Abstract

We analyze the Seidel wavefront aberrations and spot sizes of gradient index (GRIN) singlet lenses with Δn1. We consider and compare curved and planar GRIN lenses with F-numbers of 5 and 1 against equivalent refractive lenses. We find that the planar GRIN lenses generally have larger spot sizes compared to their refractive lens equivalents at wide angles. This appears to be due to an inability to correct for coma by adjusting the refractive index gradient alone. We can correct for the coma by bending the GRIN lens. This results in a singlet lens with performance close to but not exceeding that of the equivalent refractive lens. We also examine the impact of anisotropy on the planar GRIN lenses. We find that fabricating the planar GRIN lenses from a uniaxial medium has the potential to improve the performance of the lenses.

© 2012 Optical Society of America

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2010 (6)

H. F. Ma, X. Chen, X. M. Yang, H. S. Xu, Q. Cheng, and T. J. Cui, “A broadband metamaterial cylindrical lens antenna,” Chin. Sci. Bull. 55, 2066–2070 (2010).
[CrossRef]

H. F. Ma, X. Chen, X. M. Yang, W. X. Jiang, and T. J. Cui, “Design of multibeam scanning antennas with high gains and low sidelobes using gradient-index metamaterials,” J. Appl. Phys. 107, 014902 (2010).
[CrossRef]

B. Fuchs, R. Golubovic, A. K. Skrivervik, and J. R. Mosig, “Spherical lens antenna designs with particle swarm optimization,” Microwave Opt. Technol. Lett. 52, 1655–1659 (2010).
[CrossRef]

V. N. Nguyen, S. H. Yonak, and D. R. Smith, “Multilayer W-band artificial dielectric on liquid crystal polymer,” IEEE Antennas Wireless Propag. Lett. 9, 974–977 (2010).
[CrossRef]

J. Neu, B. Krolla, O. Paul, B. Reinhard, R. Beigang, and M. Rahm, “Metamaterial-based gradient index lens with strong focusing in the THz frequency range,” Opt. Express 18, 27748–27757 (2010).
[CrossRef]

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

2009 (3)

R. Liu, Q. Cheng, J. Y. Chin, J. J. Mock, T. J. Cui, and D. R. Smith, “Broadband gradient index microwave quasi-optical elements based on non-resonant metamaterials,” Opt. Express 17, 21030–21041 (2009).
[CrossRef]

K. Do-Hoon and D. H. Werner, “Beam scanning using flat transformation electromagnetic focusing lenses,” IEEE Antennas Wireless Propag. Lett. 8, 1115–1118 (2009).
[CrossRef]

H. F. Ma, X. Chen, H. S. Xu, X. M. Yang, W. X. Jiang, and T. J. Cui, “Experiments on high-performance beam-scanning antennas made of gradient-index metamaterials,” Appl. Phys. Lett. 95, 094107 (2009).
[CrossRef]

2008 (3)

X. Q. Lin, T. J. Cui, J. Y. Chin, X. M. Yang, Q. Cheng, and R. Liu, “Controlling electromagnetic waves using tunable gradient dielectric metamaterial lens,” Appl. Phys. Lett. 92, 131904 (2008).
[CrossRef]

H.-T. Chen, S. Palit, T. Tyler, C. M. Bingham, J. M. O. Zide, J. F. O’Hara, D. R. Smith, A. C. Gossard, R. D. Averitt, W. J. Padilla, N. M. Jokerst, and A. J. Taylor, “Hybrid metamaterials enable fast electrical modulation of freely propagating terahertz waves,” Appl. Phys. Lett. 93, 091117 (2008).
[CrossRef]

W. X. Jiang, T. J. Cui, H. F. Ma, X. M. Yang, and Q. Cheng, “Layered high-gain lens antennas via discrete optical transformation,” Appl. Phys. Lett. 93, 221906 (2008).
[CrossRef]

2007 (2)

Y. Jin, H. Tai, A. Hiltner, E. Baer, and J. S. Shirk, “New class of bioinspired lenses with a gradient refractive index,” J. Appl. Polym. Sci. 103, 1834–1841 (2007).
[CrossRef]

R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, D. C. Vier, S. Schultz, D. R. Smith, and D. Schurig, “Microwave focusing and beam collimation using negative index of refraction lenses,” IET Microw. Antennas Propag. 1, 108–115 (2007).
[CrossRef]

2006 (3)

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

T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, “Free-space microwave focusing by a negative-index gradient lens,” Appl. Phys. Lett. 88, 081101 (2006).
[CrossRef]

D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express 14, 9794–9804 (2006).
[CrossRef]

2005 (3)

R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, and D. R. Smith, “Simulation and testing of a graded negative index of refraction lens,” Appl. Phys. Lett. 87, 091114 (2005).
[CrossRef]

D. R. Smith, J. J. Mock, A. F. Starr, and D. Schurig, “Gradient index metamaterials,” Phys. Rev. E 71, 036609 (2005).
[CrossRef]

D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E 71, 036617 (2005).
[CrossRef]

2004 (2)

D. Schurig and D. R. Smith, “Negative index lens aberrations,” Phys. Rev. E 70, 065601 (2004).
[CrossRef]

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, “Performance of a negative index of refraction lens,” Appl. Phys. Lett. 84, 3232–3234 (2004).
[CrossRef]

2002 (1)

B. Schoenlinner, W. Xidong, J. P. Ebling, G. V. Eleftheriades, and G. M. Rebeiz, “Wide-scan spherical-lens antennas for automotive radars,” IEEE Trans. Microwave Theory Tech. 50, 2166–2175 (2002).
[CrossRef]

2001 (1)

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

2000 (2)

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

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef]

1999 (1)

C. Fernandes, V. Brankovic, S. Zimmermann, M. Filipe, and L. Anunciada, “Dielectric lens antennas for wireless broadband communications,” Wireless Personal Commun. 10, 19–32 (1999).
[CrossRef]

1996 (1)

F. Bociort, “Thin-lens approximation for radial gradient-index lenses,” Opt. Eng. 35, 1292–1299 (1996).
[CrossRef]

1994 (1)

1986 (1)

1984 (1)

W. Rotman, “Analysis of an EHF aplanatic zoned dielectric lens antenna,” IEEE Trans. Antennas Propag. 32, 611–617 (1984).
[CrossRef]

1980 (1)

1976 (1)

1970 (1)

1948 (1)

W. E. Kock, “Metallic delay lenses,” Bell Sys. Tech. J. 27, 58–82 (1948).

Anunciada, L.

C. Fernandes, V. Brankovic, S. Zimmermann, M. Filipe, and L. Anunciada, “Dielectric lens antennas for wireless broadband communications,” Wireless Personal Commun. 10, 19–32 (1999).
[CrossRef]

Averitt, R. D.

H.-T. Chen, S. Palit, T. Tyler, C. M. Bingham, J. M. O. Zide, J. F. O’Hara, D. R. Smith, A. C. Gossard, R. D. Averitt, W. J. Padilla, N. M. Jokerst, and A. J. Taylor, “Hybrid metamaterials enable fast electrical modulation of freely propagating terahertz waves,” Appl. Phys. Lett. 93, 091117 (2008).
[CrossRef]

Awai, I.

I. Awai, S. Kida, and O. Mizue, “Very thin and flat lens antenna made of artificial dielectrics,” in Proceedings of 2007 Korea-Japan Microwave Conference (2007), pp. 177–180.

Baer, E.

Y. Jin, H. Tai, A. Hiltner, E. Baer, and J. S. Shirk, “New class of bioinspired lenses with a gradient refractive index,” J. Appl. Polym. Sci. 103, 1834–1841 (2007).
[CrossRef]

Basov, D. N.

T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, “Free-space microwave focusing by a negative-index gradient lens,” Appl. Phys. Lett. 88, 081101 (2006).
[CrossRef]

Beigang, R.

Bingham, C. M.

H.-T. Chen, S. Palit, T. Tyler, C. M. Bingham, J. M. O. Zide, J. F. O’Hara, D. R. Smith, A. C. Gossard, R. D. Averitt, W. J. Padilla, N. M. Jokerst, and A. J. Taylor, “Hybrid metamaterials enable fast electrical modulation of freely propagating terahertz waves,” Appl. Phys. Lett. 93, 091117 (2008).
[CrossRef]

Binzer, T.

T. Binzer, M. Klar, and V. Gross, “Development of 77 GHz radar lens antennas for automotive applications based on given requirements,” in 2nd International ITG Conference on Antennas (2007), pp. 205–209.

Bobrov, S. T.

G. I. Greisukh, S. T. Bobrov, and S. A. Stephanov, Optics of Diffractive and Gradient-Index Elements and Systems, 1st ed. (SPIE, 1997), p. 391.

Bociort, F.

F. Bociort, “Thin-lens approximation for radial gradient-index lenses,” Opt. Eng. 35, 1292–1299 (1996).
[CrossRef]

F. Bociort and J. Kross, “Seidel aberration coefficients for radial gradient-index lenses,” J. Opt. Soc. Am. A 11, 2647–2656 (1994).
[CrossRef]

Brankovic, V.

C. Fernandes, V. Brankovic, S. Zimmermann, M. Filipe, and L. Anunciada, “Dielectric lens antennas for wireless broadband communications,” Wireless Personal Commun. 10, 19–32 (1999).
[CrossRef]

Chen, H.-T.

H.-T. Chen, S. Palit, T. Tyler, C. M. Bingham, J. M. O. Zide, J. F. O’Hara, D. R. Smith, A. C. Gossard, R. D. Averitt, W. J. Padilla, N. M. Jokerst, and A. J. Taylor, “Hybrid metamaterials enable fast electrical modulation of freely propagating terahertz waves,” Appl. Phys. Lett. 93, 091117 (2008).
[CrossRef]

Chen, X.

H. F. Ma, X. Chen, X. M. Yang, H. S. Xu, Q. Cheng, and T. J. Cui, “A broadband metamaterial cylindrical lens antenna,” Chin. Sci. Bull. 55, 2066–2070 (2010).
[CrossRef]

H. F. Ma, X. Chen, X. M. Yang, W. X. Jiang, and T. J. Cui, “Design of multibeam scanning antennas with high gains and low sidelobes using gradient-index metamaterials,” J. Appl. Phys. 107, 014902 (2010).
[CrossRef]

H. F. Ma, X. Chen, H. S. Xu, X. M. Yang, W. X. Jiang, and T. J. Cui, “Experiments on high-performance beam-scanning antennas made of gradient-index metamaterials,” Appl. Phys. Lett. 95, 094107 (2009).
[CrossRef]

Cheng, Q.

H. F. Ma, X. Chen, X. M. Yang, H. S. Xu, Q. Cheng, and T. J. Cui, “A broadband metamaterial cylindrical lens antenna,” Chin. Sci. Bull. 55, 2066–2070 (2010).
[CrossRef]

R. Liu, Q. Cheng, J. Y. Chin, J. J. Mock, T. J. Cui, and D. R. Smith, “Broadband gradient index microwave quasi-optical elements based on non-resonant metamaterials,” Opt. Express 17, 21030–21041 (2009).
[CrossRef]

X. Q. Lin, T. J. Cui, J. Y. Chin, X. M. Yang, Q. Cheng, and R. Liu, “Controlling electromagnetic waves using tunable gradient dielectric metamaterial lens,” Appl. Phys. Lett. 92, 131904 (2008).
[CrossRef]

W. X. Jiang, T. J. Cui, H. F. Ma, X. M. Yang, and Q. Cheng, “Layered high-gain lens antennas via discrete optical transformation,” Appl. Phys. Lett. 93, 221906 (2008).
[CrossRef]

Chin, J. Y.

R. Liu, Q. Cheng, J. Y. Chin, J. J. Mock, T. J. Cui, and D. R. Smith, “Broadband gradient index microwave quasi-optical elements based on non-resonant metamaterials,” Opt. Express 17, 21030–21041 (2009).
[CrossRef]

X. Q. Lin, T. J. Cui, J. Y. Chin, X. M. Yang, Q. Cheng, and R. Liu, “Controlling electromagnetic waves using tunable gradient dielectric metamaterial lens,” Appl. Phys. Lett. 92, 131904 (2008).
[CrossRef]

Collin, R. E.

R. E. Collin, Field Theory of Guided Waves, 2nd ed. (IEEE, 1991), pp. xii, 852.

Cui, T. J.

H. F. Ma, X. Chen, X. M. Yang, W. X. Jiang, and T. J. Cui, “Design of multibeam scanning antennas with high gains and low sidelobes using gradient-index metamaterials,” J. Appl. Phys. 107, 014902 (2010).
[CrossRef]

H. F. Ma, X. Chen, X. M. Yang, H. S. Xu, Q. Cheng, and T. J. Cui, “A broadband metamaterial cylindrical lens antenna,” Chin. Sci. Bull. 55, 2066–2070 (2010).
[CrossRef]

H. F. Ma, X. Chen, H. S. Xu, X. M. Yang, W. X. Jiang, and T. J. Cui, “Experiments on high-performance beam-scanning antennas made of gradient-index metamaterials,” Appl. Phys. Lett. 95, 094107 (2009).
[CrossRef]

R. Liu, Q. Cheng, J. Y. Chin, J. J. Mock, T. J. Cui, and D. R. Smith, “Broadband gradient index microwave quasi-optical elements based on non-resonant metamaterials,” Opt. Express 17, 21030–21041 (2009).
[CrossRef]

X. Q. Lin, T. J. Cui, J. Y. Chin, X. M. Yang, Q. Cheng, and R. Liu, “Controlling electromagnetic waves using tunable gradient dielectric metamaterial lens,” Appl. Phys. Lett. 92, 131904 (2008).
[CrossRef]

W. X. Jiang, T. J. Cui, H. F. Ma, X. M. Yang, and Q. Cheng, “Layered high-gain lens antennas via discrete optical transformation,” Appl. Phys. Lett. 93, 221906 (2008).
[CrossRef]

Cummer, S. A.

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

Do-Hoon, K.

K. Do-Hoon and D. H. Werner, “Beam scanning using flat transformation electromagnetic focusing lenses,” IEEE Antennas Wireless Propag. Lett. 8, 1115–1118 (2009).
[CrossRef]

Driscoll, T.

T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, “Free-space microwave focusing by a negative-index gradient lens,” Appl. Phys. Lett. 88, 081101 (2006).
[CrossRef]

Ebling, J. P.

B. Schoenlinner, W. Xidong, J. P. Ebling, G. V. Eleftheriades, and G. M. Rebeiz, “Wide-scan spherical-lens antennas for automotive radars,” IEEE Trans. Microwave Theory Tech. 50, 2166–2175 (2002).
[CrossRef]

Eleftheriades, G. V.

B. Schoenlinner, W. Xidong, J. P. Ebling, G. V. Eleftheriades, and G. M. Rebeiz, “Wide-scan spherical-lens antennas for automotive radars,” IEEE Trans. Microwave Theory Tech. 50, 2166–2175 (2002).
[CrossRef]

Fernandes, C.

C. Fernandes, V. Brankovic, S. Zimmermann, M. Filipe, and L. Anunciada, “Dielectric lens antennas for wireless broadband communications,” Wireless Personal Commun. 10, 19–32 (1999).
[CrossRef]

Filipe, M.

C. Fernandes, V. Brankovic, S. Zimmermann, M. Filipe, and L. Anunciada, “Dielectric lens antennas for wireless broadband communications,” Wireless Personal Commun. 10, 19–32 (1999).
[CrossRef]

Freundt, D.

D. Freundt and B. Lucas, “Long range radar sensor for high-volume driver assistance systems market,” in SAE World Congress (SAE International, 2008), pp. 117–123.

Fuchs, B.

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Golubovic, R.

B. Fuchs, R. Golubovic, A. K. Skrivervik, and J. R. Mosig, “Spherical lens antenna designs with particle swarm optimization,” Microwave Opt. Technol. Lett. 52, 1655–1659 (2010).
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H.-T. Chen, S. Palit, T. Tyler, C. M. Bingham, J. M. O. Zide, J. F. O’Hara, D. R. Smith, A. C. Gossard, R. D. Averitt, W. J. Padilla, N. M. Jokerst, and A. J. Taylor, “Hybrid metamaterials enable fast electrical modulation of freely propagating terahertz waves,” Appl. Phys. Lett. 93, 091117 (2008).
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R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, D. C. Vier, S. Schultz, D. R. Smith, and D. Schurig, “Microwave focusing and beam collimation using negative index of refraction lenses,” IET Microw. Antennas Propag. 1, 108–115 (2007).
[CrossRef]

R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, and D. R. Smith, “Simulation and testing of a graded negative index of refraction lens,” Appl. Phys. Lett. 87, 091114 (2005).
[CrossRef]

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, “Performance of a negative index of refraction lens,” Appl. Phys. Lett. 84, 3232–3234 (2004).
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G. I. Greisukh, S. T. Bobrov, and S. A. Stephanov, Optics of Diffractive and Gradient-Index Elements and Systems, 1st ed. (SPIE, 1997), p. 391.

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T. Binzer, M. Klar, and V. Gross, “Development of 77 GHz radar lens antennas for automotive applications based on given requirements,” in 2nd International ITG Conference on Antennas (2007), pp. 205–209.

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Y. Jin, H. Tai, A. Hiltner, E. Baer, and J. S. Shirk, “New class of bioinspired lenses with a gradient refractive index,” J. Appl. Polym. Sci. 103, 1834–1841 (2007).
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C. Xi, M. Huifeng, Y. Xinmi, C. Qiang, J. W. Xiang, and C. T. Jun, “X-band high directivity lens antenna realized by gradient index metamaterials,” in Microwave Conference, 2009 (APMC, 2009), pp. 793–797.

Jiang, W. X.

H. F. Ma, X. Chen, X. M. Yang, W. X. Jiang, and T. J. Cui, “Design of multibeam scanning antennas with high gains and low sidelobes using gradient-index metamaterials,” J. Appl. Phys. 107, 014902 (2010).
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H. F. Ma, X. Chen, H. S. Xu, X. M. Yang, W. X. Jiang, and T. J. Cui, “Experiments on high-performance beam-scanning antennas made of gradient-index metamaterials,” Appl. Phys. Lett. 95, 094107 (2009).
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W. X. Jiang, T. J. Cui, H. F. Ma, X. M. Yang, and Q. Cheng, “Layered high-gain lens antennas via discrete optical transformation,” Appl. Phys. Lett. 93, 221906 (2008).
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Jin, Y.

Y. Jin, H. Tai, A. Hiltner, E. Baer, and J. S. Shirk, “New class of bioinspired lenses with a gradient refractive index,” J. Appl. Polym. Sci. 103, 1834–1841 (2007).
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H.-T. Chen, S. Palit, T. Tyler, C. M. Bingham, J. M. O. Zide, J. F. O’Hara, D. R. Smith, A. C. Gossard, R. D. Averitt, W. J. Padilla, N. M. Jokerst, and A. J. Taylor, “Hybrid metamaterials enable fast electrical modulation of freely propagating terahertz waves,” Appl. Phys. Lett. 93, 091117 (2008).
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C. Xi, M. Huifeng, Y. Xinmi, C. Qiang, J. W. Xiang, and C. T. Jun, “X-band high directivity lens antenna realized by gradient index metamaterials,” in Microwave Conference, 2009 (APMC, 2009), pp. 793–797.

Justice, B. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
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M. J. Kidger, Fundamental Optical Design (SPIE, 2002), p. 290.

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T. Binzer, M. Klar, and V. Gross, “Development of 77 GHz radar lens antennas for automotive applications based on given requirements,” in 2nd International ITG Conference on Antennas (2007), pp. 205–209.

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D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E 71, 036617 (2005).
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Kross, J.

Kundtz, N.

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

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J. P. Turpin, Z. Jiang, D.-H. Kwon, P. L. Werner, and D. H. Werner, “Metamaterial-enabled transformation optics lenses for antenna applications,” in Proceedings of the Fourth European Conference on Antennas and Propagation (2010), pp. 1–5.

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R. LaGuerra, “Automotive radar/lidar systems: a component-level market analysis of radar, lidar, ultrasonic, and optics-based automotive safety systems” (Technical Report) (ABI Research, 2004).

Li, K.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, “Performance of a negative index of refraction lens,” Appl. Phys. Lett. 84, 3232–3234 (2004).
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Lin, X. Q.

X. Q. Lin, T. J. Cui, J. Y. Chin, X. M. Yang, Q. Cheng, and R. Liu, “Controlling electromagnetic waves using tunable gradient dielectric metamaterial lens,” Appl. Phys. Lett. 92, 131904 (2008).
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Liu, R.

R. Liu, Q. Cheng, J. Y. Chin, J. J. Mock, T. J. Cui, and D. R. Smith, “Broadband gradient index microwave quasi-optical elements based on non-resonant metamaterials,” Opt. Express 17, 21030–21041 (2009).
[CrossRef]

X. Q. Lin, T. J. Cui, J. Y. Chin, X. M. Yang, Q. Cheng, and R. Liu, “Controlling electromagnetic waves using tunable gradient dielectric metamaterial lens,” Appl. Phys. Lett. 92, 131904 (2008).
[CrossRef]

Lucas, B.

D. Freundt and B. Lucas, “Long range radar sensor for high-volume driver assistance systems market,” in SAE World Congress (SAE International, 2008), pp. 117–123.

Ma, H. F.

H. F. Ma, X. Chen, X. M. Yang, W. X. Jiang, and T. J. Cui, “Design of multibeam scanning antennas with high gains and low sidelobes using gradient-index metamaterials,” J. Appl. Phys. 107, 014902 (2010).
[CrossRef]

H. F. Ma, X. Chen, X. M. Yang, H. S. Xu, Q. Cheng, and T. J. Cui, “A broadband metamaterial cylindrical lens antenna,” Chin. Sci. Bull. 55, 2066–2070 (2010).
[CrossRef]

H. F. Ma, X. Chen, H. S. Xu, X. M. Yang, W. X. Jiang, and T. J. Cui, “Experiments on high-performance beam-scanning antennas made of gradient-index metamaterials,” Appl. Phys. Lett. 95, 094107 (2009).
[CrossRef]

W. X. Jiang, T. J. Cui, H. F. Ma, X. M. Yang, and Q. Cheng, “Layered high-gain lens antennas via discrete optical transformation,” Appl. Phys. Lett. 93, 221906 (2008).
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V. N. Mahajan, Optical Imaging and Aberrations (SPIE, 1998), Vol. 1, p. 469.

Marchand, E. W.

Mizue, O.

I. Awai, S. Kida, and O. Mizue, “Very thin and flat lens antenna made of artificial dielectrics,” in Proceedings of 2007 Korea-Japan Microwave Conference (2007), pp. 177–180.

Mock, J. J.

R. Liu, Q. Cheng, J. Y. Chin, J. J. Mock, T. J. Cui, and D. R. Smith, “Broadband gradient index microwave quasi-optical elements based on non-resonant metamaterials,” Opt. Express 17, 21030–21041 (2009).
[CrossRef]

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

D. R. Smith, J. J. Mock, A. F. Starr, and D. Schurig, “Gradient index metamaterials,” Phys. Rev. E 71, 036609 (2005).
[CrossRef]

Moore, D. T.

Mosig, J. R.

B. Fuchs, R. Golubovic, A. K. Skrivervik, and J. R. Mosig, “Spherical lens antenna designs with particle swarm optimization,” Microwave Opt. Technol. Lett. 52, 1655–1659 (2010).
[CrossRef]

Nemat-Nasser, S.

T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, “Free-space microwave focusing by a negative-index gradient lens,” Appl. Phys. Lett. 88, 081101 (2006).
[CrossRef]

Nemat-Nasser, S. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef]

Neu, J.

Nguyen, V. N.

V. N. Nguyen, S. H. Yonak, and D. R. Smith, “Multilayer W-band artificial dielectric on liquid crystal polymer,” IEEE Antennas Wireless Propag. Lett. 9, 974–977 (2010).
[CrossRef]

V. N. Nguyen, S. H. Yonak, and D. R. Smith, “Millimeter-wave artificial dielectric gradient index lenses,” in Proceedings of 3rd European Conference on Antennas and Propagation (IEEE, 2009), pp. 1886–1890.

Nielsen, J. A.

R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, D. C. Vier, S. Schultz, D. R. Smith, and D. Schurig, “Microwave focusing and beam collimation using negative index of refraction lenses,” IET Microw. Antennas Propag. 1, 108–115 (2007).
[CrossRef]

R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, and D. R. Smith, “Simulation and testing of a graded negative index of refraction lens,” Appl. Phys. Lett. 87, 091114 (2005).
[CrossRef]

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, “Performance of a negative index of refraction lens,” Appl. Phys. Lett. 84, 3232–3234 (2004).
[CrossRef]

O’Hara, J. F.

H.-T. Chen, S. Palit, T. Tyler, C. M. Bingham, J. M. O. Zide, J. F. O’Hara, D. R. Smith, A. C. Gossard, R. D. Averitt, W. J. Padilla, N. M. Jokerst, and A. J. Taylor, “Hybrid metamaterials enable fast electrical modulation of freely propagating terahertz waves,” Appl. Phys. Lett. 93, 091117 (2008).
[CrossRef]

Padilla, W. J.

H.-T. Chen, S. Palit, T. Tyler, C. M. Bingham, J. M. O. Zide, J. F. O’Hara, D. R. Smith, A. C. Gossard, R. D. Averitt, W. J. Padilla, N. M. Jokerst, and A. J. Taylor, “Hybrid metamaterials enable fast electrical modulation of freely propagating terahertz waves,” Appl. Phys. Lett. 93, 091117 (2008).
[CrossRef]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef]

Palit, S.

H.-T. Chen, S. Palit, T. Tyler, C. M. Bingham, J. M. O. Zide, J. F. O’Hara, D. R. Smith, A. C. Gossard, R. D. Averitt, W. J. Padilla, N. M. Jokerst, and A. J. Taylor, “Hybrid metamaterials enable fast electrical modulation of freely propagating terahertz waves,” Appl. Phys. Lett. 93, 091117 (2008).
[CrossRef]

Parazzoli, C. G.

R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, D. C. Vier, S. Schultz, D. R. Smith, and D. Schurig, “Microwave focusing and beam collimation using negative index of refraction lenses,” IET Microw. Antennas Propag. 1, 108–115 (2007).
[CrossRef]

R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, and D. R. Smith, “Simulation and testing of a graded negative index of refraction lens,” Appl. Phys. Lett. 87, 091114 (2005).
[CrossRef]

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, “Performance of a negative index of refraction lens,” Appl. Phys. Lett. 84, 3232–3234 (2004).
[CrossRef]

Paul, O.

Pendry, J. B.

D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express 14, 9794–9804 (2006).
[CrossRef]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
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J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[CrossRef]

Qiang, C.

C. Xi, M. Huifeng, Y. Xinmi, C. Qiang, J. W. Xiang, and C. T. Jun, “X-band high directivity lens antenna realized by gradient index metamaterials,” in Microwave Conference, 2009 (APMC, 2009), pp. 793–797.

Rahm, M.

Rebeiz, G. M.

B. Schoenlinner, W. Xidong, J. P. Ebling, G. V. Eleftheriades, and G. M. Rebeiz, “Wide-scan spherical-lens antennas for automotive radars,” IEEE Trans. Microwave Theory Tech. 50, 2166–2175 (2002).
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Rotman, W.

W. Rotman, “Analysis of an EHF aplanatic zoned dielectric lens antenna,” IEEE Trans. Antennas Propag. 32, 611–617 (1984).
[CrossRef]

Rye, P. M.

T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, “Free-space microwave focusing by a negative-index gradient lens,” Appl. Phys. Lett. 88, 081101 (2006).
[CrossRef]

Sands, P. J.

Schoenlinner, B.

B. Schoenlinner, W. Xidong, J. P. Ebling, G. V. Eleftheriades, and G. M. Rebeiz, “Wide-scan spherical-lens antennas for automotive radars,” IEEE Trans. Microwave Theory Tech. 50, 2166–2175 (2002).
[CrossRef]

Schultz, S.

R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, D. C. Vier, S. Schultz, D. R. Smith, and D. Schurig, “Microwave focusing and beam collimation using negative index of refraction lenses,” IET Microw. Antennas Propag. 1, 108–115 (2007).
[CrossRef]

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

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef]

Schurig, D.

R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, D. C. Vier, S. Schultz, D. R. Smith, and D. Schurig, “Microwave focusing and beam collimation using negative index of refraction lenses,” IET Microw. Antennas Propag. 1, 108–115 (2007).
[CrossRef]

T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, “Free-space microwave focusing by a negative-index gradient lens,” Appl. Phys. Lett. 88, 081101 (2006).
[CrossRef]

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

D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express 14, 9794–9804 (2006).
[CrossRef]

D. R. Smith, J. J. Mock, A. F. Starr, and D. Schurig, “Gradient index metamaterials,” Phys. Rev. E 71, 036609 (2005).
[CrossRef]

D. Schurig and D. R. Smith, “Negative index lens aberrations,” Phys. Rev. E 70, 065601 (2004).
[CrossRef]

Shelby, R. A.

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

Shirk, J. S.

Y. Jin, H. Tai, A. Hiltner, E. Baer, and J. S. Shirk, “New class of bioinspired lenses with a gradient refractive index,” J. Appl. Polym. Sci. 103, 1834–1841 (2007).
[CrossRef]

Skrivervik, A. K.

B. Fuchs, R. Golubovic, A. K. Skrivervik, and J. R. Mosig, “Spherical lens antenna designs with particle swarm optimization,” Microwave Opt. Technol. Lett. 52, 1655–1659 (2010).
[CrossRef]

Smith, D. R.

V. N. Nguyen, S. H. Yonak, and D. R. Smith, “Multilayer W-band artificial dielectric on liquid crystal polymer,” IEEE Antennas Wireless Propag. Lett. 9, 974–977 (2010).
[CrossRef]

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

R. Liu, Q. Cheng, J. Y. Chin, J. J. Mock, T. J. Cui, and D. R. Smith, “Broadband gradient index microwave quasi-optical elements based on non-resonant metamaterials,” Opt. Express 17, 21030–21041 (2009).
[CrossRef]

H.-T. Chen, S. Palit, T. Tyler, C. M. Bingham, J. M. O. Zide, J. F. O’Hara, D. R. Smith, A. C. Gossard, R. D. Averitt, W. J. Padilla, N. M. Jokerst, and A. J. Taylor, “Hybrid metamaterials enable fast electrical modulation of freely propagating terahertz waves,” Appl. Phys. Lett. 93, 091117 (2008).
[CrossRef]

R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, D. C. Vier, S. Schultz, D. R. Smith, and D. Schurig, “Microwave focusing and beam collimation using negative index of refraction lenses,” IET Microw. Antennas Propag. 1, 108–115 (2007).
[CrossRef]

T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, “Free-space microwave focusing by a negative-index gradient lens,” Appl. Phys. Lett. 88, 081101 (2006).
[CrossRef]

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

D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express 14, 9794–9804 (2006).
[CrossRef]

R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, and D. R. Smith, “Simulation and testing of a graded negative index of refraction lens,” Appl. Phys. Lett. 87, 091114 (2005).
[CrossRef]

D. R. Smith, J. J. Mock, A. F. Starr, and D. Schurig, “Gradient index metamaterials,” Phys. Rev. E 71, 036609 (2005).
[CrossRef]

D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E 71, 036617 (2005).
[CrossRef]

D. Schurig and D. R. Smith, “Negative index lens aberrations,” Phys. Rev. E 70, 065601 (2004).
[CrossRef]

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

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef]

V. N. Nguyen, S. H. Yonak, and D. R. Smith, “Millimeter-wave artificial dielectric gradient index lenses,” in Proceedings of 3rd European Conference on Antennas and Propagation (IEEE, 2009), pp. 1886–1890.

Smith, W. J.

W. J. Smith, Modern Optical Engineering, 4th ed. (McGraw Hill, 2008), p. 764.

Soukoulis, C. M.

D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E 71, 036617 (2005).
[CrossRef]

Starr, A. F.

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

T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, “Free-space microwave focusing by a negative-index gradient lens,” Appl. Phys. Lett. 88, 081101 (2006).
[CrossRef]

D. R. Smith, J. J. Mock, A. F. Starr, and D. Schurig, “Gradient index metamaterials,” Phys. Rev. E 71, 036609 (2005).
[CrossRef]

Stephanov, S. A.

G. I. Greisukh, S. T. Bobrov, and S. A. Stephanov, Optics of Diffractive and Gradient-Index Elements and Systems, 1st ed. (SPIE, 1997), p. 391.

Tai, H.

Y. Jin, H. Tai, A. Hiltner, E. Baer, and J. S. Shirk, “New class of bioinspired lenses with a gradient refractive index,” J. Appl. Polym. Sci. 103, 1834–1841 (2007).
[CrossRef]

Tanielian, M. H.

R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, D. C. Vier, S. Schultz, D. R. Smith, and D. Schurig, “Microwave focusing and beam collimation using negative index of refraction lenses,” IET Microw. Antennas Propag. 1, 108–115 (2007).
[CrossRef]

R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, and D. R. Smith, “Simulation and testing of a graded negative index of refraction lens,” Appl. Phys. Lett. 87, 091114 (2005).
[CrossRef]

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, “Performance of a negative index of refraction lens,” Appl. Phys. Lett. 84, 3232–3234 (2004).
[CrossRef]

Taylor, A. J.

H.-T. Chen, S. Palit, T. Tyler, C. M. Bingham, J. M. O. Zide, J. F. O’Hara, D. R. Smith, A. C. Gossard, R. D. Averitt, W. J. Padilla, N. M. Jokerst, and A. J. Taylor, “Hybrid metamaterials enable fast electrical modulation of freely propagating terahertz waves,” Appl. Phys. Lett. 93, 091117 (2008).
[CrossRef]

Thompson, M. A.

R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, D. C. Vier, S. Schultz, D. R. Smith, and D. Schurig, “Microwave focusing and beam collimation using negative index of refraction lenses,” IET Microw. Antennas Propag. 1, 108–115 (2007).
[CrossRef]

R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, and D. R. Smith, “Simulation and testing of a graded negative index of refraction lens,” Appl. Phys. Lett. 87, 091114 (2005).
[CrossRef]

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, “Performance of a negative index of refraction lens,” Appl. Phys. Lett. 84, 3232–3234 (2004).
[CrossRef]

Turpin, J. P.

J. P. Turpin, Z. Jiang, D.-H. Kwon, P. L. Werner, and D. H. Werner, “Metamaterial-enabled transformation optics lenses for antenna applications,” in Proceedings of the Fourth European Conference on Antennas and Propagation (2010), pp. 1–5.

Tyler, T.

H.-T. Chen, S. Palit, T. Tyler, C. M. Bingham, J. M. O. Zide, J. F. O’Hara, D. R. Smith, A. C. Gossard, R. D. Averitt, W. J. Padilla, N. M. Jokerst, and A. J. Taylor, “Hybrid metamaterials enable fast electrical modulation of freely propagating terahertz waves,” Appl. Phys. Lett. 93, 091117 (2008).
[CrossRef]

Vetter, A. M.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, “Performance of a negative index of refraction lens,” Appl. Phys. Lett. 84, 3232–3234 (2004).
[CrossRef]

Vier, D. C.

R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, D. C. Vier, S. Schultz, D. R. Smith, and D. Schurig, “Microwave focusing and beam collimation using negative index of refraction lenses,” IET Microw. Antennas Propag. 1, 108–115 (2007).
[CrossRef]

D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E 71, 036617 (2005).
[CrossRef]

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, “Performance of a negative index of refraction lens,” Appl. Phys. Lett. 84, 3232–3234 (2004).
[CrossRef]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef]

Welford, W. T.

W. T. Welford, Aberrations of Optical Systems, Adam Hilger Series on Optics and Optoelectronics (Hilger, 1986).

Werner, D. H.

K. Do-Hoon and D. H. Werner, “Beam scanning using flat transformation electromagnetic focusing lenses,” IEEE Antennas Wireless Propag. Lett. 8, 1115–1118 (2009).
[CrossRef]

J. P. Turpin, Z. Jiang, D.-H. Kwon, P. L. Werner, and D. H. Werner, “Metamaterial-enabled transformation optics lenses for antenna applications,” in Proceedings of the Fourth European Conference on Antennas and Propagation (2010), pp. 1–5.

Werner, P. L.

J. P. Turpin, Z. Jiang, D.-H. Kwon, P. L. Werner, and D. H. Werner, “Metamaterial-enabled transformation optics lenses for antenna applications,” in Proceedings of the Fourth European Conference on Antennas and Propagation (2010), pp. 1–5.

Xi, C.

C. Xi, M. Huifeng, Y. Xinmi, C. Qiang, J. W. Xiang, and C. T. Jun, “X-band high directivity lens antenna realized by gradient index metamaterials,” in Microwave Conference, 2009 (APMC, 2009), pp. 793–797.

Xiang, J. W.

C. Xi, M. Huifeng, Y. Xinmi, C. Qiang, J. W. Xiang, and C. T. Jun, “X-band high directivity lens antenna realized by gradient index metamaterials,” in Microwave Conference, 2009 (APMC, 2009), pp. 793–797.

Xidong, W.

B. Schoenlinner, W. Xidong, J. P. Ebling, G. V. Eleftheriades, and G. M. Rebeiz, “Wide-scan spherical-lens antennas for automotive radars,” IEEE Trans. Microwave Theory Tech. 50, 2166–2175 (2002).
[CrossRef]

Xinmi, Y.

C. Xi, M. Huifeng, Y. Xinmi, C. Qiang, J. W. Xiang, and C. T. Jun, “X-band high directivity lens antenna realized by gradient index metamaterials,” in Microwave Conference, 2009 (APMC, 2009), pp. 793–797.

Xu, H. S.

H. F. Ma, X. Chen, X. M. Yang, H. S. Xu, Q. Cheng, and T. J. Cui, “A broadband metamaterial cylindrical lens antenna,” Chin. Sci. Bull. 55, 2066–2070 (2010).
[CrossRef]

H. F. Ma, X. Chen, H. S. Xu, X. M. Yang, W. X. Jiang, and T. J. Cui, “Experiments on high-performance beam-scanning antennas made of gradient-index metamaterials,” Appl. Phys. Lett. 95, 094107 (2009).
[CrossRef]

Yang, X. M.

H. F. Ma, X. Chen, X. M. Yang, H. S. Xu, Q. Cheng, and T. J. Cui, “A broadband metamaterial cylindrical lens antenna,” Chin. Sci. Bull. 55, 2066–2070 (2010).
[CrossRef]

H. F. Ma, X. Chen, X. M. Yang, W. X. Jiang, and T. J. Cui, “Design of multibeam scanning antennas with high gains and low sidelobes using gradient-index metamaterials,” J. Appl. Phys. 107, 014902 (2010).
[CrossRef]

H. F. Ma, X. Chen, H. S. Xu, X. M. Yang, W. X. Jiang, and T. J. Cui, “Experiments on high-performance beam-scanning antennas made of gradient-index metamaterials,” Appl. Phys. Lett. 95, 094107 (2009).
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X. Q. Lin, T. J. Cui, J. Y. Chin, X. M. Yang, Q. Cheng, and R. Liu, “Controlling electromagnetic waves using tunable gradient dielectric metamaterial lens,” Appl. Phys. Lett. 92, 131904 (2008).
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Zide, J. M. O.

H.-T. Chen, S. Palit, T. Tyler, C. M. Bingham, J. M. O. Zide, J. F. O’Hara, D. R. Smith, A. C. Gossard, R. D. Averitt, W. J. Padilla, N. M. Jokerst, and A. J. Taylor, “Hybrid metamaterials enable fast electrical modulation of freely propagating terahertz waves,” Appl. Phys. Lett. 93, 091117 (2008).
[CrossRef]

Zimmermann, S.

C. Fernandes, V. Brankovic, S. Zimmermann, M. Filipe, and L. Anunciada, “Dielectric lens antennas for wireless broadband communications,” Wireless Personal Commun. 10, 19–32 (1999).
[CrossRef]

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W. X. Jiang, T. J. Cui, H. F. Ma, X. M. Yang, and Q. Cheng, “Layered high-gain lens antennas via discrete optical transformation,” Appl. Phys. Lett. 93, 221906 (2008).
[CrossRef]

H.-T. Chen, S. Palit, T. Tyler, C. M. Bingham, J. M. O. Zide, J. F. O’Hara, D. R. Smith, A. C. Gossard, R. D. Averitt, W. J. Padilla, N. M. Jokerst, and A. J. Taylor, “Hybrid metamaterials enable fast electrical modulation of freely propagating terahertz waves,” Appl. Phys. Lett. 93, 091117 (2008).
[CrossRef]

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, “Performance of a negative index of refraction lens,” Appl. Phys. Lett. 84, 3232–3234 (2004).
[CrossRef]

R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, and D. R. Smith, “Simulation and testing of a graded negative index of refraction lens,” Appl. Phys. Lett. 87, 091114 (2005).
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T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, “Free-space microwave focusing by a negative-index gradient lens,” Appl. Phys. Lett. 88, 081101 (2006).
[CrossRef]

H. F. Ma, X. Chen, H. S. Xu, X. M. Yang, W. X. Jiang, and T. J. Cui, “Experiments on high-performance beam-scanning antennas made of gradient-index metamaterials,” Appl. Phys. Lett. 95, 094107 (2009).
[CrossRef]

X. Q. Lin, T. J. Cui, J. Y. Chin, X. M. Yang, Q. Cheng, and R. Liu, “Controlling electromagnetic waves using tunable gradient dielectric metamaterial lens,” Appl. Phys. Lett. 92, 131904 (2008).
[CrossRef]

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[CrossRef]

IEEE Antennas Wireless Propag. Lett. (2)

K. Do-Hoon and D. H. Werner, “Beam scanning using flat transformation electromagnetic focusing lenses,” IEEE Antennas Wireless Propag. Lett. 8, 1115–1118 (2009).
[CrossRef]

V. N. Nguyen, S. H. Yonak, and D. R. Smith, “Multilayer W-band artificial dielectric on liquid crystal polymer,” IEEE Antennas Wireless Propag. Lett. 9, 974–977 (2010).
[CrossRef]

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[CrossRef]

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B. Schoenlinner, W. Xidong, J. P. Ebling, G. V. Eleftheriades, and G. M. Rebeiz, “Wide-scan spherical-lens antennas for automotive radars,” IEEE Trans. Microwave Theory Tech. 50, 2166–2175 (2002).
[CrossRef]

IET Microw. Antennas Propag. (1)

R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, D. C. Vier, S. Schultz, D. R. Smith, and D. Schurig, “Microwave focusing and beam collimation using negative index of refraction lenses,” IET Microw. Antennas Propag. 1, 108–115 (2007).
[CrossRef]

J. Appl. Phys. (1)

H. F. Ma, X. Chen, X. M. Yang, W. X. Jiang, and T. J. Cui, “Design of multibeam scanning antennas with high gains and low sidelobes using gradient-index metamaterials,” J. Appl. Phys. 107, 014902 (2010).
[CrossRef]

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W. J. Smith, Modern Optical Engineering, 4th ed. (McGraw Hill, 2008), p. 764.

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Figures (20)

Fig. 1.
Fig. 1.

Analytically calculated primary Seidel wavefront aberration coefficients as function of shape factor ( q ) for a thin F/5 conventional lens at 15°.

Fig. 2.
Fig. 2.

Analytically calculated primary Seidel wavefront aberration coefficients as function of angle for thin F/5 conventional lens with shape factor q = 5 / 3 .

Fig. 3.
Fig. 3.

GRIN lens primary Seidel wavefront aberrations as a function of k at 15° field angle at 76.5 GHz. The lens thickness d is selected for each value of k to maintain the 275 mm focal length.

Fig. 4.
Fig. 4.

GRIN lens primary Seidel wavefront aberrations as a function of N 4 at 15° and at 76.5 GHz.

Fig. 5.
Fig. 5.

Radial refractive index profile for fourth-order F/5 GRIN lens.

Fig. 6.
Fig. 6.

Seidel wavefront aberrations plotted as a function of radius of curvature for a curved GRIN lens with n 0 = 2.0 , k = 1.307 × 10 3 mm 2 , N 4 = 0.2442 mm 2 , and 1.385 mm thickness for a 15° field angle.

Fig. 7.
Fig. 7.

Refractive index profile for optimized F/5 curved GRIN lens. Inset, curved sixth-order GRIN lens.

Fig. 8.
Fig. 8.

Analytically calculated primary Seidel wavefront aberrations for fourth-order F/5 conventional refractive lens (top), Wood lens (middle), and curved GRIN lens (bottom) as a function of field angle.

Fig. 9.
Fig. 9.

F/5 lens spot diagrams. The circles represent the diffraction limit.

Fig. 10.
Fig. 10.

Aberration coefficients as a function of shape factor for conventional F/1 lens at 76.5 GHz. Inset, final sixth-order F/1 conventional refractive lens design.

Fig. 11.
Fig. 11.

Seidel wavefront aberrations as a function of quadratic coefficient ( k ) for GRIN F/1 lens at 76.5 GHz and 15°.

Fig. 12.
Fig. 12.

Seidel wavefront aberrations as a function of fourth-order coefficient ( N 4 ) for GRIN F/1 lens at 76.5 GHz.

Fig. 13.
Fig. 13.

Refractive index profile for sixth-order planar F/1 GRIN lens.

Fig. 14.
Fig. 14.

Optimized sixth-order refractive index profile for F/1 curved GRIN lens. Inset, sixth-order curved GRIN lens.

Fig. 15.
Fig. 15.

Analytically calculated primary Seidel wavefront aberrations for fourth-order F/1 conventional refractive lens (top), Wood lens (middle), and curved GRIN lens (bottom) as a function of field angle.

Fig. 16.
Fig. 16.

Sixth-order F/1 lens spot diagrams. The circles represent the diffraction limit.

Fig. 17.
Fig. 17.

Extraordinary ray spot diagram for sixth-order anistropic F/5 Wood lens. The dark circles have radii of 24.1 mm and represent the diffraction limit.

Fig. 18.
Fig. 18.

Extraordinary ray spot diagrams for sixth-order anisotropic F/1 Wood lens. The dark circles have 5.43 mm radii and represent the diffraction limit.

Fig. 19.
Fig. 19.

Basic paraxial ray-trace definitions.

Fig. 20.
Fig. 20.

Definitions of the variables used at lens interface.

Tables (6)

Tables Icon

Table 1. Analytic and Fit Seidel Wavefront Aberrations for Fourth-Order F/5 Lenses at 76.5 GHz

Tables Icon

Table 2. F/5 Lens Spot Sizes in Micrometers

Tables Icon

Table 3. Analytic and Fit Seidel Wavefront Aberrations for Fourth-Order F/1 Lenses at 76.5 GHz

Tables Icon

Table 4. Sixth-Order F/1 Lens Spot Sizes in Micrometers

Tables Icon

Table 5. Fitted Extraordinary Ray Seidel Wavefront Aberrations for Sixth-Order F/5 Wood Lens

Tables Icon

Table 6. Fitted Extraordinary Ray Seidel Wavefront Aberrations for Sixth-Order F/1 Wood Lens

Equations (50)

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

n 2 ( r ) = n 0 2 ( 1 k r 2 + N 4 k 2 r 4 ) + n 6 r 6 ,
q = C 1 + C 2 C 1 C 2 = R 2 + R 1 R 2 R 1 ,
k 1 n 0 f d ,
d ( 1.02 n 0 0.41 ) f .
ε r ( r ) = ( ε x x 0 0 0 ε y y 0 0 0 ε z z ) = ( n 2 ( r ) 0 0 0 n 2 ( r ) 0 0 0 1 ) ,
W ( ρ , θ ) = n = 1 m = 0 n W n m ρ n cos m ( θ ) ,
u = 1 n ( n u h C ( n n ) ) ,
u ¯ = 1 n ( n u ¯ h ¯ C ( n n ) ) ,
h = u t + h ,
h ¯ = u ¯ t + h ¯ ,
u = n u n ,
u ¯ = n u ¯ n ,
h = h ,
h ¯ = h ¯ .
u = u cos ( k d ) h k sin ( k d ) ,
u ¯ = u ¯ cos ( k d ) h ¯ k sin ( k d ) ,
h = u k sin ( k d ) + h cos ( k d ) ,
h ¯ = u ¯ k sin ( k d ) + h ¯ cos ( k d ) .
W sph = 1 8 S sph = 1 8 A 2 h Δ ( u n ) + a 4 Δ ( n ) h 4 ,
W coma = 1 2 S coma = 1 2 A A ¯ h Δ ( u n ) ,
W astig = 1 2 S astig = 1 2 A ¯ 2 h Δ ( u n ) ,
W curv = 1 4 ( S astig + S curv ) = 1 4 ( A ¯ 2 h Δ ( u n ) + H 2 C Δ ( 1 n ) ) ,
W dist = 1 2 S dist = 1 2 [ A ¯ 3 h Δ ( 1 n 2 ) + h ¯ A ¯ ( 2 h A ¯ h ¯ A ) C Δ ( 1 n ) ] ,
A = n I = n u ,
A ¯ = n I ¯ = n u ¯ ,
H = n ( u h ¯ u ¯ h ) ,
W sph = 1 8 S sph = h 4 32 f 3 [ n 2 ( n 1 ) 2 + n + 2 n ( n 1 ) 2 ( q 2 ( n 2 1 ) n + 2 ) 2 n n + 2 ] ,
W coma = 1 2 S coma = h 2 H 4 f 2 [ ( n + 1 ) q n ( n 1 ) 2 n + 1 n ] ,
W astig = 1 2 S astig = H 2 2 f ,
W curv = 1 4 ( S astig + S curv ) = H 2 ( n + 1 ) 4 n f ,
W dist = 1 2 S dist = 0 ,
W sph = 1 8 ( S sph , 1 + S sph , 1 * + T sph + S sph , 2 * + S sph , 2 ) ,
W coma = 1 2 ( S coma , 1 + S coma , 1 * + T coma + S coma , 2 * + S coma , 2 ) ,
W astig = 1 2 ( S astig , 1 + S astig , 1 * + T astig + S astig , 2 * + S astig , 2 ) ,
W curv = 1 4 ( S astig , 1 + S astig , 1 * + T astig + S astig , 2 * + S astig , 2 + S curv , 1 + T curv + S curv , 2 ) ,
W dist = 1 2 ( S dist , 1 + S dist , 1 * + T dist + S dist , 2 * + S dist , 2 ) .
S sph = ( n 0 u ) 2 h Δ ( u n 0 ) + a 4 Δ ( n ) h 4 ,
S coma = ( n 0 u ) ( n 0 u ¯ ) h Δ ( u n 0 ) ,
S astig = ( n 0 u ¯ ) 2 h Δ ( u n 0 ) ,
S curv = ( ( n 0 u ¯ ) 2 h Δ ( u n 0 ) + H 2 C Δ ( 1 n 0 ) ) ,
S dist = ( n 0 u ¯ ) 3 h Δ ( 1 n 0 2 ) + h ¯ ( n 0 u ¯ ) ( 2 h ( n 0 u ¯ ) h ¯ ( n 0 u ) ) C Δ ( 1 n 0 ) ,
S sph * = 2 h 4 C Δ ( n 0 k ) ,
S coma * = 2 h 3 h ¯ C Δ ( n 0 k ) ,
S astig * = 2 h 2 h ¯ 2 C Δ ( n 0 k ) ,
S dist * = 2 h h ¯ 3 C Δ ( n 0 k ) .
T sph = n 0 d e 1 2 ( 1 3 N 4 2 ) n 0 ( 1 + N 4 ) Δ ( h u 3 ) + 5 2 n 0 N 4 e 1 Δ ( h u ) .
T coma = n 0 d e 1 e 2 ( 1 3 N 4 2 ) n 0 ( 1 + N 4 ) Δ ( h u 2 u ¯ ) + 5 2 n 0 N 4 e 1 Δ ( h u ) N 4 H Δ ( u 2 ) ,
T astig = n 0 d e 2 2 ( 1 3 N 4 2 ) n 0 ( 1 + N 4 ) Δ ( h u u ¯ 2 ) + 5 2 n 0 N 4 e 3 Δ ( h u ) 2 N 4 H Δ ( u u ¯ ) 1 2 N 4 T curv ,
T curv = k d H 2 n 0 ,
T dist = n 0 d e 2 e 3 ( 1 3 N 4 2 ) n 0 ( 1 + N 4 ) Δ ( h u ¯ 3 ) + 5 2 n 0 N 4 e 3 Δ ( h ¯ u ) 1 2 N 4 H Δ ( u ¯ 2 ) .

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