Abstract

A modified Luneburg lens based on Hamiltonian optical transformation with planar feeds is proposed in this Letter. The lens, made of conventional all-dielectric materials, does not have any kind of anisotropy. Therefore, in theory, its bandwidth of operation has no upper frequency limitations in contrast with recent designs utilizing metamaterials. Results for wide-angle radiation and broadband operation are presented.

© 2012 Optical Society of America

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References

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  1. R. Luneburg, Mathematical Theory of Optics (Brown University, 1944).
  2. R. Ilinsky, J. Opt. A 2, 449 (2000).
    [CrossRef]
  3. A. Demetriadou and Y. Hao, Opt. Express 19, 19925(2011).
    [CrossRef]
  4. A. S. Gutman, J. Appl. Phys. 25, 855 (1954).
    [CrossRef]
  5. N. Kundtz and D. R. Smith, Nat. Mater. 9, 129 (2010).
    [CrossRef]
  6. R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, Science 323, 366 (2009).
    [CrossRef]
  7. A. Demetriadou and Y. Hao, IEEE Antennas Wireless Propag. Lett. 10, 1590 (2011).
  8. Y. Zhao, C. Argyropoulos, and Y. Hao, Opt. Express 16, 6717 (2008).
    [CrossRef]
  9. Y. Hao and R. Mittra, FDTD Modeling of Metamaterials: Theory and Applications (Artech House, 2008).
  10. B. Nistad and J. Skaar, Phys. Rev. E 78, 036603(2008).
    [CrossRef]
  11. K. Palmer, IEEE Spectrum 49, 13 (2012).
    [CrossRef]
  12. S. Tretyakov and S. Maslovski, IEEE Antennas Propag. Mag. 49, 37 (2007).
    [CrossRef]
  13. K. Z. Rajab, Y. Hao, D. Bao, C. G. Parini, J. Vazquez, and M. Philippakis, J. Appl. Phys. 108, 054904 (2010).
    [CrossRef]
  14. S. Hrabar, I. Krois, I. Bonic, and A. Kiricenko, Appl. Phys. Lett. 99, 254103 (2011).
    [CrossRef]

2012 (1)

K. Palmer, IEEE Spectrum 49, 13 (2012).
[CrossRef]

2011 (3)

A. Demetriadou and Y. Hao, IEEE Antennas Wireless Propag. Lett. 10, 1590 (2011).

A. Demetriadou and Y. Hao, Opt. Express 19, 19925(2011).
[CrossRef]

S. Hrabar, I. Krois, I. Bonic, and A. Kiricenko, Appl. Phys. Lett. 99, 254103 (2011).
[CrossRef]

2010 (2)

K. Z. Rajab, Y. Hao, D. Bao, C. G. Parini, J. Vazquez, and M. Philippakis, J. Appl. Phys. 108, 054904 (2010).
[CrossRef]

N. Kundtz and D. R. Smith, Nat. Mater. 9, 129 (2010).
[CrossRef]

2009 (1)

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, Science 323, 366 (2009).
[CrossRef]

2008 (2)

2007 (1)

S. Tretyakov and S. Maslovski, IEEE Antennas Propag. Mag. 49, 37 (2007).
[CrossRef]

2000 (1)

R. Ilinsky, J. Opt. A 2, 449 (2000).
[CrossRef]

1954 (1)

A. S. Gutman, J. Appl. Phys. 25, 855 (1954).
[CrossRef]

Argyropoulos, C.

Bao, D.

K. Z. Rajab, Y. Hao, D. Bao, C. G. Parini, J. Vazquez, and M. Philippakis, J. Appl. Phys. 108, 054904 (2010).
[CrossRef]

Bonic, I.

S. Hrabar, I. Krois, I. Bonic, and A. Kiricenko, Appl. Phys. Lett. 99, 254103 (2011).
[CrossRef]

Chin, J. Y.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, Science 323, 366 (2009).
[CrossRef]

Cui, T. J.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, Science 323, 366 (2009).
[CrossRef]

Demetriadou, A.

A. Demetriadou and Y. Hao, IEEE Antennas Wireless Propag. Lett. 10, 1590 (2011).

A. Demetriadou and Y. Hao, Opt. Express 19, 19925(2011).
[CrossRef]

Gutman, A. S.

A. S. Gutman, J. Appl. Phys. 25, 855 (1954).
[CrossRef]

Hao, Y.

A. Demetriadou and Y. Hao, Opt. Express 19, 19925(2011).
[CrossRef]

A. Demetriadou and Y. Hao, IEEE Antennas Wireless Propag. Lett. 10, 1590 (2011).

K. Z. Rajab, Y. Hao, D. Bao, C. G. Parini, J. Vazquez, and M. Philippakis, J. Appl. Phys. 108, 054904 (2010).
[CrossRef]

Y. Zhao, C. Argyropoulos, and Y. Hao, Opt. Express 16, 6717 (2008).
[CrossRef]

Y. Hao and R. Mittra, FDTD Modeling of Metamaterials: Theory and Applications (Artech House, 2008).

Hrabar, S.

S. Hrabar, I. Krois, I. Bonic, and A. Kiricenko, Appl. Phys. Lett. 99, 254103 (2011).
[CrossRef]

Ilinsky, R.

R. Ilinsky, J. Opt. A 2, 449 (2000).
[CrossRef]

Ji, C.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, Science 323, 366 (2009).
[CrossRef]

Kiricenko, A.

S. Hrabar, I. Krois, I. Bonic, and A. Kiricenko, Appl. Phys. Lett. 99, 254103 (2011).
[CrossRef]

Krois, I.

S. Hrabar, I. Krois, I. Bonic, and A. Kiricenko, Appl. Phys. Lett. 99, 254103 (2011).
[CrossRef]

Kundtz, N.

N. Kundtz and D. R. Smith, Nat. Mater. 9, 129 (2010).
[CrossRef]

Liu, R.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, Science 323, 366 (2009).
[CrossRef]

Luneburg, R.

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

Maslovski, S.

S. Tretyakov and S. Maslovski, IEEE Antennas Propag. Mag. 49, 37 (2007).
[CrossRef]

Mittra, R.

Y. Hao and R. Mittra, FDTD Modeling of Metamaterials: Theory and Applications (Artech House, 2008).

Mock, J. J.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, Science 323, 366 (2009).
[CrossRef]

Nistad, B.

B. Nistad and J. Skaar, Phys. Rev. E 78, 036603(2008).
[CrossRef]

Palmer, K.

K. Palmer, IEEE Spectrum 49, 13 (2012).
[CrossRef]

Parini, C. G.

K. Z. Rajab, Y. Hao, D. Bao, C. G. Parini, J. Vazquez, and M. Philippakis, J. Appl. Phys. 108, 054904 (2010).
[CrossRef]

Philippakis, M.

K. Z. Rajab, Y. Hao, D. Bao, C. G. Parini, J. Vazquez, and M. Philippakis, J. Appl. Phys. 108, 054904 (2010).
[CrossRef]

Rajab, K. Z.

K. Z. Rajab, Y. Hao, D. Bao, C. G. Parini, J. Vazquez, and M. Philippakis, J. Appl. Phys. 108, 054904 (2010).
[CrossRef]

Skaar, J.

B. Nistad and J. Skaar, Phys. Rev. E 78, 036603(2008).
[CrossRef]

Smith, D. R.

N. Kundtz and D. R. Smith, Nat. Mater. 9, 129 (2010).
[CrossRef]

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, Science 323, 366 (2009).
[CrossRef]

Tretyakov, S.

S. Tretyakov and S. Maslovski, IEEE Antennas Propag. Mag. 49, 37 (2007).
[CrossRef]

Vazquez, J.

K. Z. Rajab, Y. Hao, D. Bao, C. G. Parini, J. Vazquez, and M. Philippakis, J. Appl. Phys. 108, 054904 (2010).
[CrossRef]

Zhao, Y.

Appl. Phys. Lett. (1)

S. Hrabar, I. Krois, I. Bonic, and A. Kiricenko, Appl. Phys. Lett. 99, 254103 (2011).
[CrossRef]

IEEE Antennas Propag. Mag. (1)

S. Tretyakov and S. Maslovski, IEEE Antennas Propag. Mag. 49, 37 (2007).
[CrossRef]

IEEE Antennas Wireless Propag. Lett. (1)

A. Demetriadou and Y. Hao, IEEE Antennas Wireless Propag. Lett. 10, 1590 (2011).

IEEE Spectrum (1)

K. Palmer, IEEE Spectrum 49, 13 (2012).
[CrossRef]

J. Appl. Phys. (2)

K. Z. Rajab, Y. Hao, D. Bao, C. G. Parini, J. Vazquez, and M. Philippakis, J. Appl. Phys. 108, 054904 (2010).
[CrossRef]

A. S. Gutman, J. Appl. Phys. 25, 855 (1954).
[CrossRef]

J. Opt. A (1)

R. Ilinsky, J. Opt. A 2, 449 (2000).
[CrossRef]

Nat. Mater. (1)

N. Kundtz and D. R. Smith, Nat. Mater. 9, 129 (2010).
[CrossRef]

Opt. Express (2)

Phys. Rev. E (1)

B. Nistad and J. Skaar, Phys. Rev. E 78, 036603(2008).
[CrossRef]

Science (1)

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, Science 323, 366 (2009).
[CrossRef]

Other (2)

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

Y. Hao and R. Mittra, FDTD Modeling of Metamaterials: Theory and Applications (Artech House, 2008).

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Figures (4)

Fig. 1.
Fig. 1.

(a),(b) Conventional Luneburg lens: (a) 2D permittivity map of a Luneburg lens following the expression of Eq. (1) when R=3λ; (b) normalized field distribution in the Luneburg lens when it is fed from one of its edges with a normal line source. (c),(d) Modified Luneburg lens: (c) 2D permittivity map of a Luneburg lens following the expression of Eq. (2) when R=3λ and f=R/2; (d) normalized field distribution in the modified Luneburg lens when it is fed with a normal line source in its focal point.

Fig. 2.
Fig. 2.

(a) 2D permittivity map of a modified Luneburg lens with a planar shape of feeding after eight layers discretization, with R=3.33λ and f=0.25R. (b)–(f) Ez component at 10 GHz for different positions of the feeding (x0=0mm to x0=30mm).

Fig. 3.
Fig. 3.

Ez component at different frequencies for two positions of the feeding (x0=0mm and x0=25mm).

Fig. 4.
Fig. 4.

(a),(b) CST Microwave Studio simulation of normalized electric far field at two different frequencies (10 and 21 GHz) for two positions of the feeding in the proposed modified Luneburg lens and the one presented in [5]. The discretization is 15 layers for the lens presented in [5] and only eight layers for the proposed modified Luneburg lens. (c) Electric field distribution for a 2D in-house FDTD simulation at 10 GHz for the proposed modified Luneburg lens and the one presented in [5] for two positions of the feeding. Different simulations are presented: continuous variation of the dielectric map, including or not materials with ϵr1, and discretized maps (15 layers for the case of [5]).

Equations (2)

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ϵr=2(rR)2
ϵr=1+(fR)2(rR)2(fR)2,

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