Abstract

Luneburg lens is a marvellous optical lens but is extremely difficult to be applied in any practical antenna system due to its large spherical shape. In this paper, we propose a transformation that reduces the profile of the original Luneburg lens without affecting its unique properties. The new transformed slim lens is then discretized and simplified for a practical antenna application, where its properties were examined numerically. It is found that the transformed lens can be used to replace conventional antenna systems (i.e. Fabry-Perot resonant antennas) producing a high-directivity beam with low side-lobes. In addition, it provides excellent steering capabilities for wide angles, maintaining the directivity and side-lobes at high and low values respectively.

© 2011 OSA

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  1. G. V. Trentini, “Partially reflecting sheet arrays,” IRE Trans. Antennas Propag. 4, 666–671 (1956).
    [CrossRef]
  2. D. R. Jackson and N. G. Alexopoulos, “Gain Enhancement methods for printed circuit antennas,” IEEE Trans. Antennas Propag. 33, 976–987 (1985).
    [CrossRef]
  3. D. Jackson and A. Oliner, “A leaky-wave analysis of the high-gain printed antenna configuration,” IEEE Trans. Antennas Propag. 36, 905–910 (1988).
    [CrossRef]
  4. A. Feresidis and J. Vardaxoglou, “High gain planar antenna using optimised partially reflective surfaces,” IEE Proc. Microwaves, Antennas Propag. 148, 345–350 (2001).
    [CrossRef]
  5. Y. Lee, J. Yeo, R. Mittra, and W. Park, “Design of a high-directivity electromagnetic band gap resonator antenna using a frequency-selective surface superstrate,” Microwave Opt. Technol. Lett. 43, 462–467 (2004).
    [CrossRef]
  6. M. Thevenot, C. Cheype, A. Reineix, and B. Jecko, “Directive photonic-bandgap antennas,” IEEE Trans. Antennas Propag. 47, 2115–2122 (1999).
  7. C. Cheype, C. Serier, M. Thevenot, T. Monediere, A. Reineix, and B. Jecko, “An electromagnetic bandgap resonator antenna,” IEEE Trans. Antennas Propag. 50, 21285–21290 (2002).
    [CrossRef]
  8. A. Goncharov, M. Owner-Petersen, and D. Puryayev, “Intrinsic apodization effect in a compact two-mirror system with a spherical primary mirror,” Opt. Eng. 41, 3111–3115 (2002).
    [CrossRef]
  9. O. Guyon, “Phase-induced amplitude apodization of telescope pupils for extrasolar terrestrial planet imaging,” Astron. Astrophys. 404, 379–387 (2008).
    [CrossRef]
  10. R. Gardelli, M. Albani, and F. Capolino, “Array thinning by using antennas in a Fabry-Perot cavity for gain enhancement,” IEEE Trans. Antennas Propag. 54, 1979–1990 (2006).
    [CrossRef]
  11. A. Weily, K. Esselle, T. Bird, and B. Sanders, “Dual resonator 1-D EBG antenna with slot array feed for improved radiation bandwidth,” IET Microwave Antennas Propag. 1, 198–203 (2007).
    [CrossRef]
  12. G. Palikaras, A. Feresidis, and J. Vardaxoglou, “Cylindrical electromagnetic bandgap structures for directive base station antennas,” IEEE Antenna Wirel. Propag. Lett. 3, 87–89 (2004).
    [CrossRef]
  13. H. Boutayeb, T. Denidni, K. Mahdjoubi, A. Tarot, A. Sebak, and L. Talbi, “Analysis and design of a cylindrical EBG based directive antenna,” IEEE Trans. Antennas Propag. 54, 211–219 (2006).
    [CrossRef]
  14. A. Feresidis, M. Maragou, G. Palikaras, and J. Vardaxoglou, “Cylindrical-conformal resonant cavity antennas using passive periodic surfaces,” in International Conference on Electromagnetics in Advanced Applications (2007), pp. 165–168.
  15. Y. Hao, A. Alomainy, and C. Parini, “Antenna-beam shaping from offset defects in UC-EBG cavities,” Microwave Opt. Tech. Lett. 43, 108–111 (2004).
    [CrossRef]
  16. A. Ourir, S. Burokur, and A. de Lustrac, “Phase-varying metamaterial for compact steerable directive antennas,” Electron. Lett. 43, 493–494 (2007).
    [CrossRef]
  17. A. Ourir, S. Burokur, and A. de Lustrac, “Electronically reconfigurable metamaterial for compact directive cavity antennas,” Electron. Lett. 43, 698–700 (2007).
    [CrossRef]
  18. V. Veselago, “The electrodynamics of substances with simultaneously negative values of ɛ and μ,” Soviet Phys. Ups. 10, 509–514 (1968).
    [CrossRef]
  19. J. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
    [CrossRef] [PubMed]
  20. R. Shelby, D. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
    [CrossRef] [PubMed]
  21. J. Pendry, D. Schurig, and D. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
    [CrossRef] [PubMed]
  22. D. Schurig, J. Mock, B. Justice, S. Cummer, J. Pendry, A. Starr, and D. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
    [CrossRef] [PubMed]
  23. R. Luneburg, Mathematical Theory of Optics (Brown University, 1944).
  24. R. Ilinsky, “Gradient-index meniscus lens free of spherical aberration,” J. Opt. A: Pure Appl. Opt. 2, 449–451 (2000).
    [CrossRef]
  25. C. Argyropoulos, Y. Zhao, and Y. Hao, “A radially-dependent dispersive finite-difference time-domain method for the evaluation of electromagnetic cloaks,” IEEE Trans. Antennas Propag. 57, 1432–1441 (2009).
    [CrossRef]
  26. D. Schurig, “An aberration-free lens with zero f-number,” N. J. Phys. 10, 115034 (2008).
    [CrossRef]
  27. N. Kundtz and D. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9, 129–132 (2010).
    [CrossRef]

2010 (1)

N. Kundtz and D. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9, 129–132 (2010).
[CrossRef]

2009 (1)

C. Argyropoulos, Y. Zhao, and Y. Hao, “A radially-dependent dispersive finite-difference time-domain method for the evaluation of electromagnetic cloaks,” IEEE Trans. Antennas Propag. 57, 1432–1441 (2009).
[CrossRef]

2008 (2)

D. Schurig, “An aberration-free lens with zero f-number,” N. J. Phys. 10, 115034 (2008).
[CrossRef]

O. Guyon, “Phase-induced amplitude apodization of telescope pupils for extrasolar terrestrial planet imaging,” Astron. Astrophys. 404, 379–387 (2008).
[CrossRef]

2007 (3)

A. Weily, K. Esselle, T. Bird, and B. Sanders, “Dual resonator 1-D EBG antenna with slot array feed for improved radiation bandwidth,” IET Microwave Antennas Propag. 1, 198–203 (2007).
[CrossRef]

A. Ourir, S. Burokur, and A. de Lustrac, “Phase-varying metamaterial for compact steerable directive antennas,” Electron. Lett. 43, 493–494 (2007).
[CrossRef]

A. Ourir, S. Burokur, and A. de Lustrac, “Electronically reconfigurable metamaterial for compact directive cavity antennas,” Electron. Lett. 43, 698–700 (2007).
[CrossRef]

2006 (4)

H. Boutayeb, T. Denidni, K. Mahdjoubi, A. Tarot, A. Sebak, and L. Talbi, “Analysis and design of a cylindrical EBG based directive antenna,” IEEE Trans. Antennas Propag. 54, 211–219 (2006).
[CrossRef]

R. Gardelli, M. Albani, and F. Capolino, “Array thinning by using antennas in a Fabry-Perot cavity for gain enhancement,” IEEE Trans. Antennas Propag. 54, 1979–1990 (2006).
[CrossRef]

J. Pendry, D. Schurig, and D. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[CrossRef] [PubMed]

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

2004 (3)

G. Palikaras, A. Feresidis, and J. Vardaxoglou, “Cylindrical electromagnetic bandgap structures for directive base station antennas,” IEEE Antenna Wirel. Propag. Lett. 3, 87–89 (2004).
[CrossRef]

Y. Hao, A. Alomainy, and C. Parini, “Antenna-beam shaping from offset defects in UC-EBG cavities,” Microwave Opt. Tech. Lett. 43, 108–111 (2004).
[CrossRef]

Y. Lee, J. Yeo, R. Mittra, and W. Park, “Design of a high-directivity electromagnetic band gap resonator antenna using a frequency-selective surface superstrate,” Microwave Opt. Technol. Lett. 43, 462–467 (2004).
[CrossRef]

2002 (2)

C. Cheype, C. Serier, M. Thevenot, T. Monediere, A. Reineix, and B. Jecko, “An electromagnetic bandgap resonator antenna,” IEEE Trans. Antennas Propag. 50, 21285–21290 (2002).
[CrossRef]

A. Goncharov, M. Owner-Petersen, and D. Puryayev, “Intrinsic apodization effect in a compact two-mirror system with a spherical primary mirror,” Opt. Eng. 41, 3111–3115 (2002).
[CrossRef]

2001 (2)

A. Feresidis and J. Vardaxoglou, “High gain planar antenna using optimised partially reflective surfaces,” IEE Proc. Microwaves, Antennas Propag. 148, 345–350 (2001).
[CrossRef]

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

2000 (2)

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

R. Ilinsky, “Gradient-index meniscus lens free of spherical aberration,” J. Opt. A: Pure Appl. Opt. 2, 449–451 (2000).
[CrossRef]

1999 (1)

M. Thevenot, C. Cheype, A. Reineix, and B. Jecko, “Directive photonic-bandgap antennas,” IEEE Trans. Antennas Propag. 47, 2115–2122 (1999).

1988 (1)

D. Jackson and A. Oliner, “A leaky-wave analysis of the high-gain printed antenna configuration,” IEEE Trans. Antennas Propag. 36, 905–910 (1988).
[CrossRef]

1985 (1)

D. R. Jackson and N. G. Alexopoulos, “Gain Enhancement methods for printed circuit antennas,” IEEE Trans. Antennas Propag. 33, 976–987 (1985).
[CrossRef]

1968 (1)

V. Veselago, “The electrodynamics of substances with simultaneously negative values of ɛ and μ,” Soviet Phys. Ups. 10, 509–514 (1968).
[CrossRef]

1956 (1)

G. V. Trentini, “Partially reflecting sheet arrays,” IRE Trans. Antennas Propag. 4, 666–671 (1956).
[CrossRef]

Albani, M.

R. Gardelli, M. Albani, and F. Capolino, “Array thinning by using antennas in a Fabry-Perot cavity for gain enhancement,” IEEE Trans. Antennas Propag. 54, 1979–1990 (2006).
[CrossRef]

Alexopoulos, N. G.

D. R. Jackson and N. G. Alexopoulos, “Gain Enhancement methods for printed circuit antennas,” IEEE Trans. Antennas Propag. 33, 976–987 (1985).
[CrossRef]

Alomainy, A.

Y. Hao, A. Alomainy, and C. Parini, “Antenna-beam shaping from offset defects in UC-EBG cavities,” Microwave Opt. Tech. Lett. 43, 108–111 (2004).
[CrossRef]

Argyropoulos, C.

C. Argyropoulos, Y. Zhao, and Y. Hao, “A radially-dependent dispersive finite-difference time-domain method for the evaluation of electromagnetic cloaks,” IEEE Trans. Antennas Propag. 57, 1432–1441 (2009).
[CrossRef]

Bird, T.

A. Weily, K. Esselle, T. Bird, and B. Sanders, “Dual resonator 1-D EBG antenna with slot array feed for improved radiation bandwidth,” IET Microwave Antennas Propag. 1, 198–203 (2007).
[CrossRef]

Boutayeb, H.

H. Boutayeb, T. Denidni, K. Mahdjoubi, A. Tarot, A. Sebak, and L. Talbi, “Analysis and design of a cylindrical EBG based directive antenna,” IEEE Trans. Antennas Propag. 54, 211–219 (2006).
[CrossRef]

Burokur, S.

A. Ourir, S. Burokur, and A. de Lustrac, “Phase-varying metamaterial for compact steerable directive antennas,” Electron. Lett. 43, 493–494 (2007).
[CrossRef]

A. Ourir, S. Burokur, and A. de Lustrac, “Electronically reconfigurable metamaterial for compact directive cavity antennas,” Electron. Lett. 43, 698–700 (2007).
[CrossRef]

Capolino, F.

R. Gardelli, M. Albani, and F. Capolino, “Array thinning by using antennas in a Fabry-Perot cavity for gain enhancement,” IEEE Trans. Antennas Propag. 54, 1979–1990 (2006).
[CrossRef]

Cheype, C.

C. Cheype, C. Serier, M. Thevenot, T. Monediere, A. Reineix, and B. Jecko, “An electromagnetic bandgap resonator antenna,” IEEE Trans. Antennas Propag. 50, 21285–21290 (2002).
[CrossRef]

M. Thevenot, C. Cheype, A. Reineix, and B. Jecko, “Directive photonic-bandgap antennas,” IEEE Trans. Antennas Propag. 47, 2115–2122 (1999).

Cummer, S.

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

de Lustrac, A.

A. Ourir, S. Burokur, and A. de Lustrac, “Electronically reconfigurable metamaterial for compact directive cavity antennas,” Electron. Lett. 43, 698–700 (2007).
[CrossRef]

A. Ourir, S. Burokur, and A. de Lustrac, “Phase-varying metamaterial for compact steerable directive antennas,” Electron. Lett. 43, 493–494 (2007).
[CrossRef]

Denidni, T.

H. Boutayeb, T. Denidni, K. Mahdjoubi, A. Tarot, A. Sebak, and L. Talbi, “Analysis and design of a cylindrical EBG based directive antenna,” IEEE Trans. Antennas Propag. 54, 211–219 (2006).
[CrossRef]

Esselle, K.

A. Weily, K. Esselle, T. Bird, and B. Sanders, “Dual resonator 1-D EBG antenna with slot array feed for improved radiation bandwidth,” IET Microwave Antennas Propag. 1, 198–203 (2007).
[CrossRef]

Feresidis, A.

G. Palikaras, A. Feresidis, and J. Vardaxoglou, “Cylindrical electromagnetic bandgap structures for directive base station antennas,” IEEE Antenna Wirel. Propag. Lett. 3, 87–89 (2004).
[CrossRef]

A. Feresidis and J. Vardaxoglou, “High gain planar antenna using optimised partially reflective surfaces,” IEE Proc. Microwaves, Antennas Propag. 148, 345–350 (2001).
[CrossRef]

A. Feresidis, M. Maragou, G. Palikaras, and J. Vardaxoglou, “Cylindrical-conformal resonant cavity antennas using passive periodic surfaces,” in International Conference on Electromagnetics in Advanced Applications (2007), pp. 165–168.

Gardelli, R.

R. Gardelli, M. Albani, and F. Capolino, “Array thinning by using antennas in a Fabry-Perot cavity for gain enhancement,” IEEE Trans. Antennas Propag. 54, 1979–1990 (2006).
[CrossRef]

Goncharov, A.

A. Goncharov, M. Owner-Petersen, and D. Puryayev, “Intrinsic apodization effect in a compact two-mirror system with a spherical primary mirror,” Opt. Eng. 41, 3111–3115 (2002).
[CrossRef]

Guyon, O.

O. Guyon, “Phase-induced amplitude apodization of telescope pupils for extrasolar terrestrial planet imaging,” Astron. Astrophys. 404, 379–387 (2008).
[CrossRef]

Hao, Y.

C. Argyropoulos, Y. Zhao, and Y. Hao, “A radially-dependent dispersive finite-difference time-domain method for the evaluation of electromagnetic cloaks,” IEEE Trans. Antennas Propag. 57, 1432–1441 (2009).
[CrossRef]

Y. Hao, A. Alomainy, and C. Parini, “Antenna-beam shaping from offset defects in UC-EBG cavities,” Microwave Opt. Tech. Lett. 43, 108–111 (2004).
[CrossRef]

Ilinsky, R.

R. Ilinsky, “Gradient-index meniscus lens free of spherical aberration,” J. Opt. A: Pure Appl. Opt. 2, 449–451 (2000).
[CrossRef]

Jackson, D.

D. Jackson and A. Oliner, “A leaky-wave analysis of the high-gain printed antenna configuration,” IEEE Trans. Antennas Propag. 36, 905–910 (1988).
[CrossRef]

Jackson, D. R.

D. R. Jackson and N. G. Alexopoulos, “Gain Enhancement methods for printed circuit antennas,” IEEE Trans. Antennas Propag. 33, 976–987 (1985).
[CrossRef]

Jecko, B.

C. Cheype, C. Serier, M. Thevenot, T. Monediere, A. Reineix, and B. Jecko, “An electromagnetic bandgap resonator antenna,” IEEE Trans. Antennas Propag. 50, 21285–21290 (2002).
[CrossRef]

M. Thevenot, C. Cheype, A. Reineix, and B. Jecko, “Directive photonic-bandgap antennas,” IEEE Trans. Antennas Propag. 47, 2115–2122 (1999).

Justice, B.

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

Kundtz, N.

N. Kundtz and D. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9, 129–132 (2010).
[CrossRef]

Lee, Y.

Y. Lee, J. Yeo, R. Mittra, and W. Park, “Design of a high-directivity electromagnetic band gap resonator antenna using a frequency-selective surface superstrate,” Microwave Opt. Technol. Lett. 43, 462–467 (2004).
[CrossRef]

Luneburg, R.

R. Luneburg, Mathematical Theory of Optics (Brown University, 1944).

Mahdjoubi, K.

H. Boutayeb, T. Denidni, K. Mahdjoubi, A. Tarot, A. Sebak, and L. Talbi, “Analysis and design of a cylindrical EBG based directive antenna,” IEEE Trans. Antennas Propag. 54, 211–219 (2006).
[CrossRef]

Maragou, M.

A. Feresidis, M. Maragou, G. Palikaras, and J. Vardaxoglou, “Cylindrical-conformal resonant cavity antennas using passive periodic surfaces,” in International Conference on Electromagnetics in Advanced Applications (2007), pp. 165–168.

Mittra, R.

Y. Lee, J. Yeo, R. Mittra, and W. Park, “Design of a high-directivity electromagnetic band gap resonator antenna using a frequency-selective surface superstrate,” Microwave Opt. Technol. Lett. 43, 462–467 (2004).
[CrossRef]

Mock, J.

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

Monediere, T.

C. Cheype, C. Serier, M. Thevenot, T. Monediere, A. Reineix, and B. Jecko, “An electromagnetic bandgap resonator antenna,” IEEE Trans. Antennas Propag. 50, 21285–21290 (2002).
[CrossRef]

Oliner, A.

D. Jackson and A. Oliner, “A leaky-wave analysis of the high-gain printed antenna configuration,” IEEE Trans. Antennas Propag. 36, 905–910 (1988).
[CrossRef]

Ourir, A.

A. Ourir, S. Burokur, and A. de Lustrac, “Phase-varying metamaterial for compact steerable directive antennas,” Electron. Lett. 43, 493–494 (2007).
[CrossRef]

A. Ourir, S. Burokur, and A. de Lustrac, “Electronically reconfigurable metamaterial for compact directive cavity antennas,” Electron. Lett. 43, 698–700 (2007).
[CrossRef]

Owner-Petersen, M.

A. Goncharov, M. Owner-Petersen, and D. Puryayev, “Intrinsic apodization effect in a compact two-mirror system with a spherical primary mirror,” Opt. Eng. 41, 3111–3115 (2002).
[CrossRef]

Palikaras, G.

G. Palikaras, A. Feresidis, and J. Vardaxoglou, “Cylindrical electromagnetic bandgap structures for directive base station antennas,” IEEE Antenna Wirel. Propag. Lett. 3, 87–89 (2004).
[CrossRef]

A. Feresidis, M. Maragou, G. Palikaras, and J. Vardaxoglou, “Cylindrical-conformal resonant cavity antennas using passive periodic surfaces,” in International Conference on Electromagnetics in Advanced Applications (2007), pp. 165–168.

Parini, C.

Y. Hao, A. Alomainy, and C. Parini, “Antenna-beam shaping from offset defects in UC-EBG cavities,” Microwave Opt. Tech. Lett. 43, 108–111 (2004).
[CrossRef]

Park, W.

Y. Lee, J. Yeo, R. Mittra, and W. Park, “Design of a high-directivity electromagnetic band gap resonator antenna using a frequency-selective surface superstrate,” Microwave Opt. Technol. Lett. 43, 462–467 (2004).
[CrossRef]

Pendry, J.

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

J. Pendry, D. Schurig, and D. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[CrossRef] [PubMed]

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

Puryayev, D.

A. Goncharov, M. Owner-Petersen, and D. Puryayev, “Intrinsic apodization effect in a compact two-mirror system with a spherical primary mirror,” Opt. Eng. 41, 3111–3115 (2002).
[CrossRef]

Reineix, A.

C. Cheype, C. Serier, M. Thevenot, T. Monediere, A. Reineix, and B. Jecko, “An electromagnetic bandgap resonator antenna,” IEEE Trans. Antennas Propag. 50, 21285–21290 (2002).
[CrossRef]

M. Thevenot, C. Cheype, A. Reineix, and B. Jecko, “Directive photonic-bandgap antennas,” IEEE Trans. Antennas Propag. 47, 2115–2122 (1999).

Sanders, B.

A. Weily, K. Esselle, T. Bird, and B. Sanders, “Dual resonator 1-D EBG antenna with slot array feed for improved radiation bandwidth,” IET Microwave Antennas Propag. 1, 198–203 (2007).
[CrossRef]

Schultz, S.

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

Schurig, D.

D. Schurig, “An aberration-free lens with zero f-number,” N. J. Phys. 10, 115034 (2008).
[CrossRef]

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

J. Pendry, D. Schurig, and D. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[CrossRef] [PubMed]

Sebak, A.

H. Boutayeb, T. Denidni, K. Mahdjoubi, A. Tarot, A. Sebak, and L. Talbi, “Analysis and design of a cylindrical EBG based directive antenna,” IEEE Trans. Antennas Propag. 54, 211–219 (2006).
[CrossRef]

Serier, C.

C. Cheype, C. Serier, M. Thevenot, T. Monediere, A. Reineix, and B. Jecko, “An electromagnetic bandgap resonator antenna,” IEEE Trans. Antennas Propag. 50, 21285–21290 (2002).
[CrossRef]

Shelby, R.

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

Smith, D.

N. Kundtz and D. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9, 129–132 (2010).
[CrossRef]

J. Pendry, D. Schurig, and D. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[CrossRef] [PubMed]

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

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

Starr, A.

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

Talbi, L.

H. Boutayeb, T. Denidni, K. Mahdjoubi, A. Tarot, A. Sebak, and L. Talbi, “Analysis and design of a cylindrical EBG based directive antenna,” IEEE Trans. Antennas Propag. 54, 211–219 (2006).
[CrossRef]

Tarot, A.

H. Boutayeb, T. Denidni, K. Mahdjoubi, A. Tarot, A. Sebak, and L. Talbi, “Analysis and design of a cylindrical EBG based directive antenna,” IEEE Trans. Antennas Propag. 54, 211–219 (2006).
[CrossRef]

Thevenot, M.

C. Cheype, C. Serier, M. Thevenot, T. Monediere, A. Reineix, and B. Jecko, “An electromagnetic bandgap resonator antenna,” IEEE Trans. Antennas Propag. 50, 21285–21290 (2002).
[CrossRef]

M. Thevenot, C. Cheype, A. Reineix, and B. Jecko, “Directive photonic-bandgap antennas,” IEEE Trans. Antennas Propag. 47, 2115–2122 (1999).

Trentini, G. V.

G. V. Trentini, “Partially reflecting sheet arrays,” IRE Trans. Antennas Propag. 4, 666–671 (1956).
[CrossRef]

Vardaxoglou, J.

G. Palikaras, A. Feresidis, and J. Vardaxoglou, “Cylindrical electromagnetic bandgap structures for directive base station antennas,” IEEE Antenna Wirel. Propag. Lett. 3, 87–89 (2004).
[CrossRef]

A. Feresidis and J. Vardaxoglou, “High gain planar antenna using optimised partially reflective surfaces,” IEE Proc. Microwaves, Antennas Propag. 148, 345–350 (2001).
[CrossRef]

A. Feresidis, M. Maragou, G. Palikaras, and J. Vardaxoglou, “Cylindrical-conformal resonant cavity antennas using passive periodic surfaces,” in International Conference on Electromagnetics in Advanced Applications (2007), pp. 165–168.

Veselago, V.

V. Veselago, “The electrodynamics of substances with simultaneously negative values of ɛ and μ,” Soviet Phys. Ups. 10, 509–514 (1968).
[CrossRef]

Weily, A.

A. Weily, K. Esselle, T. Bird, and B. Sanders, “Dual resonator 1-D EBG antenna with slot array feed for improved radiation bandwidth,” IET Microwave Antennas Propag. 1, 198–203 (2007).
[CrossRef]

Yeo, J.

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Figures (8)

Fig. 1
Fig. 1

For R ∼ 13λ, (a) ɛ(r) for the conventional Luneburg lens. (b) Field configuration for a conventional Luneburg lens with a point source at (−R,0) and (c) with a point source at (−Rcos(π/4), −Rcos(π/4)). (d)ɛ′ for the transformed slim Luneburg lens for δ = 6. (e) field configuration for the slim Luneburg lens for a point source excited at (R/6,0) and (f) at (R/6,−0.5R).

Fig. 2
Fig. 2

For Rλ, field configurations for the slim Luneburg lens (a) for a point source excited at (R/6,0), (b) (R/6,−R/2) (c) (R/2,0) and (d)(R/2,−R/2).

Fig. 3
Fig. 3

(a)The cross-section of the antenna system set-up. (b) The yz-cross-section of the discretized lens showing the dielectric layers and dimensions. (c)The maximum directivity (red square dots), the FSLL (first side lobe level) for ϕ = 0° (green x-points) and for ϕ = 90° (blue star-point) plotted against the distance b from the patch antenna, where FSLL = DfirstsidelobeDmainlobe.

Fig. 4
Fig. 4

|E|2 along the optical axes of the lens for different levels of discretization (i.e. number of layers), when the lens is illuminated with a plane wave. The set-up of the lens is identical to Fig. 2, where the lens’s centre is at the origin point and the plane wave is incident from the right towards the left.

Fig. 5
Fig. 5

The directivity pattern for (a) ϕ = 0° and (b)ϕ = 90°, plotted against θ for various values of b.

Fig. 6
Fig. 6

The directivity pattern for (a) ϕ = 0° and (b)ϕ = 90°, plotted against θ for various values of c.

Fig. 7
Fig. 7

(a)The directivity and steered angle of the main lobe plotted against c for b = 31mm. (b) The FSLL for ϕ = 0° and ϕ = 90°, and steered angle plotted against c for b = 31mm.

Fig. 8
Fig. 8

The Ex-field for b = 31mm and (a)c = 0mm, (b)c = 2mm, (c) c = 4mm, (d) c = 6mm, (e) c = 10mm, (f) c = 16mm, (g) c = 20mm and (h) c = 24mm.

Tables (1)

Tables Icon

Table 1 The dimensions of the discretized lens, as they were used for the CST Microwave Studio simulations, where ɛ is the dielectric permittivity of each layer, Ry and Rz are defined in Fig. 3(b).

Equations (5)

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

ɛ ( r ) = 2 r 2 R 2 = n 2 ( r )
y = y z = z / δ
ɛ = ɛ ( 1 / δ 0 0 δ ) = ( 2 y 2 + ( δ z ) 2 R 2 ) ( 1 / δ 0 0 δ )
μ = ( 1 / δ 0 0 δ )
ɛ = ɛ z z = δ ( 2 y 2 + ( δ z ) 2 R 2 )

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