B 23(3), 485–489 (2006).
    [Crossref]
  46. W. C. Chew, Waves and Fields in Inhomogenous Media (Wiley IEEE Press, 1999).
  47. T. M. Grzegorczyk, X. Chen, J. Pacheco, B.-I. Wu, and J. A. Kong, “Reflection coefficients and goos-hanchen shifts in anisotropic and bianisotropic left-handed metamaterials,” Prog. Electromagn. Res. 51, 83–113 (2005).
    [Crossref]
  48. S. Tretyakov, “Uniaxial omega medium as a physically realizable alternative for the perfectly matched layer (pml),” J. Electromagn. Waves Appl. 12(6), 821–837 (1998).
    [Crossref]
  49. L. Sun, X. Yang, and J. Gao, “Loss-compensated broadband epsilon-near-zero metamaterials with gain media,” Appl. Phys. Lett. 103(20), 201109 (2013).
    [Crossref]
  50. D. Ye, Z. Wang, K. Xu, H. Li, J. Huangfu, Z. Wang, and L. Ran, “Ultrawideband dispersion control of a metamaterial surface for perfectly-matched-layer-like absorption,” Phys. Rev. Lett. 111(18), 187402 (2013).
    [Crossref]
  51. D. Ye, K. Chang, L. Ran, and H. Xin, “Microwave gain medium with negative refractive index,” Nat. Commun. 5(1), 5841 (2014).
    [Crossref]

2018 (1)

H. Odabasi, K. Sainath, and F. L. Teixeira, “Launching and controlling gaussian beams from point sources via planar transformation media,” Phys. Rev. B 97(7), 075105 (2018).
[Crossref]

2016 (1)

S. Savoia, G. Castaldi, and V. Galdi, “Complex-coordinate non-hermitian transformation optics,” J. Opt. 18(4), 044027 (2016).
[Crossref]

2015 (1)

2014 (1)

D. Ye, K. Chang, L. Ran, and H. Xin, “Microwave gain medium with negative refractive index,” Nat. Commun. 5(1), 5841 (2014).
[Crossref]

2013 (3)

L. Sun, X. Yang, and J. Gao, “Loss-compensated broadband epsilon-near-zero metamaterials with gain media,” Appl. Phys. Lett. 103(20), 201109 (2013).
[Crossref]

D. Ye, Z. Wang, K. Xu, H. Li, J. Huangfu, Z. Wang, and L. Ran, “Ultrawideband dispersion control of a metamaterial surface for perfectly-matched-layer-like absorption,” Phys. Rev. Lett. 111(18), 187402 (2013).
[Crossref]

G. Castaldi, S. Savoia, V. Galdi, A. Alù, and N. Engheta, “$\mathcal {PT}$PT metamaterials via complex-coordinate transformation optics,” Phys. Rev. Lett. 110(17), 173901 (2013).
[Crossref]

2011 (2)

B.-I. Popa and S. A. Cummer, “Complex coordinates in transformation optics,” Phys. Rev. A 84(6), 063837 (2011).
[Crossref]

H. Odabasi, F. L. Teixeira, and W. C. Chew, “Impedance-matched absorbers and optical pseudo black holes,” J. Opt. Soc. Am. B 28(5), 1317–1323 (2011).
[Crossref]

2010 (3)

H. Chen, R.-X. Miao, and M. Li, “Transformation optics that mimics the system outside a schwarzschild black hole,” Opt. Express 18(14), 15183–15188 (2010).
[Crossref]

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9(5), 387–396 (2010).
[Crossref]

R. E. Collin, “Frequency dispersion limits resolution in veselago lens,” Prog. Electromagn. Res. 19, 233–261 (2010).
[Crossref]

2009 (2)

W. X. Jiang, J. Y. Chin, and T. J. Cui, “Anisotropic metamaterial devices,” Mater. Today 12(12), 26–33 (2009).
[Crossref]

E. E. Narimanov and A. V. Kildishev, “Optical black hole: Broadband omnidirectional light absorber,” Appl. Phys. Lett. 95(4), 041106 (2009).
[Crossref]

2008 (1)

M. Tsang and D. Psaltis, “Magnifying perfect lens and superlens design by coordinate transformation,” Phys. Rev. B 77(3), 035122 (2008).
[Crossref]

2007 (3)

A. V. Kildishev and E. E. Narimanov, “Impedance-matched hyperlens,” Opt. Lett. 32(23), 3432–3434 (2007).
[Crossref]

I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, “Magnifying superlens in the visible frequency range,” Science 315(5819), 1699–1701 (2007).
[Crossref]

M. I. Stockman, “Criterion for negative refraction with low optical losses from a fundamental principle of causality,” Phys. Rev. Lett. 98(17), 177404 (2007).
[Crossref]

2006 (7)

U. Leonhardt and T. G. Philbin, “General relativity in electrical engineering,” New J. Phys. 8(10), 247 (2006).
[Crossref]

M. Kuzuoglu, “Analysis of perfectly matched double negative layers via complex coordinate transformations,” IEEE Trans. Antennas Propag. 54(12), 3695–3699 (2006).
[Crossref]

Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical hyperlens: Far-field imaging beyond the diffraction limit,” Opt. Express 14(18), 8247–8256 (2006).
[Crossref]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref]

U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
[Crossref]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[Crossref]

T. Koschny, R. Moussa, and C. M. Soukoulis, “Limits on the amplification of evanescent waves of left-handed materials,” J. Opt. Soc. Am. B 23(3), 485–489 (2006).
[Crossref]

2005 (3)

T. M. Grzegorczyk, X. Chen, J. Pacheco, B.-I. Wu, and J. A. Kong, “Reflection coefficients and goos-hanchen shifts in anisotropic and bianisotropic left-handed metamaterials,” Prog. Electromagn. Res. 51, 83–113 (2005).
[Crossref]

V. A. Podolskiy and E. E. Narimanov, “Near-sighted superlens,” Opt. Lett. 30(1), 75–77 (2005).
[Crossref]

W. C. Chew, “Some reflections on double negative materials,” Prog. Electromagn. Res. 51, 1–26 (2005).
[Crossref]

2004 (1)

A. Grbic and G. V. Eleftheriades, “Overcoming the diffraction limit with a planar left-handed transmission-line lens,” Phys. Rev. Lett. 92(11), 117403 (2004).
[Crossref]

2003 (2)

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, “Limitations on subdiffraction imaging with a negative refractive index slab,” Appl. Phys. Lett. 82(10), 1506–1508 (2003).
[Crossref]

F. L. Teixeira, “On aspects of the physical realizability of perfectly matched absorbers for electromagnetic waves,” Radio Sci. 38(2), 15 (2003). 8014.
[Crossref]

2001 (3)

E. Heyman and L. B. Felsen, “Gaussian beam and pulsed-beam dynamics: complex-source and complex-spectrum formulations within and beyond paraxial asymptotics,” J. Opt. Soc. Am. A 18(7), 1588–1611 (2001).
[Crossref]

R. W. Ziolkowski and E. Heyman, “Wave propagation in media having negative permittivity and permeability,” Phys. Rev. E 64(5), 056625 (2001).
[Crossref]

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[Crossref]

2000 (3)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[Crossref]

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(18), 4184–4187 (2000).
[Crossref]

F. L. Teixeira and W. C. Chew, “Complex space approach to perfectly matched layers: a review and some new developments,” Int. J. Numer. Model. 13(5), 441–455 (2000).
[Crossref]

1999 (2)

F. Teixeira and W. Chew, “Differential forms, metrics, and the reflectionless absorption of electromagnetic waves,” J. Electromagn. Waves Appl. 13(5), 665–686 (1999).
[Crossref]

F. L. Teixeira and W. C. Chew, “On causality and dynamic stability of perfectly matched layers for fdtd simulations,” IEEE Trans. Microwave Theory Tech. 47(6), 775–785 (1999).
[Crossref]

1998 (1)

S. Tretyakov, “Uniaxial omega medium as a physically realizable alternative for the perfectly matched layer (pml),” J. Electromagn. Waves Appl. 12(6), 821–837 (1998).
[Crossref]

1995 (1)

Z. S. Sacks, D. M. Kingsland, R. Lee, and J.-F. Lee, “A perfectly matched anisotropic absorber for use as an absorbing boundary condition,” IEEE Trans. Antennas Propag. 43(12), 1460–1463 (1995).
[Crossref]

1994 (2)

W. C. Chew and W. H. Weedon, “A 3d perfectly matched medium from modified maxwell’s equations with stretched coordinates,” Microw. Opt. Technol. Lett. 7(13), 599–604 (1994).
[Crossref]

J.-P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114(2), 185–200 (1994).
[Crossref]

1976 (1)

L. B. Felsen, “Complex source point solution of the eld equations and their relation to the propagation and scattering of gaussian beams,” Symp. Matematica 18, 40–56 (1976).

1971 (2)

J. B. Keller and W. Streifer, “Complex rays with an application to gaussian beams,” J. Opt. Soc. Am. 61(1), 40–43 (1971).
[Crossref]

G. A. Deschamps, “Gaussian beam as a bundle of complex rays,” Electron. Lett. 7(23), 684–685 (1971).
[Crossref]

1968 (1)

V. G. Veselago, “The Electrodynamics of Substances with Simultaneously Negative Values of $\epsilon$ϵ and $\mu$μ,” Phys.-Usp. 10(4), 509–514 (1968).
[Crossref]

Alekseyev, L. V.

Alù, A.

G. Castaldi, S. Savoia, V. Galdi, A. Alù, and N. Engheta, “$\mathcal {PT}$PT metamaterials via complex-coordinate transformation optics,” Phys. Rev. Lett. 110(17), 173901 (2013).
[Crossref]

Berenger, J.-P.

J.-P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114(2), 185–200 (1994).
[Crossref]

Castaldi, G.

S. Savoia, G. Castaldi, and V. Galdi, “Complex-coordinate non-hermitian transformation optics,” J. Opt. 18(4), 044027 (2016).
[Crossref]

G. Castaldi, S. Savoia, V. Galdi, A. Alù, and N. Engheta, “$\mathcal {PT}$PT metamaterials via complex-coordinate transformation optics,” Phys. Rev. Lett. 110(17), 173901 (2013).
[Crossref]

Chan, C. T.

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9(5), 387–396 (2010).
[Crossref]

Chang, K.

D. Ye, K. Chang, L. Ran, and H. Xin, “Microwave gain medium with negative refractive index,” Nat. Commun. 5(1), 5841 (2014).
[Crossref]

Chen, H.

Chen, X.

T. M. Grzegorczyk, X. Chen, J. Pacheco, B.-I. Wu, and J. A. Kong, “Reflection coefficients and goos-hanchen shifts in anisotropic and bianisotropic left-handed metamaterials,” Prog. Electromagn. Res. 51, 83–113 (2005).
[Crossref]

Chew, W.

F. Teixeira and W. Chew, “Differential forms, metrics, and the reflectionless absorption of electromagnetic waves,” J. Electromagn. Waves Appl. 13(5), 665–686 (1999).
[Crossref]

Chew, W. C.

H. Odabasi, F. L. Teixeira, and W. C. Chew, “Impedance-matched absorbers and optical pseudo black holes,” J. Opt. Soc. Am. B 28(5), 1317–1323 (2011).
[Crossref]

W. C. Chew, “Some reflections on double negative materials,” Prog. Electromagn. Res. 51, 1–26 (2005).
[Crossref]

F. L. Teixeira and W. C. Chew, “Complex space approach to perfectly matched layers: a review and some new developments,” Int. J. Numer. Model. 13(5), 441–455 (2000).
[Crossref]

F. L. Teixeira and W. C. Chew, “On causality and dynamic stability of perfectly matched layers for fdtd simulations,” IEEE Trans. Microwave Theory Tech. 47(6), 775–785 (1999).
[Crossref]

W. C. Chew and W. H. Weedon, “A 3d perfectly matched medium from modified maxwell’s equations with stretched coordinates,” Microw. Opt. Technol. Lett. 7(13), 599–604 (1994).
[Crossref]

W. C. Chew, Waves and Fields in Inhomogenous Media (Wiley IEEE Press, 1999).

Chin, J. Y.

W. X. Jiang, J. Y. Chin, and T. J. Cui, “Anisotropic metamaterial devices,” Mater. Today 12(12), 26–33 (2009).
[Crossref]

Collin, R. E.

R. E. Collin, “Frequency dispersion limits resolution in veselago lens,” Prog. Electromagn. Res. 19, 233–261 (2010).
[Crossref]

Cui, T. J.

W. X. Jiang, J. Y. Chin, and T. J. Cui, “Anisotropic metamaterial devices,” Mater. Today 12(12), 26–33 (2009).
[Crossref]

Cummer, S. A.

B.-I. Popa and S. A. Cummer, “Complex coordinates in transformation optics,” Phys. Rev. A 84(6), 063837 (2011).
[Crossref]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[Crossref]

Davis, C. C.

I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, “Magnifying superlens in the visible frequency range,” Science 315(5819), 1699–1701 (2007).
[Crossref]

Deschamps, G. A.

G. A. Deschamps, “Gaussian beam as a bundle of complex rays,” Electron. Lett. 7(23), 684–685 (1971).
[Crossref]

Eleftheriades, G. V.

A. Grbic and G. V. Eleftheriades, “Overcoming the diffraction limit with a planar left-handed transmission-line lens,” Phys. Rev. Lett. 92(11), 117403 (2004).
[Crossref]

Engheta, N.

G. Castaldi, S. Savoia, V. Galdi, A. Alù, and N. Engheta, “$\mathcal {PT}$PT metamaterials via complex-coordinate transformation optics,” Phys. Rev. Lett. 110(17), 173901 (2013).
[Crossref]

Felsen, L. B.

E. Heyman and L. B. Felsen, “Gaussian beam and pulsed-beam dynamics: complex-source and complex-spectrum formulations within and beyond paraxial asymptotics,” J. Opt. Soc. Am. A 18(7), 1588–1611 (2001).
[Crossref]

L. B. Felsen, “Complex source point solution of the eld equations and their relation to the propagation and scattering of gaussian beams,” Symp. Matematica 18, 40–56 (1976).

Galdi, V.

S. Savoia, G. Castaldi, and V. Galdi, “Complex-coordinate non-hermitian transformation optics,” J. Opt. 18(4), 044027 (2016).
[Crossref]

G. Castaldi, S. Savoia, V. Galdi, A. Alù, and N. Engheta, “$\mathcal {PT}$PT metamaterials via complex-coordinate transformation optics,” Phys. Rev. Lett. 110(17), 173901 (2013).
[Crossref]

Gao, J.

L. Sun, X. Yang, and J. Gao, “Loss-compensated broadband epsilon-near-zero metamaterials with gain media,” Appl. Phys. Lett. 103(20), 201109 (2013).
[Crossref]

Grbic, A.

A. Grbic and G. V. Eleftheriades, “Overcoming the diffraction limit with a planar left-handed transmission-line lens,” Phys. Rev. Lett. 92(11), 117403 (2004).
[Crossref]

Grzegorczyk, T. M.

T. M. Grzegorczyk, X. Chen, J. Pacheco, B.-I. Wu, and J. A. Kong, “Reflection coefficients and goos-hanchen shifts in anisotropic and bianisotropic left-handed metamaterials,” Prog. Electromagn. Res. 51, 83–113 (2005).
[Crossref]

Harrington, R. F.

R. F. Harrington, Time-Haarmonic Electromagnetic Fields (IEE Press, 2001).

Heyman, E.

Huangfu, J.

D. Ye, Z. Wang, K. Xu, H. Li, J. Huangfu, Z. Wang, and L. Ran, “Ultrawideband dispersion control of a metamaterial surface for perfectly-matched-layer-like absorption,” Phys. Rev. Lett. 111(18), 187402 (2013).
[Crossref]

Hung, Y.-J.

I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, “Magnifying superlens in the visible frequency range,” Science 315(5819), 1699–1701 (2007).
[Crossref]

Jacob, Z.

Jiang, W. X.

W. X. Jiang, J. Y. Chin, and T. J. Cui, “Anisotropic metamaterial devices,” Mater. Today 12(12), 26–33 (2009).
[Crossref]

Justice, B. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[Crossref]

Keller, J. B.

Kildishev, A. V.

E. E. Narimanov and A. V. Kildishev, “Optical black hole: Broadband omnidirectional light absorber,” Appl. Phys. Lett. 95(4), 041106 (2009).
[Crossref]

A. V. Kildishev and E. E. Narimanov, “Impedance-matched hyperlens,” Opt. Lett. 32(23), 3432–3434 (2007).
[Crossref]

Kingsland, D. M.

Z. S. Sacks, D. M. Kingsland, R. Lee, and J.-F. Lee, “A perfectly matched anisotropic absorber for use as an absorbing boundary condition,” IEEE Trans. Antennas Propag. 43(12), 1460–1463 (1995).
[Crossref]

Kong, J. A.

T. M. Grzegorczyk, X. Chen, J. Pacheco, B.-I. Wu, and J. A. Kong, “Reflection coefficients and goos-hanchen shifts in anisotropic and bianisotropic left-handed metamaterials,” Prog. Electromagn. Res. 51, 83–113 (2005).
[Crossref]

Koschny, T.

Kuzuoglu, M.

M. Kuzuoglu, “Analysis of perfectly matched double negative layers via complex coordinate transformations,” IEEE Trans. Antennas Propag. 54(12), 3695–3699 (2006).
[Crossref]

Lee, J.-F.

Z. S. Sacks, D. M. Kingsland, R. Lee, and J.-F. Lee, “A perfectly matched anisotropic absorber for use as an absorbing boundary condition,” IEEE Trans. Antennas Propag. 43(12), 1460–1463 (1995).
[Crossref]

Lee, R.

Z. S. Sacks, D. M. Kingsland, R. Lee, and J.-F. Lee, “A perfectly matched anisotropic absorber for use as an absorbing boundary condition,” IEEE Trans. Antennas Propag. 43(12), 1460–1463 (1995).
[Crossref]

Leonhardt, U.

U. Leonhardt and T. G. Philbin, “General relativity in electrical engineering,” New J. Phys. 8(10), 247 (2006).
[Crossref]

U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
[Crossref]

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

Li, H.

D. Ye, Z. Wang, K. Xu, H. Li, J. Huangfu, Z. Wang, and L. Ran, “Ultrawideband dispersion control of a metamaterial surface for perfectly-matched-layer-like absorption,” Phys. Rev. Lett. 111(18), 187402 (2013).
[Crossref]

Li, M.

Miao, R.-X.

Mock, J. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[Crossref]

Moussa, R.

Narimanov, E.

Narimanov, E. E.

Nemat-Nasser, S. C.

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(18), 4184–4187 (2000).
[Crossref]

Odabasi, H.

H. Odabasi, K. Sainath, and F. L. Teixeira, “Launching and controlling gaussian beams from point sources via planar transformation media,” Phys. Rev. B 97(7), 075105 (2018).
[Crossref]

H. Odabasi, F. L. Teixeira, and W. C. Chew, “Impedance-matched absorbers and optical pseudo black holes,” J. Opt. Soc. Am. B 28(5), 1317–1323 (2011).
[Crossref]

Pacheco, J.

T. M. Grzegorczyk, X. Chen, J. Pacheco, B.-I. Wu, and J. A. Kong, “Reflection coefficients and goos-hanchen shifts in anisotropic and bianisotropic left-handed metamaterials,” Prog. Electromagn. Res. 51, 83–113 (2005).
[Crossref]

Padilla, W. J.

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(18), 4184–4187 (2000).
[Crossref]

Pendry, J. B.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[Crossref]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref]

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, “Limitations on subdiffraction imaging with a negative refractive index slab,” Appl. Phys. Lett. 82(10), 1506–1508 (2003).
[Crossref]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[Crossref]

Philbin, T.

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

Philbin, T. G.

U. Leonhardt and T. G. Philbin, “General relativity in electrical engineering,” New J. Phys. 8(10), 247 (2006).
[Crossref]

Podolskiy, V. A.

Popa, B.-I.

B.-I. Popa and S. A. Cummer, “Complex coordinates in transformation optics,” Phys. Rev. A 84(6), 063837 (2011).
[Crossref]

Psaltis, D.

M. Tsang and D. Psaltis, “Magnifying perfect lens and superlens design by coordinate transformation,” Phys. Rev. B 77(3), 035122 (2008).
[Crossref]

Ramakrishna, S. A.

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, “Limitations on subdiffraction imaging with a negative refractive index slab,” Appl. Phys. Lett. 82(10), 1506–1508 (2003).
[Crossref]

Ran, L.

D. Ye, K. Chang, L. Ran, and H. Xin, “Microwave gain medium with negative refractive index,” Nat. Commun. 5(1), 5841 (2014).
[Crossref]

D. Ye, Z. Wang, K. Xu, H. Li, J. Huangfu, Z. Wang, and L. Ran, “Ultrawideband dispersion control of a metamaterial surface for perfectly-matched-layer-like absorption,” Phys. Rev. Lett. 111(18), 187402 (2013).
[Crossref]

Rosenbluth, M.

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, “Limitations on subdiffraction imaging with a negative refractive index slab,” Appl. Phys. Lett. 82(10), 1506–1508 (2003).
[Crossref]

Sacks, Z. S.

Z. S. Sacks, D. M. Kingsland, R. Lee, and J.-F. Lee, “A perfectly matched anisotropic absorber for use as an absorbing boundary condition,” IEEE Trans. Antennas Propag. 43(12), 1460–1463 (1995).
[Crossref]

Sainath, K.

H. Odabasi, K. Sainath, and F. L. Teixeira, “Launching and controlling gaussian beams from point sources via planar transformation media,” Phys. Rev. B 97(7), 075105 (2018).
[Crossref]

K. Sainath and F. L. Teixeira, “Perfectly reflectionless omnidirectional absorbers and electromagnetic horizons,” J. Opt. Soc. Am. B 32(8), 1645–1650 (2015).
[Crossref]

Savoia, S.

S. Savoia, G. Castaldi, and V. Galdi, “Complex-coordinate non-hermitian transformation optics,” J. Opt. 18(4), 044027 (2016).
[Crossref]

G. Castaldi, S. Savoia, V. Galdi, A. Alù, and N. Engheta, “$\mathcal {PT}$PT metamaterials via complex-coordinate transformation optics,” Phys. Rev. Lett. 110(17), 173901 (2013).
[Crossref]

Schultz, S.

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, “Limitations on subdiffraction imaging with a negative refractive index slab,” Appl. Phys. Lett. 82(10), 1506–1508 (2003).
[Crossref]

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[Crossref]

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(18), 4184–4187 (2000).
[Crossref]

Schurig, D.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[Crossref]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref]

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, “Limitations on subdiffraction imaging with a negative refractive index slab,” Appl. Phys. Lett. 82(10), 1506–1508 (2003).
[Crossref]

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[Crossref]

Sheng, P.

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9(5), 387–396 (2010).
[Crossref]

Smith, D. R.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[Crossref]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref]

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, “Limitations on subdiffraction imaging with a negative refractive index slab,” Appl. Phys. Lett. 82(10), 1506–1508 (2003).
[Crossref]

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[Crossref]

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(18), 4184–4187 (2000).
[Crossref]

Smolyaninov, I. I.

I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, “Magnifying superlens in the visible frequency range,” Science 315(5819), 1699–1701 (2007).
[Crossref]

Soukoulis, C. M.

Starr, A. F.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[Crossref]

Stockman, M. I.

M. I. Stockman, “Criterion for negative refraction with low optical losses from a fundamental principle of causality,” Phys. Rev. Lett. 98(17), 177404 (2007).
[Crossref]

Streifer, W.

Sun, L.

L. Sun, X. Yang, and J. Gao, “Loss-compensated broadband epsilon-near-zero metamaterials with gain media,” Appl. Phys. Lett. 103(20), 201109 (2013).
[Crossref]

Tap, K.

K. Tap, “Complex source point beam expansions for some electromagnetic radiation and scattering problems,” Ph.D. thesis, Ohio State University, The Ohio State University, Columbus, Ohio, USA (2007).

Teixeira, F.

F. Teixeira and W. Chew, “Differential forms, metrics, and the reflectionless absorption of electromagnetic waves,” J. Electromagn. Waves Appl. 13(5), 665–686 (1999).
[Crossref]

Teixeira, F. L.

H. Odabasi, K. Sainath, and F. L. Teixeira, “Launching and controlling gaussian beams from point sources via planar transformation media,” Phys. Rev. B 97(7), 075105 (2018).
[Crossref]

K. Sainath and F. L. Teixeira, “Perfectly reflectionless omnidirectional absorbers and electromagnetic horizons,” J. Opt. Soc. Am. B 32(8), 1645–1650 (2015).
[Crossref]

H. Odabasi, F. L. Teixeira, and W. C. Chew, “Impedance-matched absorbers and optical pseudo black holes,” J. Opt. Soc. Am. B 28(5), 1317–1323 (2011).
[Crossref]

F. L. Teixeira, “On aspects of the physical realizability of perfectly matched absorbers for electromagnetic waves,” Radio Sci. 38(2), 15 (2003). 8014.
[Crossref]

F. L. Teixeira and W. C. Chew, “Complex space approach to perfectly matched layers: a review and some new developments,” Int. J. Numer. Model. 13(5), 441–455 (2000).
[Crossref]

F. L. Teixeira and W. C. Chew, “On causality and dynamic stability of perfectly matched layers for fdtd simulations,” IEEE Trans. Microwave Theory Tech. 47(6), 775–785 (1999).
[Crossref]

Tretyakov, S.

S. Tretyakov, “Uniaxial omega medium as a physically realizable alternative for the perfectly matched layer (pml),” J. Electromagn. Waves Appl. 12(6), 821–837 (1998).
[Crossref]

Tsang, M.

M. Tsang and D. Psaltis, “Magnifying perfect lens and superlens design by coordinate transformation,” Phys. Rev. B 77(3), 035122 (2008).
[Crossref]

Veselago, V. G.

V. G. Veselago, “The Electrodynamics of Substances with Simultaneously Negative Values of $\epsilon$ϵ and $\mu$μ,” Phys.-Usp. 10(4), 509–514 (1968).
[Crossref]

Vier, D. C.

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(18), 4184–4187 (2000).
[Crossref]

Wang, Z.

D. Ye, Z. Wang, K. Xu, H. Li, J. Huangfu, Z. Wang, and L. Ran, “Ultrawideband dispersion control of a metamaterial surface for perfectly-matched-layer-like absorption,” Phys. Rev. Lett. 111(18), 187402 (2013).
[Crossref]

D. Ye, Z. Wang, K. Xu, H. Li, J. Huangfu, Z. Wang, and L. Ran, “Ultrawideband dispersion control of a metamaterial surface for perfectly-matched-layer-like absorption,” Phys. Rev. Lett. 111(18), 187402 (2013).
[Crossref]

Weedon, W. H.

W. C. Chew and W. H. Weedon, “A 3d perfectly matched medium from modified maxwell’s equations with stretched coordinates,” Microw. Opt. Technol. Lett. 7(13), 599–604 (1994).
[Crossref]

Wu, B.-I.

T. M. Grzegorczyk, X. Chen, J. Pacheco, B.-I. Wu, and J. A. Kong, “Reflection coefficients and goos-hanchen shifts in anisotropic and bianisotropic left-handed metamaterials,” Prog. Electromagn. Res. 51, 83–113 (2005).
[Crossref]

Xin, H.

D. Ye, K. Chang, L. Ran, and H. Xin, “Microwave gain medium with negative refractive index,” Nat. Commun. 5(1), 5841 (2014).
[Crossref]

Xu, K.

D. Ye, Z. Wang, K. Xu, H. Li, J. Huangfu, Z. Wang, and L. Ran, “Ultrawideband dispersion control of a metamaterial surface for perfectly-matched-layer-like absorption,” Phys. Rev. Lett. 111(18), 187402 (2013).
[Crossref]

Yang, X.

L. Sun, X. Yang, and J. Gao, “Loss-compensated broadband epsilon-near-zero metamaterials with gain media,” Appl. Phys. Lett. 103(20), 201109 (2013).
[Crossref]

Ye, D.

D. Ye, K. Chang, L. Ran, and H. Xin, “Microwave gain medium with negative refractive index,” Nat. Commun. 5(1), 5841 (2014).
[Crossref]

D. Ye, Z. Wang, K. Xu, H. Li, J. Huangfu, Z. Wang, and L. Ran, “Ultrawideband dispersion control of a metamaterial surface for perfectly-matched-layer-like absorption,” Phys. Rev. Lett. 111(18), 187402 (2013).
[Crossref]

Ziolkowski, R. W.

R. W. Ziolkowski and E. Heyman, “Wave propagation in media having negative permittivity and permeability,” Phys. Rev. E 64(5), 056625 (2001).
[Crossref]

Appl. Phys. Lett. (3)

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, “Limitations on subdiffraction imaging with a negative refractive index slab,” Appl. Phys. Lett. 82(10), 1506–1508 (2003).
[Crossref]

E. E. Narimanov and A. V. Kildishev, “Optical black hole: Broadband omnidirectional light absorber,” Appl. Phys. Lett. 95(4), 041106 (2009).
[Crossref]

L. Sun, X. Yang, and J. Gao, “Loss-compensated broadband epsilon-near-zero metamaterials with gain media,” Appl. Phys. Lett. 103(20), 201109 (2013).
[Crossref]

Electron. Lett. (1)

G. A. Deschamps, “Gaussian beam as a bundle of complex rays,” Electron. Lett. 7(23), 684–685 (1971).
[Crossref]

IEEE Trans. Antennas Propag. (2)

M. Kuzuoglu, “Analysis of perfectly matched double negative layers via complex coordinate transformations,” IEEE Trans. Antennas Propag. 54(12), 3695–3699 (2006).
[Crossref]

Z. S. Sacks, D. M. Kingsland, R. Lee, and J.-F. Lee, “A perfectly matched anisotropic absorber for use as an absorbing boundary condition,” IEEE Trans. Antennas Propag. 43(12), 1460–1463 (1995).
[Crossref]

IEEE Trans. Microwave Theory Tech. (1)

F. L. Teixeira and W. C. Chew, “On causality and dynamic stability of perfectly matched layers for fdtd simulations,” IEEE Trans. Microwave Theory Tech. 47(6), 775–785 (1999).
[Crossref]

Int. J. Numer. Model. (1)

F. L. Teixeira and W. C. Chew, “Complex space approach to perfectly matched layers: a review and some new developments,” Int. J. Numer. Model. 13(5), 441–455 (2000).
[Crossref]

J. Comput. Phys. (1)

J.-P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114(2), 185–200 (1994).
[Crossref]

J. Electromagn. Waves Appl. (2)

F. Teixeira and W. Chew, “Differential forms, metrics, and the reflectionless absorption of electromagnetic waves,” J. Electromagn. Waves Appl. 13(5), 665–686 (1999).
[Crossref]

S. Tretyakov, “Uniaxial omega medium as a physically realizable alternative for the perfectly matched layer (pml),” J. Electromagn. Waves Appl. 12(6), 821–837 (1998).
[Crossref]

J. Opt. (1)

S. Savoia, G. Castaldi, and V. Galdi, “Complex-coordinate non-hermitian transformation optics,” J. Opt. 18(4), 044027 (2016).
[Crossref]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (3)

Mater. Today (1)

W. X. Jiang, J. Y. Chin, and T. J. Cui, “Anisotropic metamaterial devices,” Mater. Today 12(12), 26–33 (2009).
[Crossref]

Microw. Opt. Technol. Lett. (1)

W. C. Chew and W. H. Weedon, “A 3d perfectly matched medium from modified maxwell’s equations with stretched coordinates,” Microw. Opt. Technol. Lett. 7(13), 599–604 (1994).
[Crossref]

Nat. Commun. (1)

D. Ye, K. Chang, L. Ran, and H. Xin, “Microwave gain medium with negative refractive index,” Nat. Commun. 5(1), 5841 (2014).
[Crossref]

Nat. Mater. (1)

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9(5), 387–396 (2010).
[Crossref]

New J. Phys. (1)

U. Leonhardt and T. G. Philbin, “General relativity in electrical engineering,” New J. Phys. 8(10), 247 (2006).
[Crossref]

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. A (1)

B.-I. Popa and S. A. Cummer, “Complex coordinates in transformation optics,” Phys. Rev. A 84(6), 063837 (2011).
[Crossref]

Phys. Rev. B (2)

H. Odabasi, K. Sainath, and F. L. Teixeira, “Launching and controlling gaussian beams from point sources via planar transformation media,” Phys. Rev. B 97(7), 075105 (2018).
[Crossref]

M. Tsang and D. Psaltis, “Magnifying perfect lens and superlens design by coordinate transformation,” Phys. Rev. B 77(3), 035122 (2008).
[Crossref]

Phys. Rev. E (1)

R. W. Ziolkowski and E. Heyman, “Wave propagation in media having negative permittivity and permeability,” Phys. Rev. E 64(5), 056625 (2001).
[Crossref]

Phys. Rev. Lett. (6)

A. Grbic and G. V. Eleftheriades, “Overcoming the diffraction limit with a planar left-handed transmission-line lens,” Phys. Rev. Lett. 92(11), 117403 (2004).
[Crossref]

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(18), 4184–4187 (2000).
[Crossref]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[Crossref]

G. Castaldi, S. Savoia, V. Galdi, A. Alù, and N. Engheta, “$\mathcal {PT}$PT metamaterials via complex-coordinate transformation optics,” Phys. Rev. Lett. 110(17), 173901 (2013).
[Crossref]

M. I. Stockman, “Criterion for negative refraction with low optical losses from a fundamental principle of causality,” Phys. Rev. Lett. 98(17), 177404 (2007).
[Crossref]

D. Ye, Z. Wang, K. Xu, H. Li, J. Huangfu, Z. Wang, and L. Ran, “Ultrawideband dispersion control of a metamaterial surface for perfectly-matched-layer-like absorption,” Phys. Rev. Lett. 111(18), 187402 (2013).
[Crossref]

Phys.-Usp. (1)

V. G. Veselago, “The Electrodynamics of Substances with Simultaneously Negative Values of $\epsilon$ϵ and $\mu$μ,” Phys.-Usp. 10(4), 509–514 (1968).
[Crossref]

Prog. Electromagn. Res. (3)

W. C. Chew, “Some reflections on double negative materials,” Prog. Electromagn. Res. 51, 1–26 (2005).
[Crossref]

R. E. Collin, “Frequency dispersion limits resolution in veselago lens,” Prog. Electromagn. Res. 19, 233–261 (2010).
[Crossref]

T. M. Grzegorczyk, X. Chen, J. Pacheco, B.-I. Wu, and J. A. Kong, “Reflection coefficients and goos-hanchen shifts in anisotropic and bianisotropic left-handed metamaterials,” Prog. Electromagn. Res. 51, 83–113 (2005).
[Crossref]

Radio Sci. (1)

F. L. Teixeira, “On aspects of the physical realizability of perfectly matched absorbers for electromagnetic waves,” Radio Sci. 38(2), 15 (2003). 8014.
[Crossref]

Science (5)

I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, “Magnifying superlens in the visible frequency range,” Science 315(5819), 1699–1701 (2007).
[Crossref]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref]

U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
[Crossref]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[Crossref]

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[Crossref]

Symp. Matematica (1)

L. B. Felsen, “Complex source point solution of the eld equations and their relation to the propagation and scattering of gaussian beams,” Symp. Matematica 18, 40–56 (1976).

Other (4)

R. F. Harrington, Time-Haarmonic Electromagnetic Fields (IEE Press, 2001).

W. C. Chew, Waves and Fields in Inhomogenous Media (Wiley IEEE Press, 1999).

K. Tap, “Complex source point beam expansions for some electromagnetic radiation and scattering problems,” Ph.D. thesis, Ohio State University, The Ohio State University, Columbus, Ohio, USA (2007).

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

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1.
Fig. 1. The shaded map indicated the real part of the complex distance $\rho '$ for the transformation given in Eqs. (1) and (3) with $a_x =-1$ and $\sigma _x = 0.2$, with $d=2\lambda$. Superimposed on this $\rho '$ plot, we also show a representation of the complex-valued coordinate $x'$ as a function of $x$ entailed by Eqs. (1) and (3). In particular, the blue line shows $\Re e[x']$ for $a_x=-1$, the red dashed line shows $\Im m[x']$ for $b=0.4 \lambda$, and the green dash-dotted line shows $\Im m[x']$ for $b=-0.4 \lambda$. The source point gives rise to two focal points both inside and outside the transformation region in accordance with the $\sigma _x$ function. Note that while the mapping from $x$ to $\Re e[x']$ is still multivalued, the mapping from $x$ to $x$ is not multivalued anymore.
Fig. 2.
Fig. 2. Transfer function of a (a) GVP with $\left [\epsilon \right ]= \epsilon _0 \left [\Lambda \right ]$ and $\left [\mu \right ] = \mu _0 \left [\Lambda \right ]$ where $\left [\Lambda \right ]$ is given by Eq. (2) for different $\sigma _x$ values given by Eq. (3), (b) Veselago-Pendry lens with $\epsilon _r=-1+i \sigma$, $\mu _r=-1+i \sigma$, and different loss parameters.
Fig. 3.
Fig. 3. $\Re e[E_z]$ field distribution due to a point source placed next to different slabs and the corresponding field distribution along the $x=x_{f_2}$ cut with FWHM value. (a, b) VP slab with $\epsilon _r=-1+i10^{-6}$ and $\mu _r=-1+i10^{-6}$. (c, d) VP slab with $\epsilon _r=-1+i5\times 10^{-2}$ and $\mu _r=-1+i5\times 10^{-2}$. (e, f) GVP slab based on Eq. (3) with $a_x=-1$ and $\sigma _x=b/d$ with $b=0.1\lambda$ (g, h) GVP slab based on Eq. (3) with $a_x=-1$ and $\sigma _x=b/d$ with $b=-0.1\lambda$.
Fig. 4.
Fig. 4. Horizontal cut ($y=0$) for the cases given in Fig. 3. Note the field levels both inside and outside of the lens region. As expected for gain GVP (dotted magenta) the field intensity is higher than lossless (approximately) VP case (solid blue) whereas the loss GVP (dash-dotted green) is lower than the same case. As the loss level of VP lens is increased, the field intensity inside and outside (dashed red) the slab quickly decays.

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

x ( x ) = { x if x 0 s x x if 0 x d x + ( s x 1 ) d if x d
[ Λ ] = diag { 1 / s x , s x , s x }
σ x = b / d for 0 x d ,
E = z ^ I 0 k 0 η 0 4 H 0 ( 1 ) ( k ρ ρ )
ρ = ( x x s ) 2 + ( y y s ) 2
E = [ S 1 ] T E
J = det ( [ S ] ) 1 [ S ] J
ρ = 0
x f 1 = x s + 2 d 1 , y f 1 = m [ x ( x f 1 ) ]
x f 2 = x s + 2 d , y f 2 = m [ x ( x f 2 ) ]

Metrics