Abstract

A plano–concave lens with source-tailored geometric profile and transformational gradient index is proposed for broadband illumination. Such a design, capable of focusing and collimating the electromagnetic fields, fulfils the functionality of a converging lens and can also achieve a steerable beam and multiple beams efficiently. Nonresonant synthesis with a perforated dielectric plate and dielectric rod arrays is demonstrated for the lensing realization, promising a wide operating frequency band in the practical implementation.

© 2013 Optical Society of America

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  1. J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
    [CrossRef]
  2. R. Yang, W. X. Tang, Y. Hao, and I. Youngs, IEEE Antennas Wirel. Propag. Lett. 10, 99 (2011).
    [CrossRef]
  3. R. Yang, W. X. Tang, and Y. Hao, IEEE Antennas Wirel. Propag. Lett. 10, 1290 (2011).
    [CrossRef]
  4. R. Yang, W. X. Tang, and Y. Hao, Opt. Express 19, 12348 (2011).
    [CrossRef]
  5. W. E. Kock, Proc. IRE 34, 828 (1946).
    [CrossRef]
  6. C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Taniliean, and D. C. Vier, Appl. Phys. Lett. 84, 3232 (2004).
    [CrossRef]
  7. P. Vodo, P. V. Parimi, W. T. Lu, and S. Sridhar, Appl. Phys. Lett. 86, 201108 (2005).
    [CrossRef]
  8. M. Beruete, M. Navarro-Cia, M. Soralla, and I. Campillo, Opt. Express 16, 9677 (2008).
    [CrossRef]
  9. I. M. Ehrenberg, S. E. Sarma, and B. I. Wu, J. Appl. Phys. 112, 073114 (2012).
    [CrossRef]
  10. M. Navarro-Cia, M. Beruette, M. Sorolla, and N. Engheta, Phys. Rev. B 86, 165130 (2012).
    [CrossRef]
  11. J. Li and J. B. Pendry, Phys. Rev. Lett. 101, 203901 (2008).
    [CrossRef]
  12. J. D. Kraus and R. J. Marhefka, Antennas: For All Applications, 3rd ed. (McGraw-Hill, 2002).
  13. D. Schurig, J. B. Pendry, and D. R. Smith, Opt. Express 14, 9794 (2006).
    [CrossRef]

2012

I. M. Ehrenberg, S. E. Sarma, and B. I. Wu, J. Appl. Phys. 112, 073114 (2012).
[CrossRef]

M. Navarro-Cia, M. Beruette, M. Sorolla, and N. Engheta, Phys. Rev. B 86, 165130 (2012).
[CrossRef]

2011

R. Yang, W. X. Tang, Y. Hao, and I. Youngs, IEEE Antennas Wirel. Propag. Lett. 10, 99 (2011).
[CrossRef]

R. Yang, W. X. Tang, and Y. Hao, IEEE Antennas Wirel. Propag. Lett. 10, 1290 (2011).
[CrossRef]

R. Yang, W. X. Tang, and Y. Hao, Opt. Express 19, 12348 (2011).
[CrossRef]

2008

2006

D. Schurig, J. B. Pendry, and D. R. Smith, Opt. Express 14, 9794 (2006).
[CrossRef]

J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
[CrossRef]

2005

P. Vodo, P. V. Parimi, W. T. Lu, and S. Sridhar, Appl. Phys. Lett. 86, 201108 (2005).
[CrossRef]

2004

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Taniliean, and D. C. Vier, Appl. Phys. Lett. 84, 3232 (2004).
[CrossRef]

1946

W. E. Kock, Proc. IRE 34, 828 (1946).
[CrossRef]

Beruete, M.

Beruette, M.

M. Navarro-Cia, M. Beruette, M. Sorolla, and N. Engheta, Phys. Rev. B 86, 165130 (2012).
[CrossRef]

Campillo, I.

Ehrenberg, I. M.

I. M. Ehrenberg, S. E. Sarma, and B. I. Wu, J. Appl. Phys. 112, 073114 (2012).
[CrossRef]

Engheta, N.

M. Navarro-Cia, M. Beruette, M. Sorolla, and N. Engheta, Phys. Rev. B 86, 165130 (2012).
[CrossRef]

Greegor, R. B.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Taniliean, and D. C. Vier, Appl. Phys. Lett. 84, 3232 (2004).
[CrossRef]

Hao, Y.

R. Yang, W. X. Tang, and Y. Hao, Opt. Express 19, 12348 (2011).
[CrossRef]

R. Yang, W. X. Tang, Y. Hao, and I. Youngs, IEEE Antennas Wirel. Propag. Lett. 10, 99 (2011).
[CrossRef]

R. Yang, W. X. Tang, and Y. Hao, IEEE Antennas Wirel. Propag. Lett. 10, 1290 (2011).
[CrossRef]

Kock, W. E.

W. E. Kock, Proc. IRE 34, 828 (1946).
[CrossRef]

Kraus, J. D.

J. D. Kraus and R. J. Marhefka, Antennas: For All Applications, 3rd ed. (McGraw-Hill, 2002).

Li, J.

J. Li and J. B. Pendry, Phys. Rev. Lett. 101, 203901 (2008).
[CrossRef]

Li, K.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Taniliean, and D. C. Vier, Appl. Phys. Lett. 84, 3232 (2004).
[CrossRef]

Lu, W. T.

P. Vodo, P. V. Parimi, W. T. Lu, and S. Sridhar, Appl. Phys. Lett. 86, 201108 (2005).
[CrossRef]

Marhefka, R. J.

J. D. Kraus and R. J. Marhefka, Antennas: For All Applications, 3rd ed. (McGraw-Hill, 2002).

Navarro-Cia, M.

M. Navarro-Cia, M. Beruette, M. Sorolla, and N. Engheta, Phys. Rev. B 86, 165130 (2012).
[CrossRef]

M. Beruete, M. Navarro-Cia, M. Soralla, and I. Campillo, Opt. Express 16, 9677 (2008).
[CrossRef]

Nielsen, J. A.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Taniliean, and D. C. Vier, Appl. Phys. Lett. 84, 3232 (2004).
[CrossRef]

Parazzoli, C. G.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Taniliean, and D. C. Vier, Appl. Phys. Lett. 84, 3232 (2004).
[CrossRef]

Parimi, P. V.

P. Vodo, P. V. Parimi, W. T. Lu, and S. Sridhar, Appl. Phys. Lett. 86, 201108 (2005).
[CrossRef]

Pendry, J. B.

J. Li and J. B. Pendry, Phys. Rev. Lett. 101, 203901 (2008).
[CrossRef]

J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
[CrossRef]

D. Schurig, J. B. Pendry, and D. R. Smith, Opt. Express 14, 9794 (2006).
[CrossRef]

Sarma, S. E.

I. M. Ehrenberg, S. E. Sarma, and B. I. Wu, J. Appl. Phys. 112, 073114 (2012).
[CrossRef]

Schurig, D.

D. Schurig, J. B. Pendry, and D. R. Smith, Opt. Express 14, 9794 (2006).
[CrossRef]

J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
[CrossRef]

Smith, D. R.

J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
[CrossRef]

D. Schurig, J. B. Pendry, and D. R. Smith, Opt. Express 14, 9794 (2006).
[CrossRef]

Soralla, M.

Sorolla, M.

M. Navarro-Cia, M. Beruette, M. Sorolla, and N. Engheta, Phys. Rev. B 86, 165130 (2012).
[CrossRef]

Sridhar, S.

P. Vodo, P. V. Parimi, W. T. Lu, and S. Sridhar, Appl. Phys. Lett. 86, 201108 (2005).
[CrossRef]

Tang, W. X.

R. Yang, W. X. Tang, and Y. Hao, IEEE Antennas Wirel. Propag. Lett. 10, 1290 (2011).
[CrossRef]

R. Yang, W. X. Tang, and Y. Hao, Opt. Express 19, 12348 (2011).
[CrossRef]

R. Yang, W. X. Tang, Y. Hao, and I. Youngs, IEEE Antennas Wirel. Propag. Lett. 10, 99 (2011).
[CrossRef]

Taniliean, M. H.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Taniliean, and D. C. Vier, Appl. Phys. Lett. 84, 3232 (2004).
[CrossRef]

Thompson, M. A.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Taniliean, and D. C. Vier, Appl. Phys. Lett. 84, 3232 (2004).
[CrossRef]

Vetter, A. M.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Taniliean, and D. C. Vier, Appl. Phys. Lett. 84, 3232 (2004).
[CrossRef]

Vier, D. C.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Taniliean, and D. C. Vier, Appl. Phys. Lett. 84, 3232 (2004).
[CrossRef]

Vodo, P.

P. Vodo, P. V. Parimi, W. T. Lu, and S. Sridhar, Appl. Phys. Lett. 86, 201108 (2005).
[CrossRef]

Wu, B. I.

I. M. Ehrenberg, S. E. Sarma, and B. I. Wu, J. Appl. Phys. 112, 073114 (2012).
[CrossRef]

Yang, R.

R. Yang, W. X. Tang, and Y. Hao, Opt. Express 19, 12348 (2011).
[CrossRef]

R. Yang, W. X. Tang, Y. Hao, and I. Youngs, IEEE Antennas Wirel. Propag. Lett. 10, 99 (2011).
[CrossRef]

R. Yang, W. X. Tang, and Y. Hao, IEEE Antennas Wirel. Propag. Lett. 10, 1290 (2011).
[CrossRef]

Youngs, I.

R. Yang, W. X. Tang, Y. Hao, and I. Youngs, IEEE Antennas Wirel. Propag. Lett. 10, 99 (2011).
[CrossRef]

Appl. Phys. Lett.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Taniliean, and D. C. Vier, Appl. Phys. Lett. 84, 3232 (2004).
[CrossRef]

P. Vodo, P. V. Parimi, W. T. Lu, and S. Sridhar, Appl. Phys. Lett. 86, 201108 (2005).
[CrossRef]

IEEE Antennas Wirel. Propag. Lett.

R. Yang, W. X. Tang, Y. Hao, and I. Youngs, IEEE Antennas Wirel. Propag. Lett. 10, 99 (2011).
[CrossRef]

R. Yang, W. X. Tang, and Y. Hao, IEEE Antennas Wirel. Propag. Lett. 10, 1290 (2011).
[CrossRef]

J. Appl. Phys.

I. M. Ehrenberg, S. E. Sarma, and B. I. Wu, J. Appl. Phys. 112, 073114 (2012).
[CrossRef]

Opt. Express

Phys. Rev. B

M. Navarro-Cia, M. Beruette, M. Sorolla, and N. Engheta, Phys. Rev. B 86, 165130 (2012).
[CrossRef]

Phys. Rev. Lett.

J. Li and J. B. Pendry, Phys. Rev. Lett. 101, 203901 (2008).
[CrossRef]

Proc. IRE

W. E. Kock, Proc. IRE 34, 828 (1946).
[CrossRef]

Science

J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
[CrossRef]

Other

J. D. Kraus and R. J. Marhefka, Antennas: For All Applications, 3rd ed. (McGraw-Hill, 2002).

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Figures (6)

Fig. 1.
Fig. 1.

Ray tracing through plano–concave lenses.

Fig. 2.
Fig. 2.

Design procedure of the transformational plano–concave lens through QCTO. (a) Rectangular air space with an aperture of 120mm×300mm. (b) Quasi-conformal mapped plano–concave lens. The concave surface is a quarter circle with a radius of 1502mm. The circle center also works as the focal point of the lens. (c) Gradient index plano–concave lens transformed from the air rectangular. Such a lens consists solely of dielectric blocks with permittivity ranging from 1.03 to 2.44. The intact unit cell of each block has the size of 15mm×15mm. There are 18×2 blocks in the top and bottom margin areas having the permittivity value of εr=1.

Fig. 3.
Fig. 3.

Beam focusing and collimating from the transformational plano–concave lens. (a) Normalized E-field distribution at 10 GHz with a line source feeding on the focal point. The E-field is normalized by 3.42×105V/m. (b) Normalized E-field distribution at 10 GHz with a plane wave excitation in the z^ direction. The incidence converges at around 1502mm in front of the lens, also the circle center of the quadrant lensing surface. The E-field is normalized by 2.03×103V/m. (c) Radiation patterns of the transformational plano–concave lens from 8 to 12 GHz. The far-field plots within this frequency band demonstrate nicely as directive beams. The black line plot related to the E-field distribution in (a) refers to the radiation at 10 GHz. (d) Magnified picture of (c).

Fig. 4.
Fig. 4.

Beam steering from the transformational plano–concave lens with off-axis feeding. Normalized E-field distribution at 10 GHz with a line source at (a) 30 mm, (b) 60 mm, and (c) 90 mm off-axis displacement from the focal point. The E-fields are normalized by 4.15×105V/m, 4.09×105V/m, and 4.07×105V/m, respectively. (d) Far-field radiation patterns at 10 GHz with off-axis feeding. (d) Magnified picture of (c). The collimated beams are directed at 0°, 7°, 14°, and 21°, respectively, with the line source feeding on the focal point, 30, 60, and 90 mm off-axis.

Fig. 5.
Fig. 5.

Multiple beams through the transformational plano–concave lensing system. (a) Normalized E-field distribution and (b) far-field radiation pattern of the lensing system at 10 GHz with a line source at the circle center of the four lenses. The E-field is normalized by 3.23×105V/m. The collimated beams are directed to 90°, 0°, 90°, and 180°, respectively.

Fig. 6.
Fig. 6.

Graphical representation of the effective permittivity from a proforated dielectric plate or dielectric rod arrays with (a) circular and (b) square perforations or rods. The employed dielectric is F4B with εr=2.65. d refers to the size of the holes or the rods. a=3mm is the size of the unit cell; therefore, every single intact block in our transformational plano–concave lens will have 5×5 unit cells.

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