Abstract

Luneburg lens with flat focal surface has been developed to work together with planar antenna feeds for beam steering applications. According to our analysis of the conventional flattened Luneburg lens, it cannot accommodate enough feeding elements which can cover its whole scan range with half power beamwidths (HPBWs). In this paper, a novel Luneburg lens with extended flat focal surface is proposed based on the theory of Quasi-Conformal Transformation Optics (QCTO), with its beam steering features reserved. To demonstrate this design, a three-dimensional (3D) prototype of this novel extend-flattened Luneburg lens working at Ku band is fabricated based on 3D printing techniques, whose flat focal surface is attached to a 9-element microstrip antenna array to achieve different scan angles. Our measured results show that, with different antenna elements being fed, the HPBWs can cover the whole scan range.

© 2016 Optical Society of America

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References

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  7. C. A. Valagiannopoulos and N. L. Tsitsas, “Linearization of the T-matrix solution for quasi-homogeneous scatterers,” J. Opt. Soc. Am. A 26(4), 870–881 (2009).
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  8. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
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  9. N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9(2), 129–132 (2010).
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  22. H. F. Ma, G. Z. Wang, W. X. Jiang, and T. J. Cui, “Independent control of differently-polarized waves using anisotropic gradient-index metamaterials,” Sci. Rep. 4, 6337 (2014).
    [Crossref] [PubMed]
  23. M. Liang, W. Ng, K. Chang, K. Gbele, M. Gehm, and H. Xin, “A 3-D Luneburg lens antenna fabricated by polymer jetting rapid prototyping,” IEEE Trans. Antenn. Propag. 62(4), 1799–1807 (2014).
    [Crossref]
  24. M. Yin, X. Y. Tian, L. L. Wu, and D. C. Li, “All-dielectric three-dimensional broadband Eaton lens with large refractive index range,” Appl. Phys. Lett. 104(9), 094101 (2014).
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    [Crossref]

2014 (6)

C. Mateo-Segura, A. Dyke, H. Dyke, S. Haq, and Y. Hao, “Flat Luneburg lens via transformation optics for directive antenna applications,” IEEE Trans. Antenn. Propag. 62(4), 1945–1953 (2014).
[Crossref]

X. Wan, W. X. Jiang, H. F. Ma, and T. J. Cui, “A broadband transformation-optics metasurface lens,” Appl. Phys. Lett. 104(15), 151601 (2014).
[Crossref]

X. Wan, X. P. Shen, Y. Luo, and T. J. Cui, “Planar bifunctional Luneburg-fisheye lens made of an anisotropic metasurface,” Laser Photonics Rev. 8(5), 757–765 (2014).
[Crossref]

H. F. Ma, G. Z. Wang, W. X. Jiang, and T. J. Cui, “Independent control of differently-polarized waves using anisotropic gradient-index metamaterials,” Sci. Rep. 4, 6337 (2014).
[Crossref] [PubMed]

M. Liang, W. Ng, K. Chang, K. Gbele, M. Gehm, and H. Xin, “A 3-D Luneburg lens antenna fabricated by polymer jetting rapid prototyping,” IEEE Trans. Antenn. Propag. 62(4), 1799–1807 (2014).
[Crossref]

M. Yin, X. Y. Tian, L. L. Wu, and D. C. Li, “All-dielectric three-dimensional broadband Eaton lens with large refractive index range,” Appl. Phys. Lett. 104(9), 094101 (2014).
[Crossref]

2013 (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 suface waves,” Phys. Rev. B 87(12), 125137 (2013).
[Crossref]

2012 (3)

2011 (3)

A. Demetriadou and Y. Hao, “Slim Luneburg lens for antenna applications,” Opt. Express 19(21), 19925–19934 (2011).
[Crossref] [PubMed]

J. Hunt, N. Kundtz, N. Landy, V. Nguyen, T. Perram, A. Starr, and D. R. Smith, “Broadband wide angle lens implemented with dielectric metamaterials,” Sensors (Basel) 11(12), 7982–7991 (2011).
[Crossref] [PubMed]

X. Chen, H. F. Ma, X. Y. Zou, W. X. Jiang, and T. J. Cui, “Three-dimensional broadband and high-directivity lens antenna made of metamaterials,” J. Appl. Phys. 110(4), 044904 (2011).
[Crossref]

2010 (3)

N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9(2), 129–132 (2010).
[Crossref] [PubMed]

N. I. Landy, N. Kundtz, and D. R. Smith, “Designing three-dimensional transformation optical media using quasiconformal coordinate transformations,” Phys. Rev. Lett. 105(19), 193902 (2010).
[Crossref] [PubMed]

H. F. Ma and T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat. Commun. 1(8), 124 (2010).
[Crossref] [PubMed]

2009 (2)

C. A. Valagiannopoulos and N. L. Tsitsas, “Linearization of the T-matrix solution for quasi-homogeneous scatterers,” J. Opt. Soc. Am. A 26(4), 870–881 (2009).
[Crossref] [PubMed]

N. A. Mortensen, O. Sigmund, and O. Breinbjerg, “Prospects for poor-man’s cloaking with lowcontrast all-dielectric optical elements,” J. Eur. Opt. Soc. 4, 09008 (2009).
[Crossref]

2008 (2)

C. A. Valagiannopoulos and N. L. Tsitsas, “On the resonance and radiation characteristics of multi-layered spherical microstrip antennas,” Electromagnetics 28(4), 243–264 (2008).
[Crossref]

J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
[Crossref] [PubMed]

2006 (1)

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

2002 (1)

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflections and transmission coefficient,” Phys. Rev. B 65(19), 195104 (2002).
[Crossref]

Basov, D. N.

Berry, S. J.

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 suface waves,” Phys. Rev. B 87(12), 125137 (2013).
[Crossref]

Bowen, P.

Breinbjerg, O.

N. A. Mortensen, O. Sigmund, and O. Breinbjerg, “Prospects for poor-man’s cloaking with lowcontrast all-dielectric optical elements,” J. Eur. Opt. Soc. 4, 09008 (2009).
[Crossref]

Chang, K.

M. Liang, W. Ng, K. Chang, K. Gbele, M. Gehm, and H. Xin, “A 3-D Luneburg lens antenna fabricated by polymer jetting rapid prototyping,” IEEE Trans. Antenn. Propag. 62(4), 1799–1807 (2014).
[Crossref]

Chen, X.

X. Chen, H. F. Ma, X. Y. Zou, W. X. Jiang, and T. J. Cui, “Three-dimensional broadband and high-directivity lens antenna made of metamaterials,” J. Appl. Phys. 110(4), 044904 (2011).
[Crossref]

Cui, T. J.

X. Wan, X. P. Shen, Y. Luo, and T. J. Cui, “Planar bifunctional Luneburg-fisheye lens made of an anisotropic metasurface,” Laser Photonics Rev. 8(5), 757–765 (2014).
[Crossref]

H. F. Ma, G. Z. Wang, W. X. Jiang, and T. J. Cui, “Independent control of differently-polarized waves using anisotropic gradient-index metamaterials,” Sci. Rep. 4, 6337 (2014).
[Crossref] [PubMed]

X. Wan, W. X. Jiang, H. F. Ma, and T. J. Cui, “A broadband transformation-optics metasurface lens,” Appl. Phys. Lett. 104(15), 151601 (2014).
[Crossref]

X. Chen, H. F. Ma, X. Y. Zou, W. X. Jiang, and T. J. Cui, “Three-dimensional broadband and high-directivity lens antenna made of metamaterials,” J. Appl. Phys. 110(4), 044904 (2011).
[Crossref]

H. F. Ma and T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat. Commun. 1(8), 124 (2010).
[Crossref] [PubMed]

Demetriadou, A.

Dhar, S.

Dockrey, J. A.

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 suface waves,” Phys. Rev. B 87(12), 125137 (2013).
[Crossref]

Driscoll, T.

Dyke, A.

C. Mateo-Segura, A. Dyke, H. Dyke, S. Haq, and Y. Hao, “Flat Luneburg lens via transformation optics for directive antenna applications,” IEEE Trans. Antenn. Propag. 62(4), 1945–1953 (2014).
[Crossref]

Dyke, H.

C. Mateo-Segura, A. Dyke, H. Dyke, S. Haq, and Y. Hao, “Flat Luneburg lens via transformation optics for directive antenna applications,” IEEE Trans. Antenn. Propag. 62(4), 1945–1953 (2014).
[Crossref]

Gbele, K.

M. Liang, W. Ng, K. Chang, K. Gbele, M. Gehm, and H. Xin, “A 3-D Luneburg lens antenna fabricated by polymer jetting rapid prototyping,” IEEE Trans. Antenn. Propag. 62(4), 1799–1807 (2014).
[Crossref]

Gehm, M.

M. Liang, W. Ng, K. Chang, K. Gbele, M. Gehm, and H. Xin, “A 3-D Luneburg lens antenna fabricated by polymer jetting rapid prototyping,” IEEE Trans. Antenn. Propag. 62(4), 1799–1807 (2014).
[Crossref]

Hao, Y.

C. Mateo-Segura, A. Dyke, H. Dyke, S. Haq, and Y. Hao, “Flat Luneburg lens via transformation optics for directive antenna applications,” IEEE Trans. Antenn. Propag. 62(4), 1945–1953 (2014).
[Crossref]

A. Demetriadou and Y. Hao, “Slim Luneburg lens for antenna applications,” Opt. Express 19(21), 19925–19934 (2011).
[Crossref] [PubMed]

Haq, S.

C. Mateo-Segura, A. Dyke, H. Dyke, S. Haq, and Y. Hao, “Flat Luneburg lens via transformation optics for directive antenna applications,” IEEE Trans. Antenn. Propag. 62(4), 1945–1953 (2014).
[Crossref]

Hibbins, A. P.

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 suface waves,” Phys. Rev. B 87(12), 125137 (2013).
[Crossref]

Horsley, S. A. R.

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 suface waves,” Phys. Rev. B 87(12), 125137 (2013).
[Crossref]

Hunt, J.

Jiang, W. X.

X. Wan, W. X. Jiang, H. F. Ma, and T. J. Cui, “A broadband transformation-optics metasurface lens,” Appl. Phys. Lett. 104(15), 151601 (2014).
[Crossref]

H. F. Ma, G. Z. Wang, W. X. Jiang, and T. J. Cui, “Independent control of differently-polarized waves using anisotropic gradient-index metamaterials,” Sci. Rep. 4, 6337 (2014).
[Crossref] [PubMed]

X. Chen, H. F. Ma, X. Y. Zou, W. X. Jiang, and T. J. Cui, “Three-dimensional broadband and high-directivity lens antenna made of metamaterials,” J. Appl. Phys. 110(4), 044904 (2011).
[Crossref]

Jokerst, N. M.

Kovanis, V.

M. Mattheakis, G. Tsironis, and V. Kovanis, “Luneburg lens waveguide networks,” J. Opt. 14(11), 114006 (2012).
[Crossref]

Kundtz, N.

T. Driscoll, G. Lipworth, J. Hunt, N. Landy, N. Kundtz, D. N. Basov, and D. R. Smith, “Performance of a three dimensional transformation-optical-flattened Lüneburg lens,” Opt. Express 20(12), 13262–13273 (2012).
[Crossref] [PubMed]

J. Hunt, N. Kundtz, N. Landy, V. Nguyen, T. Perram, A. Starr, and D. R. Smith, “Broadband wide angle lens implemented with dielectric metamaterials,” Sensors (Basel) 11(12), 7982–7991 (2011).
[Crossref] [PubMed]

N. I. Landy, N. Kundtz, and D. R. Smith, “Designing three-dimensional transformation optical media using quasiconformal coordinate transformations,” Phys. Rev. Lett. 105(19), 193902 (2010).
[Crossref] [PubMed]

N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9(2), 129–132 (2010).
[Crossref] [PubMed]

Landy, N.

T. Driscoll, G. Lipworth, J. Hunt, N. Landy, N. Kundtz, D. N. Basov, and D. R. Smith, “Performance of a three dimensional transformation-optical-flattened Lüneburg lens,” Opt. Express 20(12), 13262–13273 (2012).
[Crossref] [PubMed]

J. Hunt, N. Kundtz, N. Landy, V. Nguyen, T. Perram, A. Starr, and D. R. Smith, “Broadband wide angle lens implemented with dielectric metamaterials,” Sensors (Basel) 11(12), 7982–7991 (2011).
[Crossref] [PubMed]

Landy, N. I.

N. I. Landy, N. Kundtz, and D. R. Smith, “Designing three-dimensional transformation optical media using quasiconformal coordinate transformations,” Phys. Rev. Lett. 105(19), 193902 (2010).
[Crossref] [PubMed]

Larouche, S.

Li, D. C.

M. Yin, X. Y. Tian, L. L. Wu, and D. C. Li, “All-dielectric three-dimensional broadband Eaton lens with large refractive index range,” Appl. Phys. Lett. 104(9), 094101 (2014).
[Crossref]

Li, J.

J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
[Crossref] [PubMed]

Liang, M.

M. Liang, W. Ng, K. Chang, K. Gbele, M. Gehm, and H. Xin, “A 3-D Luneburg lens antenna fabricated by polymer jetting rapid prototyping,” IEEE Trans. Antenn. Propag. 62(4), 1799–1807 (2014).
[Crossref]

Lipworth, G.

Lockyear, M. J.

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 suface waves,” Phys. Rev. B 87(12), 125137 (2013).
[Crossref]

Luo, Y.

X. Wan, X. P. Shen, Y. Luo, and T. J. Cui, “Planar bifunctional Luneburg-fisheye lens made of an anisotropic metasurface,” Laser Photonics Rev. 8(5), 757–765 (2014).
[Crossref]

Ma, H. F.

X. Wan, W. X. Jiang, H. F. Ma, and T. J. Cui, “A broadband transformation-optics metasurface lens,” Appl. Phys. Lett. 104(15), 151601 (2014).
[Crossref]

H. F. Ma, G. Z. Wang, W. X. Jiang, and T. J. Cui, “Independent control of differently-polarized waves using anisotropic gradient-index metamaterials,” Sci. Rep. 4, 6337 (2014).
[Crossref] [PubMed]

X. Chen, H. F. Ma, X. Y. Zou, W. X. Jiang, and T. J. Cui, “Three-dimensional broadband and high-directivity lens antenna made of metamaterials,” J. Appl. Phys. 110(4), 044904 (2011).
[Crossref]

H. F. Ma and T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat. Commun. 1(8), 124 (2010).
[Crossref] [PubMed]

Markos, P.

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflections and transmission coefficient,” Phys. Rev. B 65(19), 195104 (2002).
[Crossref]

Mateo-Segura, C.

C. Mateo-Segura, A. Dyke, H. Dyke, S. Haq, and Y. Hao, “Flat Luneburg lens via transformation optics for directive antenna applications,” IEEE Trans. Antenn. Propag. 62(4), 1945–1953 (2014).
[Crossref]

Mattheakis, M.

M. Mattheakis, G. Tsironis, and V. Kovanis, “Luneburg lens waveguide networks,” J. Opt. 14(11), 114006 (2012).
[Crossref]

Mortensen, N. A.

N. A. Mortensen, O. Sigmund, and O. Breinbjerg, “Prospects for poor-man’s cloaking with lowcontrast all-dielectric optical elements,” J. Eur. Opt. Soc. 4, 09008 (2009).
[Crossref]

Ng, W.

M. Liang, W. Ng, K. Chang, K. Gbele, M. Gehm, and H. Xin, “A 3-D Luneburg lens antenna fabricated by polymer jetting rapid prototyping,” IEEE Trans. Antenn. Propag. 62(4), 1799–1807 (2014).
[Crossref]

Nguyen, V.

J. Hunt, N. Kundtz, N. Landy, V. Nguyen, T. Perram, A. Starr, and D. R. Smith, “Broadband wide angle lens implemented with dielectric metamaterials,” Sensors (Basel) 11(12), 7982–7991 (2011).
[Crossref] [PubMed]

Pendry, J. B.

J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
[Crossref] [PubMed]

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

Perram, T.

J. Hunt, N. Kundtz, N. Landy, V. Nguyen, T. Perram, A. Starr, and D. R. Smith, “Broadband wide angle lens implemented with dielectric metamaterials,” Sensors (Basel) 11(12), 7982–7991 (2011).
[Crossref] [PubMed]

Sambles, J. R.

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 suface waves,” Phys. Rev. B 87(12), 125137 (2013).
[Crossref]

Schultz, S.

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflections and transmission coefficient,” Phys. Rev. B 65(19), 195104 (2002).
[Crossref]

Schurig, D.

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

Shen, X. P.

X. Wan, X. P. Shen, Y. Luo, and T. J. Cui, “Planar bifunctional Luneburg-fisheye lens made of an anisotropic metasurface,” Laser Photonics Rev. 8(5), 757–765 (2014).
[Crossref]

Sigmund, O.

N. A. Mortensen, O. Sigmund, and O. Breinbjerg, “Prospects for poor-man’s cloaking with lowcontrast all-dielectric optical elements,” J. Eur. Opt. Soc. 4, 09008 (2009).
[Crossref]

Smith, D. R.

J. Hunt, T. Tyler, S. Dhar, Y. J. Tsai, P. Bowen, S. Larouche, N. M. Jokerst, and D. R. Smith, “Planar, flattened Luneburg lens at infrared wavelengths,” Opt. Express 20(2), 1706–1713 (2012).
[Crossref] [PubMed]

T. Driscoll, G. Lipworth, J. Hunt, N. Landy, N. Kundtz, D. N. Basov, and D. R. Smith, “Performance of a three dimensional transformation-optical-flattened Lüneburg lens,” Opt. Express 20(12), 13262–13273 (2012).
[Crossref] [PubMed]

J. Hunt, N. Kundtz, N. Landy, V. Nguyen, T. Perram, A. Starr, and D. R. Smith, “Broadband wide angle lens implemented with dielectric metamaterials,” Sensors (Basel) 11(12), 7982–7991 (2011).
[Crossref] [PubMed]

N. I. Landy, N. Kundtz, and D. R. Smith, “Designing three-dimensional transformation optical media using quasiconformal coordinate transformations,” Phys. Rev. Lett. 105(19), 193902 (2010).
[Crossref] [PubMed]

N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9(2), 129–132 (2010).
[Crossref] [PubMed]

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

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflections and transmission coefficient,” Phys. Rev. B 65(19), 195104 (2002).
[Crossref]

Soukoulis, C. M.

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflections and transmission coefficient,” Phys. Rev. B 65(19), 195104 (2002).
[Crossref]

Starr, A.

J. Hunt, N. Kundtz, N. Landy, V. Nguyen, T. Perram, A. Starr, and D. R. Smith, “Broadband wide angle lens implemented with dielectric metamaterials,” Sensors (Basel) 11(12), 7982–7991 (2011).
[Crossref] [PubMed]

Tian, X. Y.

M. Yin, X. Y. Tian, L. L. Wu, and D. C. Li, “All-dielectric three-dimensional broadband Eaton lens with large refractive index range,” Appl. Phys. Lett. 104(9), 094101 (2014).
[Crossref]

Tsai, Y. J.

Tsironis, G.

M. Mattheakis, G. Tsironis, and V. Kovanis, “Luneburg lens waveguide networks,” J. Opt. 14(11), 114006 (2012).
[Crossref]

Tsitsas, N. L.

C. A. Valagiannopoulos and N. L. Tsitsas, “Linearization of the T-matrix solution for quasi-homogeneous scatterers,” J. Opt. Soc. Am. A 26(4), 870–881 (2009).
[Crossref] [PubMed]

C. A. Valagiannopoulos and N. L. Tsitsas, “On the resonance and radiation characteristics of multi-layered spherical microstrip antennas,” Electromagnetics 28(4), 243–264 (2008).
[Crossref]

Tyler, T.

Valagiannopoulos, C. A.

C. A. Valagiannopoulos and N. L. Tsitsas, “Linearization of the T-matrix solution for quasi-homogeneous scatterers,” J. Opt. Soc. Am. A 26(4), 870–881 (2009).
[Crossref] [PubMed]

C. A. Valagiannopoulos and N. L. Tsitsas, “On the resonance and radiation characteristics of multi-layered spherical microstrip antennas,” Electromagnetics 28(4), 243–264 (2008).
[Crossref]

Wan, X.

X. Wan, W. X. Jiang, H. F. Ma, and T. J. Cui, “A broadband transformation-optics metasurface lens,” Appl. Phys. Lett. 104(15), 151601 (2014).
[Crossref]

X. Wan, X. P. Shen, Y. Luo, and T. J. Cui, “Planar bifunctional Luneburg-fisheye lens made of an anisotropic metasurface,” Laser Photonics Rev. 8(5), 757–765 (2014).
[Crossref]

Wang, G. Z.

H. F. Ma, G. Z. Wang, W. X. Jiang, and T. J. Cui, “Independent control of differently-polarized waves using anisotropic gradient-index metamaterials,” Sci. Rep. 4, 6337 (2014).
[Crossref] [PubMed]

Wu, L. L.

M. Yin, X. Y. Tian, L. L. Wu, and D. C. Li, “All-dielectric three-dimensional broadband Eaton lens with large refractive index range,” Appl. Phys. Lett. 104(9), 094101 (2014).
[Crossref]

Xin, H.

M. Liang, W. Ng, K. Chang, K. Gbele, M. Gehm, and H. Xin, “A 3-D Luneburg lens antenna fabricated by polymer jetting rapid prototyping,” IEEE Trans. Antenn. Propag. 62(4), 1799–1807 (2014).
[Crossref]

Yin, M.

M. Yin, X. Y. Tian, L. L. Wu, and D. C. Li, “All-dielectric three-dimensional broadband Eaton lens with large refractive index range,” Appl. Phys. Lett. 104(9), 094101 (2014).
[Crossref]

Zou, X. Y.

X. Chen, H. F. Ma, X. Y. Zou, W. X. Jiang, and T. J. Cui, “Three-dimensional broadband and high-directivity lens antenna made of metamaterials,” J. Appl. Phys. 110(4), 044904 (2011).
[Crossref]

Appl. Phys. Lett. (2)

X. Wan, W. X. Jiang, H. F. Ma, and T. J. Cui, “A broadband transformation-optics metasurface lens,” Appl. Phys. Lett. 104(15), 151601 (2014).
[Crossref]

M. Yin, X. Y. Tian, L. L. Wu, and D. C. Li, “All-dielectric three-dimensional broadband Eaton lens with large refractive index range,” Appl. Phys. Lett. 104(9), 094101 (2014).
[Crossref]

Electromagnetics (1)

C. A. Valagiannopoulos and N. L. Tsitsas, “On the resonance and radiation characteristics of multi-layered spherical microstrip antennas,” Electromagnetics 28(4), 243–264 (2008).
[Crossref]

IEEE Trans. Antenn. Propag. (2)

M. Liang, W. Ng, K. Chang, K. Gbele, M. Gehm, and H. Xin, “A 3-D Luneburg lens antenna fabricated by polymer jetting rapid prototyping,” IEEE Trans. Antenn. Propag. 62(4), 1799–1807 (2014).
[Crossref]

C. Mateo-Segura, A. Dyke, H. Dyke, S. Haq, and Y. Hao, “Flat Luneburg lens via transformation optics for directive antenna applications,” IEEE Trans. Antenn. Propag. 62(4), 1945–1953 (2014).
[Crossref]

J. Appl. Phys. (1)

X. Chen, H. F. Ma, X. Y. Zou, W. X. Jiang, and T. J. Cui, “Three-dimensional broadband and high-directivity lens antenna made of metamaterials,” J. Appl. Phys. 110(4), 044904 (2011).
[Crossref]

J. Eur. Opt. Soc. (1)

N. A. Mortensen, O. Sigmund, and O. Breinbjerg, “Prospects for poor-man’s cloaking with lowcontrast all-dielectric optical elements,” J. Eur. Opt. Soc. 4, 09008 (2009).
[Crossref]

J. Opt. (1)

M. Mattheakis, G. Tsironis, and V. Kovanis, “Luneburg lens waveguide networks,” J. Opt. 14(11), 114006 (2012).
[Crossref]

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

Laser Photonics Rev. (1)

X. Wan, X. P. Shen, Y. Luo, and T. J. Cui, “Planar bifunctional Luneburg-fisheye lens made of an anisotropic metasurface,” Laser Photonics Rev. 8(5), 757–765 (2014).
[Crossref]

Nat. Commun. (1)

H. F. Ma and T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat. Commun. 1(8), 124 (2010).
[Crossref] [PubMed]

Nat. Mater. (1)

N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9(2), 129–132 (2010).
[Crossref] [PubMed]

Opt. Express (3)

Phys. Rev. B (2)

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflections and transmission coefficient,” Phys. Rev. B 65(19), 195104 (2002).
[Crossref]

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 suface waves,” Phys. Rev. B 87(12), 125137 (2013).
[Crossref]

Phys. Rev. Lett. (2)

N. I. Landy, N. Kundtz, and D. R. Smith, “Designing three-dimensional transformation optical media using quasiconformal coordinate transformations,” Phys. Rev. Lett. 105(19), 193902 (2010).
[Crossref] [PubMed]

J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
[Crossref] [PubMed]

Sci. Rep. (1)

H. F. Ma, G. Z. Wang, W. X. Jiang, and T. J. Cui, “Independent control of differently-polarized waves using anisotropic gradient-index metamaterials,” Sci. Rep. 4, 6337 (2014).
[Crossref] [PubMed]

Science (1)

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

Sensors (Basel) (1)

J. Hunt, N. Kundtz, N. Landy, V. Nguyen, T. Perram, A. Starr, and D. R. Smith, “Broadband wide angle lens implemented with dielectric metamaterials,” Sensors (Basel) 11(12), 7982–7991 (2011).
[Crossref] [PubMed]

Other (4)

N. Kundtz and D. R. Smith, “Experimental and theoretical advances in the design of complex artificial electromagnetic media,” Ph.D. thesis (Duke University, 2009).

A. W. Rudge, The Handbook of Antenna Design (Peter Peregrinus Ltd., 1983).

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

O. S. Heavens, Optical Properties of Thin Solid Films (Courier Corporation, 1991).

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Figures (12)

Fig. 1
Fig. 1

Transformation based on QCTO procedures from (a) 2D circular Luneburg lens to (b) conventional 2D flattened Luneburg lens.

Fig. 2
Fig. 2

The schematic of a flattened Luneburg lens with a feeding antenna array attached to the focal plane.

Fig. 3
Fig. 3

The values of θscanning/π, L/D2 of the 2D flattened lens and the maximum values of d/λ for HPBW-covering while θ varies from 0 to π.

Fig. 4
Fig. 4

The simulated coupling coefficient magnitudes of adjacent elements for a planar microstrip antenna array (F4B-2 substrate, εr = 2.65) with different d/λ.

Fig. 5
Fig. 5

Quasi-conformal spatial transformation from conventional 2D flattened Luneburg lens to the extend-flattened lens. (a) the conventional lens domain; (b) the extended lens domain.

Fig. 6
Fig. 6

Relative permittivity distribution of (a) conventional flattened Luneburg lens; (b) the extend-flattened Luneburg lens.

Fig. 7
Fig. 7

Simulated E-field distributions of conventional flattened lens (a, c, e) and novel extend-flattened lens (b, d, f) with a line current source on different places of the focal plane. The feeding source is located at: (a) x = 0mm; (b) x = 0mm; (c) x = −19.3mm; (d) x = −31.3mm; (e) x = −42mm; (f) and x = −68mm.

Fig. 8
Fig. 8

Simulated radiation patterns accross the scanning plane and directivities of 3D conventional flattened lens model and extend-flattened lens model for different scan angles at 15GHz.

Fig. 9
Fig. 9

Relationship between the effective permittivity and polymer cube size b.

Fig. 10
Fig. 10

(a) 3D prototype of the extend-flattened Luneburg lens; (b) Microstrip antenna array attached to the focal plane of the lens.

Fig. 11
Fig. 11

The measured return losses and coupling coefficients of antenna elements 1-5.

Fig. 12
Fig. 12

The measured radiation patterns at 15.4 GHz with only one element fed at each scan step.

Tables (1)

Tables Icon

Table 1 Parameters of conventional flattened Luneburg lens and present extend-flattened lens.

Equations (10)

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ε r =2 (r/R) 2 , μ r =1
ε ¯ ¯ r = A ε r A T det(A) , μ ¯ ¯ r = A μ r A T det(A)
ε r = ε r /det(A)= ε r ΔS Δ S , [ μ r i j ]=A A T /det(A)1
D 2 1 (2+cos θ 2 ) (1cos θ 2 ) 2 4 3 D 1 , θ scanning θ
θ HBPW =1.1λ/ D 2
N= θ scanning Δφ θ scanning θ HBPW
NL/d
d 1.1L θ scanning D 2 λ
I:0x0.9,y=1 II:{ x=0.3 cos 2 ( π 1.4 y)+0.9,0y0.7 x=0.9,0.7y1 III:y=0,1.2x2.8 IV:{ x=0.3 cos 2 ( π 1.4 y)+3.1,0y0.7 x=3.1,0.7y1 V:3.1x4,y=1
I:0x0.9,y=1 II:{ x=0.3 cos 2 [ π 1.8 (y+0.2) ]+0.9,0.2y0.7 x=0.9,0.7y1 III:y=0.2,0.6x3.4 IV:{ x=0.3 cos 2 [ π 1.8 (y+0.2) ]+3.1,0.2y0.7 x=3.1,0.7y1 V:3.1x4,y=1

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