Abstract

The metasurface lens composing of 2D periodic metallic patches on a grounded dielectric slab possesses several advantages such as being light, low-profile, compact, and also cheap to manufacture. In this paper, a Luneburg lens synthesized by a metasurface and designated for use as a surface wave antenna is proposed. Two types of unit cell will be compared, one whose surface wave modal dispersion varies significantly with the grazing direction and another that does not. In the context of being applied as surface wave antennas, it will be shown that the Luneburg lens synthesized by the latter kind of unit cell provides improved performance as compared to the former. Several aperture sub-efficiencies of the metasurface-based Luneburg-lens antenna shall be used for the characterization of the radiation. A prototype of the designed lens antenna has also been manufactured. Measurement results agree well with theoretical predictions and the efficacy of this device over a fairly wide bandwidth has been experimentally demonstrated.

© 2017 Optical Society of America

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References

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  1. J. A. Dockrey, M. J. Lockyear, S. J. Berry, S. A. R. Horsley, J. R. Sambles, and A. P. Hibbins, “Thin metamaterial Luneburg lens for surface waves,” Electromagnetic and Acoustic Materials Group, Department of Physics and Astronomy, University of Exeter, Stocker Road, Exeter EX4 4QL, United Kingdom, March 2013.
  2. O. Quevedo-Teruel, M. Ebrahimpouri, and M. Kehn, “Ultra wide band metasurface lenses based on off-shifted opposite layers,” IEEE Antennas Wirel. Propag. Lett. 11, 1362–1365 (2012).
  3. M. Casaletti, F. Caminita, and S. Maci, “A Luneburg lens designed by using a variable artificial surface,” Proc. IEEE Antennas Propag. Society Int. Symp. (APS/URSI), Jul. 11–17, 2010, 1–4 (2010).
  4. L. Xue and V. F. Fusco, “Printed holey plate Luneburg lens,” Microw. Opt. Technol. Lett. 50, 378–380 (2007).
  5. L. Xue and V. F. Fusco, “24 GHz automotive radar planar Luneburg lens,” IET Microw. Antennas Propag. 1(3), 624–628 (2007).
  6. S. Maci, G. Minatti, M. Casaletti, and M. Bosiljevac, “Metasurfing: addressing waves on impenetrable metasurfaces,”, IEEE Antennas Wirel. Propag. Lett. 10, 1499–1502 (2011).
  7. M. Bosiljevac, Z. Sipus, M. Casaletti, F. Caminita, and S. Maci, “Designing horn antennas based on variable metasurface concept,” Proc. 6th Europ. Conf. Antennas Propag. (EuCAP) 2012, 1692–1695 (2012).
  8. M. Casaletti, F. Caminita, S. Maci, M. Bosiljevac, and Z. Sipus, “New type of horn based on variable metasurface,” Proc. IEEE Antennas Propag. Symp.2011, 1048–1050 (2011).
  9. X. Xiong, Y. Liu, Z. Yao, L. Zhang, and W. Li, “Design of a metasurface Luneburg lens with flared structure,” 2014 3rd Asia-Pacif. Conf. Antennas Propag. 375–378 (2014).
  10. M. Bosiljevac, M. Casaletti, E. Caminita, Z. Sipus, and S. Maci, “Non-uniform metasurface Luneburg lens antenna design,” IEEE Trans. Antenn. Propag. 60(9), 4065–4073 (2012).
  11. R. Quarfoth and D. Sievenpiper, “Broadband Unit-Cell Design for Highly Anisotropic Impedance Surfaces,” IEEE Trans. Antenn. Propag. 62, 4143–4152 (2014).
  12. G. Goussetis, A. P. Feresidis and J. C. Vardaxoglou, “Tailoring the AMC and EBG Characteristics of Periodic Metallic Arrays Printed on Grounded Dielectric Substrate onwards,” IEEE Trans. Antennas Propag. 54(1), 54 (1), 82–89 ( 2006).
  13. O. Quevedo-Teruel, R. C. Mitchell-Thomas, T. M. McManus, S. A. R. Horsley, and Y. Hao, “Conformal surface lenses from a bed of nails,” The 8th European Conference on Antennas and Propagation (EuCAP 2014), The Hague, 2014, pp. 269–270.
  14. O. Quevedo-Teruel, “Controlled radiation from dielectric slabs over spoof surface plasmon waveguides,” Prog. Electromagnetics Res. 140, 169–179 (2013).
  15. X. Wan, Y. B. Li, B. G. Cai, and T. J. Cui, “Simultaneous controls of surface waves and propagating waves by metasurfaces,” Appl. Phys. Lett. 105, 121603 (2014).
  16. M. Ebrahimpouri, E. Rajo-Iglesias, and O. Quevedo-Teruel, “Wideband glide-symmetric holey structures for gap-waveguide technology,” 2017 11th European Conference on Antennas and Propagation (EUCAP), Paris, 2017, pp. 1658–1660.
  17. R. K. Luneburg, Mathematical Theory of Optics (Brown University Press, 1944). pp. 189–213.
  18. Per-Simon Kildal, “Characterization of Directive Antennas,” Foundation of Antenna Engineering (Kildal Antenn AB 2015), pp. 21–74.
  19. W. L. Stutzman, “Systems Communication for Antennas,” in Antenna Theory and Design (John Wiley & Sons, Inc 2013), pp.100–127.
  20. M. Ng, M. Kehn, and L. Shafai, “Characterization of dense focal plane array feeds for parabolic reflectors in achieving closely-overlapping or widely-separated multiple beams,” Radio Sci. 44(3), 1–25 (2009).
  21. W. V. Cappellen, “Efficiency and sensitivity definitions for reflector antennas in radio astronomy,” SKADS MCCT Workshop, 26~30, Nov 2007.
  22. L. Zhao, X. Chen, and C. K. Ong, “Visual observation and quantitative measurement of the microwave absorbing effect at X band,” Rev. Sci. Instrum. 79(12), 124701 (2008).
    [PubMed]
  23. R. C. Mitchell-Thomas, O. Quevedo-Teruel, J. R. Sambles, and A. P. Hibbins, “Omnidirectional surface wave cloak using an isotropic homogeneous dielectric coating,” Sci. Rep. 6, 30984 (2016).
    [PubMed]

2016 (1)

R. C. Mitchell-Thomas, O. Quevedo-Teruel, J. R. Sambles, and A. P. Hibbins, “Omnidirectional surface wave cloak using an isotropic homogeneous dielectric coating,” Sci. Rep. 6, 30984 (2016).
[PubMed]

2014 (2)

R. Quarfoth and D. Sievenpiper, “Broadband Unit-Cell Design for Highly Anisotropic Impedance Surfaces,” IEEE Trans. Antenn. Propag. 62, 4143–4152 (2014).

X. Wan, Y. B. Li, B. G. Cai, and T. J. Cui, “Simultaneous controls of surface waves and propagating waves by metasurfaces,” Appl. Phys. Lett. 105, 121603 (2014).

2013 (1)

O. Quevedo-Teruel, “Controlled radiation from dielectric slabs over spoof surface plasmon waveguides,” Prog. Electromagnetics Res. 140, 169–179 (2013).

2012 (2)

O. Quevedo-Teruel, M. Ebrahimpouri, and M. Kehn, “Ultra wide band metasurface lenses based on off-shifted opposite layers,” IEEE Antennas Wirel. Propag. Lett. 11, 1362–1365 (2012).

M. Bosiljevac, M. Casaletti, E. Caminita, Z. Sipus, and S. Maci, “Non-uniform metasurface Luneburg lens antenna design,” IEEE Trans. Antenn. Propag. 60(9), 4065–4073 (2012).

2011 (1)

S. Maci, G. Minatti, M. Casaletti, and M. Bosiljevac, “Metasurfing: addressing waves on impenetrable metasurfaces,”, IEEE Antennas Wirel. Propag. Lett. 10, 1499–1502 (2011).

2009 (1)

M. Ng, M. Kehn, and L. Shafai, “Characterization of dense focal plane array feeds for parabolic reflectors in achieving closely-overlapping or widely-separated multiple beams,” Radio Sci. 44(3), 1–25 (2009).

2008 (1)

L. Zhao, X. Chen, and C. K. Ong, “Visual observation and quantitative measurement of the microwave absorbing effect at X band,” Rev. Sci. Instrum. 79(12), 124701 (2008).
[PubMed]

2007 (2)

L. Xue and V. F. Fusco, “Printed holey plate Luneburg lens,” Microw. Opt. Technol. Lett. 50, 378–380 (2007).

L. Xue and V. F. Fusco, “24 GHz automotive radar planar Luneburg lens,” IET Microw. Antennas Propag. 1(3), 624–628 (2007).

Bosiljevac, M.

M. Bosiljevac, M. Casaletti, E. Caminita, Z. Sipus, and S. Maci, “Non-uniform metasurface Luneburg lens antenna design,” IEEE Trans. Antenn. Propag. 60(9), 4065–4073 (2012).

S. Maci, G. Minatti, M. Casaletti, and M. Bosiljevac, “Metasurfing: addressing waves on impenetrable metasurfaces,”, IEEE Antennas Wirel. Propag. Lett. 10, 1499–1502 (2011).

M. Casaletti, F. Caminita, S. Maci, M. Bosiljevac, and Z. Sipus, “New type of horn based on variable metasurface,” Proc. IEEE Antennas Propag. Symp.2011, 1048–1050 (2011).

Cai, B. G.

X. Wan, Y. B. Li, B. G. Cai, and T. J. Cui, “Simultaneous controls of surface waves and propagating waves by metasurfaces,” Appl. Phys. Lett. 105, 121603 (2014).

Caminita, E.

M. Bosiljevac, M. Casaletti, E. Caminita, Z. Sipus, and S. Maci, “Non-uniform metasurface Luneburg lens antenna design,” IEEE Trans. Antenn. Propag. 60(9), 4065–4073 (2012).

Caminita, F.

M. Casaletti, F. Caminita, S. Maci, M. Bosiljevac, and Z. Sipus, “New type of horn based on variable metasurface,” Proc. IEEE Antennas Propag. Symp.2011, 1048–1050 (2011).

M. Casaletti, F. Caminita, and S. Maci, “A Luneburg lens designed by using a variable artificial surface,” Proc. IEEE Antennas Propag. Society Int. Symp. (APS/URSI), Jul. 11–17, 2010, 1–4 (2010).

Cappellen, W. V.

W. V. Cappellen, “Efficiency and sensitivity definitions for reflector antennas in radio astronomy,” SKADS MCCT Workshop, 26~30, Nov 2007.

Casaletti, M.

M. Bosiljevac, M. Casaletti, E. Caminita, Z. Sipus, and S. Maci, “Non-uniform metasurface Luneburg lens antenna design,” IEEE Trans. Antenn. Propag. 60(9), 4065–4073 (2012).

S. Maci, G. Minatti, M. Casaletti, and M. Bosiljevac, “Metasurfing: addressing waves on impenetrable metasurfaces,”, IEEE Antennas Wirel. Propag. Lett. 10, 1499–1502 (2011).

M. Casaletti, F. Caminita, S. Maci, M. Bosiljevac, and Z. Sipus, “New type of horn based on variable metasurface,” Proc. IEEE Antennas Propag. Symp.2011, 1048–1050 (2011).

M. Casaletti, F. Caminita, and S. Maci, “A Luneburg lens designed by using a variable artificial surface,” Proc. IEEE Antennas Propag. Society Int. Symp. (APS/URSI), Jul. 11–17, 2010, 1–4 (2010).

Chen, X.

L. Zhao, X. Chen, and C. K. Ong, “Visual observation and quantitative measurement of the microwave absorbing effect at X band,” Rev. Sci. Instrum. 79(12), 124701 (2008).
[PubMed]

Cui, T. J.

X. Wan, Y. B. Li, B. G. Cai, and T. J. Cui, “Simultaneous controls of surface waves and propagating waves by metasurfaces,” Appl. Phys. Lett. 105, 121603 (2014).

Ebrahimpouri, M.

O. Quevedo-Teruel, M. Ebrahimpouri, and M. Kehn, “Ultra wide band metasurface lenses based on off-shifted opposite layers,” IEEE Antennas Wirel. Propag. Lett. 11, 1362–1365 (2012).

Fusco, V. F.

L. Xue and V. F. Fusco, “24 GHz automotive radar planar Luneburg lens,” IET Microw. Antennas Propag. 1(3), 624–628 (2007).

L. Xue and V. F. Fusco, “Printed holey plate Luneburg lens,” Microw. Opt. Technol. Lett. 50, 378–380 (2007).

Hibbins, A. P.

R. C. Mitchell-Thomas, O. Quevedo-Teruel, J. R. Sambles, and A. P. Hibbins, “Omnidirectional surface wave cloak using an isotropic homogeneous dielectric coating,” Sci. Rep. 6, 30984 (2016).
[PubMed]

Kehn, M.

O. Quevedo-Teruel, M. Ebrahimpouri, and M. Kehn, “Ultra wide band metasurface lenses based on off-shifted opposite layers,” IEEE Antennas Wirel. Propag. Lett. 11, 1362–1365 (2012).

M. Ng, M. Kehn, and L. Shafai, “Characterization of dense focal plane array feeds for parabolic reflectors in achieving closely-overlapping or widely-separated multiple beams,” Radio Sci. 44(3), 1–25 (2009).

Li, Y. B.

X. Wan, Y. B. Li, B. G. Cai, and T. J. Cui, “Simultaneous controls of surface waves and propagating waves by metasurfaces,” Appl. Phys. Lett. 105, 121603 (2014).

Maci, S.

M. Bosiljevac, M. Casaletti, E. Caminita, Z. Sipus, and S. Maci, “Non-uniform metasurface Luneburg lens antenna design,” IEEE Trans. Antenn. Propag. 60(9), 4065–4073 (2012).

S. Maci, G. Minatti, M. Casaletti, and M. Bosiljevac, “Metasurfing: addressing waves on impenetrable metasurfaces,”, IEEE Antennas Wirel. Propag. Lett. 10, 1499–1502 (2011).

M. Casaletti, F. Caminita, and S. Maci, “A Luneburg lens designed by using a variable artificial surface,” Proc. IEEE Antennas Propag. Society Int. Symp. (APS/URSI), Jul. 11–17, 2010, 1–4 (2010).

M. Casaletti, F. Caminita, S. Maci, M. Bosiljevac, and Z. Sipus, “New type of horn based on variable metasurface,” Proc. IEEE Antennas Propag. Symp.2011, 1048–1050 (2011).

Minatti, G.

S. Maci, G. Minatti, M. Casaletti, and M. Bosiljevac, “Metasurfing: addressing waves on impenetrable metasurfaces,”, IEEE Antennas Wirel. Propag. Lett. 10, 1499–1502 (2011).

Mitchell-Thomas, R. C.

R. C. Mitchell-Thomas, O. Quevedo-Teruel, J. R. Sambles, and A. P. Hibbins, “Omnidirectional surface wave cloak using an isotropic homogeneous dielectric coating,” Sci. Rep. 6, 30984 (2016).
[PubMed]

Ng, M.

M. Ng, M. Kehn, and L. Shafai, “Characterization of dense focal plane array feeds for parabolic reflectors in achieving closely-overlapping or widely-separated multiple beams,” Radio Sci. 44(3), 1–25 (2009).

Ong, C. K.

L. Zhao, X. Chen, and C. K. Ong, “Visual observation and quantitative measurement of the microwave absorbing effect at X band,” Rev. Sci. Instrum. 79(12), 124701 (2008).
[PubMed]

Quarfoth, R.

R. Quarfoth and D. Sievenpiper, “Broadband Unit-Cell Design for Highly Anisotropic Impedance Surfaces,” IEEE Trans. Antenn. Propag. 62, 4143–4152 (2014).

Quevedo-Teruel, O.

R. C. Mitchell-Thomas, O. Quevedo-Teruel, J. R. Sambles, and A. P. Hibbins, “Omnidirectional surface wave cloak using an isotropic homogeneous dielectric coating,” Sci. Rep. 6, 30984 (2016).
[PubMed]

O. Quevedo-Teruel, “Controlled radiation from dielectric slabs over spoof surface plasmon waveguides,” Prog. Electromagnetics Res. 140, 169–179 (2013).

O. Quevedo-Teruel, M. Ebrahimpouri, and M. Kehn, “Ultra wide band metasurface lenses based on off-shifted opposite layers,” IEEE Antennas Wirel. Propag. Lett. 11, 1362–1365 (2012).

Sambles, J. R.

R. C. Mitchell-Thomas, O. Quevedo-Teruel, J. R. Sambles, and A. P. Hibbins, “Omnidirectional surface wave cloak using an isotropic homogeneous dielectric coating,” Sci. Rep. 6, 30984 (2016).
[PubMed]

Shafai, L.

M. Ng, M. Kehn, and L. Shafai, “Characterization of dense focal plane array feeds for parabolic reflectors in achieving closely-overlapping or widely-separated multiple beams,” Radio Sci. 44(3), 1–25 (2009).

Sievenpiper, D.

R. Quarfoth and D. Sievenpiper, “Broadband Unit-Cell Design for Highly Anisotropic Impedance Surfaces,” IEEE Trans. Antenn. Propag. 62, 4143–4152 (2014).

Sipus, Z.

M. Bosiljevac, M. Casaletti, E. Caminita, Z. Sipus, and S. Maci, “Non-uniform metasurface Luneburg lens antenna design,” IEEE Trans. Antenn. Propag. 60(9), 4065–4073 (2012).

M. Casaletti, F. Caminita, S. Maci, M. Bosiljevac, and Z. Sipus, “New type of horn based on variable metasurface,” Proc. IEEE Antennas Propag. Symp.2011, 1048–1050 (2011).

Wan, X.

X. Wan, Y. B. Li, B. G. Cai, and T. J. Cui, “Simultaneous controls of surface waves and propagating waves by metasurfaces,” Appl. Phys. Lett. 105, 121603 (2014).

Xue, L.

L. Xue and V. F. Fusco, “Printed holey plate Luneburg lens,” Microw. Opt. Technol. Lett. 50, 378–380 (2007).

L. Xue and V. F. Fusco, “24 GHz automotive radar planar Luneburg lens,” IET Microw. Antennas Propag. 1(3), 624–628 (2007).

Zhao, L.

L. Zhao, X. Chen, and C. K. Ong, “Visual observation and quantitative measurement of the microwave absorbing effect at X band,” Rev. Sci. Instrum. 79(12), 124701 (2008).
[PubMed]

Appl. Phys. Lett. (1)

X. Wan, Y. B. Li, B. G. Cai, and T. J. Cui, “Simultaneous controls of surface waves and propagating waves by metasurfaces,” Appl. Phys. Lett. 105, 121603 (2014).

IEEE Antennas Wirel. Propag. Lett. (2)

O. Quevedo-Teruel, M. Ebrahimpouri, and M. Kehn, “Ultra wide band metasurface lenses based on off-shifted opposite layers,” IEEE Antennas Wirel. Propag. Lett. 11, 1362–1365 (2012).

S. Maci, G. Minatti, M. Casaletti, and M. Bosiljevac, “Metasurfing: addressing waves on impenetrable metasurfaces,”, IEEE Antennas Wirel. Propag. Lett. 10, 1499–1502 (2011).

IEEE Trans. Antenn. Propag. (2)

M. Bosiljevac, M. Casaletti, E. Caminita, Z. Sipus, and S. Maci, “Non-uniform metasurface Luneburg lens antenna design,” IEEE Trans. Antenn. Propag. 60(9), 4065–4073 (2012).

R. Quarfoth and D. Sievenpiper, “Broadband Unit-Cell Design for Highly Anisotropic Impedance Surfaces,” IEEE Trans. Antenn. Propag. 62, 4143–4152 (2014).

IET Microw. Antennas Propag. (1)

L. Xue and V. F. Fusco, “24 GHz automotive radar planar Luneburg lens,” IET Microw. Antennas Propag. 1(3), 624–628 (2007).

Microw. Opt. Technol. Lett. (1)

L. Xue and V. F. Fusco, “Printed holey plate Luneburg lens,” Microw. Opt. Technol. Lett. 50, 378–380 (2007).

Prog. Electromagnetics Res. (1)

O. Quevedo-Teruel, “Controlled radiation from dielectric slabs over spoof surface plasmon waveguides,” Prog. Electromagnetics Res. 140, 169–179 (2013).

Radio Sci. (1)

M. Ng, M. Kehn, and L. Shafai, “Characterization of dense focal plane array feeds for parabolic reflectors in achieving closely-overlapping or widely-separated multiple beams,” Radio Sci. 44(3), 1–25 (2009).

Rev. Sci. Instrum. (1)

L. Zhao, X. Chen, and C. K. Ong, “Visual observation and quantitative measurement of the microwave absorbing effect at X band,” Rev. Sci. Instrum. 79(12), 124701 (2008).
[PubMed]

Sci. Rep. (1)

R. C. Mitchell-Thomas, O. Quevedo-Teruel, J. R. Sambles, and A. P. Hibbins, “Omnidirectional surface wave cloak using an isotropic homogeneous dielectric coating,” Sci. Rep. 6, 30984 (2016).
[PubMed]

Other (12)

W. V. Cappellen, “Efficiency and sensitivity definitions for reflector antennas in radio astronomy,” SKADS MCCT Workshop, 26~30, Nov 2007.

J. A. Dockrey, M. J. Lockyear, S. J. Berry, S. A. R. Horsley, J. R. Sambles, and A. P. Hibbins, “Thin metamaterial Luneburg lens for surface waves,” Electromagnetic and Acoustic Materials Group, Department of Physics and Astronomy, University of Exeter, Stocker Road, Exeter EX4 4QL, United Kingdom, March 2013.

M. Casaletti, F. Caminita, and S. Maci, “A Luneburg lens designed by using a variable artificial surface,” Proc. IEEE Antennas Propag. Society Int. Symp. (APS/URSI), Jul. 11–17, 2010, 1–4 (2010).

M. Bosiljevac, Z. Sipus, M. Casaletti, F. Caminita, and S. Maci, “Designing horn antennas based on variable metasurface concept,” Proc. 6th Europ. Conf. Antennas Propag. (EuCAP) 2012, 1692–1695 (2012).

M. Casaletti, F. Caminita, S. Maci, M. Bosiljevac, and Z. Sipus, “New type of horn based on variable metasurface,” Proc. IEEE Antennas Propag. Symp.2011, 1048–1050 (2011).

X. Xiong, Y. Liu, Z. Yao, L. Zhang, and W. Li, “Design of a metasurface Luneburg lens with flared structure,” 2014 3rd Asia-Pacif. Conf. Antennas Propag. 375–378 (2014).

G. Goussetis, A. P. Feresidis and J. C. Vardaxoglou, “Tailoring the AMC and EBG Characteristics of Periodic Metallic Arrays Printed on Grounded Dielectric Substrate onwards,” IEEE Trans. Antennas Propag. 54(1), 54 (1), 82–89 ( 2006).

O. Quevedo-Teruel, R. C. Mitchell-Thomas, T. M. McManus, S. A. R. Horsley, and Y. Hao, “Conformal surface lenses from a bed of nails,” The 8th European Conference on Antennas and Propagation (EuCAP 2014), The Hague, 2014, pp. 269–270.

M. Ebrahimpouri, E. Rajo-Iglesias, and O. Quevedo-Teruel, “Wideband glide-symmetric holey structures for gap-waveguide technology,” 2017 11th European Conference on Antennas and Propagation (EUCAP), Paris, 2017, pp. 1658–1660.

R. K. Luneburg, Mathematical Theory of Optics (Brown University Press, 1944). pp. 189–213.

Per-Simon Kildal, “Characterization of Directive Antennas,” Foundation of Antenna Engineering (Kildal Antenn AB 2015), pp. 21–74.

W. L. Stutzman, “Systems Communication for Antennas,” in Antenna Theory and Design (John Wiley & Sons, Inc 2013), pp.100–127.

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Figures (11)

Fig. 1
Fig. 1 Dispersion diagram of array of square patches printed on grounded substrate with square unit cell, for various patch sizes as annotated. p = 2 mm, h = 1.28mm.
Fig. 2
Fig. 2 Dispersion for various azimuth angles as annotated, (a) square unit cell with p = 2 mm, h = 1.28 mm, and a = 1.8 mm, and (b) hexagonal unit cell with D = 2 mm, d = 0.9 mm, and h = 1.28 mm.
Fig. 3
Fig. 3 Ez-field distribution of Luneburg lens composed of periodic square cells and excited by a point source at the right side of the lens at 12GHz.
Fig. 4
Fig. 4 Variation of refractive index with patch size or radius d of hexagonal patch within hexagonal unit cell.
Fig. 5
Fig. 5 Luneburg lens composed of both hexagonal (in one semicircle) and square (the other half) lattice arrangements: (a) top view, and (b) zoomed-in illustration of the third and fifth layers.
Fig. 6
Fig. 6 (a) Ez-field distribution of Luneburg lens synthesized by hybridized array of hexagonal and square unit cells, and (b) directivity patterns in H plane for Luneburg lens antenna synthesized by purely square lattices, and hybrid of square and hexagonal cells.
Fig. 7
Fig. 7 Comparison of subefficiencies between Luneburg lens antenna synthesized by traditional “entirely square cells” way and new approach composed of square and hexagonal cells; (a) polarization efficiency (b) phase efficiency, and (c) illumination efficiency.
Fig. 8
Fig. 8 (a) Photograph of a fabricated Luneburg lens synthesized by hexagonal and square unit cells (one semicircle for each), and (b) experimental setup
Fig. 9
Fig. 9 Measured (a) amplitude distribution, and (b) phase pattern of wavefront over surface of lens at 12 GHz. Because of symmetry, only one half is required for the phase pattern. Due to the time-consuming and labor-intensive nature of the measurements, resolution of measured data points made high only in upper right quadrant of wavefront pattern in which bending towards the focal point at (x = 0, y = 80) occurs. Upper left quadrant containing essential planar wavefronts clearly visible despite coarser resolution.
Fig. 10
Fig. 10 Graphs of measured field level plotted versus the dimension along the breadth of the planar aperture containing the focal point; for (a) 11 GHz, (b) 12 GHz, (c) 13 GHz, and (d) illustration of axis for probe distance in graphs (a) to (c), with indicated locations of 0 and 16 cm.
Fig. 11
Fig. 11 Measured far-field radiation patterns of manufactured Luneburg lens antenna, with simulated patterns included. Good agreement of maximum directive gain level and width of main beam between simulation and experiment observed.

Equations (6)

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

n= k s / k 0 .
n= 2 ( r/R ) 2 .
G= ε ap D= ε ap 4π λ 2 A p = 4π λ 2 A e .
ε pol = A | E co | 2 ds A p ( | E co | 2 + | E cross | 2 )ds .
ε ph = | A p E co ds | 2 ( A p | E co |ds ) 2 .
ε ill = 1 A | A p E co ds | 2 A p | E co | 2 ds .

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