Abstract

An epsilon-near-zero graded-index converging lens with planar faces is proposed and analyzed. Each perfectly-electric conducting (PEC) waveguide comprising the lens operates slightly above its cut-off frequency and has the same length but different cross-sectional dimensions. This allows controlling individually the propagation constant and the normalized characteristic impedance of each waveguide for the desired phase front at the lens output while Fresnel reflection losses are minimized. A complete theoretical analysis based on the waveguide theory and Fermat’s principle is provided. This is complemented with numerical simulation results of two-dimensional and three-dimensional lenses, made of PEC and aluminum, respectively, and working in the terahertz regime, which show good agreement with the analytical work.

© 2013 OSA

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2013 (1)

S. Ishii, V. M. Shalaev, and A. V. Kildishev, “Holey-metal lenses: sieving single modes with proper phases,” Nano Lett.13(1), 159–163 (2013).
[CrossRef] [PubMed]

2012 (1)

M. Navarro-Cía, M. Beruete, M. Sorolla, and N. Engheta, “Lensing system and Fourier transformation using epsilon-near-zero metamaterials,” Phys. Rev. B86(16), 165130 (2012).
[CrossRef]

2011 (6)

N. Llombart, G. Chattopadhyay, A. Skalare, and I. Mehdi, “Novel terahertz antenna based on a silicon lens fed by a leaky wave enhanced waveguide,” IEEE Trans. Antenn. Propag.59(6), 2160–2168 (2011).
[CrossRef]

C. Ma, M. Escobar, and Z. Liu, “Extraordinary light focusing and Fourier transform properties of gradient-index metalenses,” Phys. Rev. B84(19), 195142 (2011).
[CrossRef]

S. Ishii, A. V. Kildishev, V. M. Shalaev, and V. P. Drachev, “Controlling the wave focal structure of metallic nanoslit lenses with liquid crystals,” Laser Phys. Lett.8(11), 828–832 (2011).
[CrossRef]

M. Navarro-Cía, M. Beruete, I. Campillo, and M. Sorolla Ayza, “Beamforming by left-handed extraordinary transmission metamaterial bi- and plano-concave lens at millimeter-waves,” IEEE Trans. Antenn. Propag.59(6), 2141–2151 (2011).
[CrossRef]

M. Navarro-Cía, M. Beruete, I. Campillo, and M. Sorolla, “Enhanced lens by ε and μ near-zero metamaterial boosted by extraordinary optical transmission,” Phys. Rev. B83(11), 115112 (2011).
[CrossRef]

S. Ishii, A. V. Kildishev, V. M. Shalaev, K. P. Chen, and V. P. Drachev, “Metal nanoslit lenses with polarization-selective design,” Opt. Lett.36(4), 451–453 (2011).
[CrossRef] [PubMed]

2010 (1)

C. Ma and Z. Liu, “A super resolution metalens with phase compensation mechanism,” Appl. Phys. Lett.96(18), 183103 (2010).
[CrossRef]

2009 (2)

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett.103(3), 033902 (2009).
[CrossRef] [PubMed]

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses Based on Nanoscale Slit Arrays in a metallic film,” Nano Lett.9(1), 235–238 (2009).
[CrossRef] [PubMed]

2008 (2)

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett.100(3), 033903 (2008).
[CrossRef] [PubMed]

A. Alù, M. G. Silveirinha, and N. Engheta, “Transmission-line analysis of ε -near-zero-filled narrow channels,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.78(1), 016604 (2008).
[CrossRef] [PubMed]

2007 (3)

M. G. Silveirinha and N. Engheta, “Theory of supercoupling, squeezing wave energy, and field confinement in narrow channels and tight bends using ε near-zero metamaterials,” Phys. Rev. B76(24), 245109 (2007).
[CrossRef]

M. Beruete, I. Campillo, M. Navarro-Cia, F. Falcone, and M. Sorolla Ayza, “Molding left- or right-handed metamaterials by stacked cutoff metallic hole arrays,” IEEE Trans. Antenn. Propag.55(6), 1514–1521 (2007).
[CrossRef]

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: tailoring the radiation phase pattern,” Phys. Rev. B75(15), 155410 (2007).
[CrossRef]

2006 (1)

M. G. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using ε-near-zero materials,” Phys. Rev. Lett.97(15), 157403 (2006).
[CrossRef] [PubMed]

2005 (2)

2004 (2)

R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.70(4), 046608 (2004).
[CrossRef] [PubMed]

Z. Sun and H. K. Kim, “Refractive transmission of light and beam shaping with metallic nano-optic lenses,” Appl. Phys. Lett.85(4), 642–644 (2004).
[CrossRef]

2000 (1)

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(18), 4184–4187 (2000).
[CrossRef] [PubMed]

1993 (1)

D. Filipovic, S. Gearhart, and G. Rebeiz, “Double-slot antennas on extended hemispherical and elliptical silicon dielectric lenses,” IEEE T. Microw. Theory41(10), 1738–1749 (1993).
[CrossRef]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972).
[CrossRef]

1950 (1)

J. Ruze, “Wide-angle metal-plate optics,” Proceedings of the IRE38(1), 853–855 (1950).
[CrossRef]

1946 (1)

W. Kock, “Metal-lens antennas,” Proceedings of the IRE34(11), 828–836 (1946).
[CrossRef]

Alù, A.

A. Alù, M. G. Silveirinha, and N. Engheta, “Transmission-line analysis of ε -near-zero-filled narrow channels,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.78(1), 016604 (2008).
[CrossRef] [PubMed]

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett.100(3), 033903 (2008).
[CrossRef] [PubMed]

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: tailoring the radiation phase pattern,” Phys. Rev. B75(15), 155410 (2007).
[CrossRef]

Barnard, E. S.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses Based on Nanoscale Slit Arrays in a metallic film,” Nano Lett.9(1), 235–238 (2009).
[CrossRef] [PubMed]

Beruete, M.

M. Navarro-Cía, M. Beruete, M. Sorolla, and N. Engheta, “Lensing system and Fourier transformation using epsilon-near-zero metamaterials,” Phys. Rev. B86(16), 165130 (2012).
[CrossRef]

M. Navarro-Cía, M. Beruete, I. Campillo, and M. Sorolla Ayza, “Beamforming by left-handed extraordinary transmission metamaterial bi- and plano-concave lens at millimeter-waves,” IEEE Trans. Antenn. Propag.59(6), 2141–2151 (2011).
[CrossRef]

M. Navarro-Cía, M. Beruete, I. Campillo, and M. Sorolla, “Enhanced lens by ε and μ near-zero metamaterial boosted by extraordinary optical transmission,” Phys. Rev. B83(11), 115112 (2011).
[CrossRef]

M. Beruete, I. Campillo, M. Navarro-Cia, F. Falcone, and M. Sorolla Ayza, “Molding left- or right-handed metamaterials by stacked cutoff metallic hole arrays,” IEEE Trans. Antenn. Propag.55(6), 1514–1521 (2007).
[CrossRef]

Bolivar, P.

Brongersma, M. L.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses Based on Nanoscale Slit Arrays in a metallic film,” Nano Lett.9(1), 235–238 (2009).
[CrossRef] [PubMed]

Campillo, I.

M. Navarro-Cía, M. Beruete, I. Campillo, and M. Sorolla, “Enhanced lens by ε and μ near-zero metamaterial boosted by extraordinary optical transmission,” Phys. Rev. B83(11), 115112 (2011).
[CrossRef]

M. Navarro-Cía, M. Beruete, I. Campillo, and M. Sorolla Ayza, “Beamforming by left-handed extraordinary transmission metamaterial bi- and plano-concave lens at millimeter-waves,” IEEE Trans. Antenn. Propag.59(6), 2141–2151 (2011).
[CrossRef]

M. Beruete, I. Campillo, M. Navarro-Cia, F. Falcone, and M. Sorolla Ayza, “Molding left- or right-handed metamaterials by stacked cutoff metallic hole arrays,” IEEE Trans. Antenn. Propag.55(6), 1514–1521 (2007).
[CrossRef]

Catrysse, P. B.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses Based on Nanoscale Slit Arrays in a metallic film,” Nano Lett.9(1), 235–238 (2009).
[CrossRef] [PubMed]

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett.103(3), 033902 (2009).
[CrossRef] [PubMed]

Chattopadhyay, G.

N. Llombart, G. Chattopadhyay, A. Skalare, and I. Mehdi, “Novel terahertz antenna based on a silicon lens fed by a leaky wave enhanced waveguide,” IEEE Trans. Antenn. Propag.59(6), 2160–2168 (2011).
[CrossRef]

Chen, K. P.

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972).
[CrossRef]

Dong, X.

Drachev, V. P.

S. Ishii, A. V. Kildishev, V. M. Shalaev, and V. P. Drachev, “Controlling the wave focal structure of metallic nanoslit lenses with liquid crystals,” Laser Phys. Lett.8(11), 828–832 (2011).
[CrossRef]

S. Ishii, A. V. Kildishev, V. M. Shalaev, K. P. Chen, and V. P. Drachev, “Metal nanoslit lenses with polarization-selective design,” Opt. Lett.36(4), 451–453 (2011).
[CrossRef] [PubMed]

Du, C.

Edwards, B.

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett.100(3), 033903 (2008).
[CrossRef] [PubMed]

Engheta, N.

M. Navarro-Cía, M. Beruete, M. Sorolla, and N. Engheta, “Lensing system and Fourier transformation using epsilon-near-zero metamaterials,” Phys. Rev. B86(16), 165130 (2012).
[CrossRef]

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett.100(3), 033903 (2008).
[CrossRef] [PubMed]

A. Alù, M. G. Silveirinha, and N. Engheta, “Transmission-line analysis of ε -near-zero-filled narrow channels,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.78(1), 016604 (2008).
[CrossRef] [PubMed]

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: tailoring the radiation phase pattern,” Phys. Rev. B75(15), 155410 (2007).
[CrossRef]

M. G. Silveirinha and N. Engheta, “Theory of supercoupling, squeezing wave energy, and field confinement in narrow channels and tight bends using ε near-zero metamaterials,” Phys. Rev. B76(24), 245109 (2007).
[CrossRef]

M. G. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using ε-near-zero materials,” Phys. Rev. Lett.97(15), 157403 (2006).
[CrossRef] [PubMed]

Escobar, M.

C. Ma, M. Escobar, and Z. Liu, “Extraordinary light focusing and Fourier transform properties of gradient-index metalenses,” Phys. Rev. B84(19), 195142 (2011).
[CrossRef]

Falcone, F.

M. Beruete, I. Campillo, M. Navarro-Cia, F. Falcone, and M. Sorolla Ayza, “Molding left- or right-handed metamaterials by stacked cutoff metallic hole arrays,” IEEE Trans. Antenn. Propag.55(6), 1514–1521 (2007).
[CrossRef]

Fan, S.

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett.103(3), 033902 (2009).
[CrossRef] [PubMed]

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses Based on Nanoscale Slit Arrays in a metallic film,” Nano Lett.9(1), 235–238 (2009).
[CrossRef] [PubMed]

Filipovic, D.

D. Filipovic, S. Gearhart, and G. Rebeiz, “Double-slot antennas on extended hemispherical and elliptical silicon dielectric lenses,” IEEE T. Microw. Theory41(10), 1738–1749 (1993).
[CrossRef]

Gao, H.

Gearhart, S.

D. Filipovic, S. Gearhart, and G. Rebeiz, “Double-slot antennas on extended hemispherical and elliptical silicon dielectric lenses,” IEEE T. Microw. Theory41(10), 1738–1749 (1993).
[CrossRef]

Gómez Rivas, J.

Ishii, S.

S. Ishii, V. M. Shalaev, and A. V. Kildishev, “Holey-metal lenses: sieving single modes with proper phases,” Nano Lett.13(1), 159–163 (2013).
[CrossRef] [PubMed]

S. Ishii, A. V. Kildishev, V. M. Shalaev, K. P. Chen, and V. P. Drachev, “Metal nanoslit lenses with polarization-selective design,” Opt. Lett.36(4), 451–453 (2011).
[CrossRef] [PubMed]

S. Ishii, A. V. Kildishev, V. M. Shalaev, and V. P. Drachev, “Controlling the wave focal structure of metallic nanoslit lenses with liquid crystals,” Laser Phys. Lett.8(11), 828–832 (2011).
[CrossRef]

Janke, C.

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972).
[CrossRef]

Kildishev, A. V.

S. Ishii, V. M. Shalaev, and A. V. Kildishev, “Holey-metal lenses: sieving single modes with proper phases,” Nano Lett.13(1), 159–163 (2013).
[CrossRef] [PubMed]

S. Ishii, A. V. Kildishev, V. M. Shalaev, K. P. Chen, and V. P. Drachev, “Metal nanoslit lenses with polarization-selective design,” Opt. Lett.36(4), 451–453 (2011).
[CrossRef] [PubMed]

S. Ishii, A. V. Kildishev, V. M. Shalaev, and V. P. Drachev, “Controlling the wave focal structure of metallic nanoslit lenses with liquid crystals,” Laser Phys. Lett.8(11), 828–832 (2011).
[CrossRef]

Kim, H. K.

Z. Sun and H. K. Kim, “Refractive transmission of light and beam shaping with metallic nano-optic lenses,” Appl. Phys. Lett.85(4), 642–644 (2004).
[CrossRef]

Kock, W.

W. Kock, “Metal-lens antennas,” Proceedings of the IRE34(11), 828–836 (1946).
[CrossRef]

Kurz, H.

Liu, Z.

C. Ma, M. Escobar, and Z. Liu, “Extraordinary light focusing and Fourier transform properties of gradient-index metalenses,” Phys. Rev. B84(19), 195142 (2011).
[CrossRef]

C. Ma and Z. Liu, “A super resolution metalens with phase compensation mechanism,” Appl. Phys. Lett.96(18), 183103 (2010).
[CrossRef]

Llombart, N.

N. Llombart, G. Chattopadhyay, A. Skalare, and I. Mehdi, “Novel terahertz antenna based on a silicon lens fed by a leaky wave enhanced waveguide,” IEEE Trans. Antenn. Propag.59(6), 2160–2168 (2011).
[CrossRef]

Luo, X.

Ma, C.

C. Ma, M. Escobar, and Z. Liu, “Extraordinary light focusing and Fourier transform properties of gradient-index metalenses,” Phys. Rev. B84(19), 195142 (2011).
[CrossRef]

C. Ma and Z. Liu, “A super resolution metalens with phase compensation mechanism,” Appl. Phys. Lett.96(18), 183103 (2010).
[CrossRef]

Mehdi, I.

N. Llombart, G. Chattopadhyay, A. Skalare, and I. Mehdi, “Novel terahertz antenna based on a silicon lens fed by a leaky wave enhanced waveguide,” IEEE Trans. Antenn. Propag.59(6), 2160–2168 (2011).
[CrossRef]

Navarro-Cia, M.

M. Beruete, I. Campillo, M. Navarro-Cia, F. Falcone, and M. Sorolla Ayza, “Molding left- or right-handed metamaterials by stacked cutoff metallic hole arrays,” IEEE Trans. Antenn. Propag.55(6), 1514–1521 (2007).
[CrossRef]

Navarro-Cía, M.

M. Navarro-Cía, M. Beruete, M. Sorolla, and N. Engheta, “Lensing system and Fourier transformation using epsilon-near-zero metamaterials,” Phys. Rev. B86(16), 165130 (2012).
[CrossRef]

M. Navarro-Cía, M. Beruete, I. Campillo, and M. Sorolla Ayza, “Beamforming by left-handed extraordinary transmission metamaterial bi- and plano-concave lens at millimeter-waves,” IEEE Trans. Antenn. Propag.59(6), 2141–2151 (2011).
[CrossRef]

M. Navarro-Cía, M. Beruete, I. Campillo, and M. Sorolla, “Enhanced lens by ε and μ near-zero metamaterial boosted by extraordinary optical transmission,” Phys. Rev. B83(11), 115112 (2011).
[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(18), 4184–4187 (2000).
[CrossRef] [PubMed]

Padilla, W. J.

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(18), 4184–4187 (2000).
[CrossRef] [PubMed]

Rebeiz, G.

D. Filipovic, S. Gearhart, and G. Rebeiz, “Double-slot antennas on extended hemispherical and elliptical silicon dielectric lenses,” IEEE T. Microw. Theory41(10), 1738–1749 (1993).
[CrossRef]

Ruze, J.

J. Ruze, “Wide-angle metal-plate optics,” Proceedings of the IRE38(1), 853–855 (1950).
[CrossRef]

Salandrino, A.

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: tailoring the radiation phase pattern,” Phys. Rev. B75(15), 155410 (2007).
[CrossRef]

Schultz, S.

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(18), 4184–4187 (2000).
[CrossRef] [PubMed]

Shalaev, V. M.

S. Ishii, V. M. Shalaev, and A. V. Kildishev, “Holey-metal lenses: sieving single modes with proper phases,” Nano Lett.13(1), 159–163 (2013).
[CrossRef] [PubMed]

S. Ishii, A. V. Kildishev, V. M. Shalaev, K. P. Chen, and V. P. Drachev, “Metal nanoslit lenses with polarization-selective design,” Opt. Lett.36(4), 451–453 (2011).
[CrossRef] [PubMed]

S. Ishii, A. V. Kildishev, V. M. Shalaev, and V. P. Drachev, “Controlling the wave focal structure of metallic nanoslit lenses with liquid crystals,” Laser Phys. Lett.8(11), 828–832 (2011).
[CrossRef]

Shi, H.

Silveirinha, M.

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett.100(3), 033903 (2008).
[CrossRef] [PubMed]

Silveirinha, M. G.

A. Alù, M. G. Silveirinha, and N. Engheta, “Transmission-line analysis of ε -near-zero-filled narrow channels,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.78(1), 016604 (2008).
[CrossRef] [PubMed]

M. G. Silveirinha and N. Engheta, “Theory of supercoupling, squeezing wave energy, and field confinement in narrow channels and tight bends using ε near-zero metamaterials,” Phys. Rev. B76(24), 245109 (2007).
[CrossRef]

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: tailoring the radiation phase pattern,” Phys. Rev. B75(15), 155410 (2007).
[CrossRef]

M. G. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using ε-near-zero materials,” Phys. Rev. Lett.97(15), 157403 (2006).
[CrossRef] [PubMed]

Skalare, A.

N. Llombart, G. Chattopadhyay, A. Skalare, and I. Mehdi, “Novel terahertz antenna based on a silicon lens fed by a leaky wave enhanced waveguide,” IEEE Trans. Antenn. Propag.59(6), 2160–2168 (2011).
[CrossRef]

Smith, D. R.

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(18), 4184–4187 (2000).
[CrossRef] [PubMed]

Sorolla, M.

M. Navarro-Cía, M. Beruete, M. Sorolla, and N. Engheta, “Lensing system and Fourier transformation using epsilon-near-zero metamaterials,” Phys. Rev. B86(16), 165130 (2012).
[CrossRef]

M. Navarro-Cía, M. Beruete, I. Campillo, and M. Sorolla, “Enhanced lens by ε and μ near-zero metamaterial boosted by extraordinary optical transmission,” Phys. Rev. B83(11), 115112 (2011).
[CrossRef]

Sorolla Ayza, M.

M. Navarro-Cía, M. Beruete, I. Campillo, and M. Sorolla Ayza, “Beamforming by left-handed extraordinary transmission metamaterial bi- and plano-concave lens at millimeter-waves,” IEEE Trans. Antenn. Propag.59(6), 2141–2151 (2011).
[CrossRef]

M. Beruete, I. Campillo, M. Navarro-Cia, F. Falcone, and M. Sorolla Ayza, “Molding left- or right-handed metamaterials by stacked cutoff metallic hole arrays,” IEEE Trans. Antenn. Propag.55(6), 1514–1521 (2007).
[CrossRef]

Sun, Z.

Z. Sun and H. K. Kim, “Refractive transmission of light and beam shaping with metallic nano-optic lenses,” Appl. Phys. Lett.85(4), 642–644 (2004).
[CrossRef]

Verslegers, L.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses Based on Nanoscale Slit Arrays in a metallic film,” Nano Lett.9(1), 235–238 (2009).
[CrossRef] [PubMed]

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett.103(3), 033902 (2009).
[CrossRef] [PubMed]

Vier, D. 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(18), 4184–4187 (2000).
[CrossRef] [PubMed]

Wang, C.

White, J. S.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses Based on Nanoscale Slit Arrays in a metallic film,” Nano Lett.9(1), 235–238 (2009).
[CrossRef] [PubMed]

Young, M. E.

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett.100(3), 033903 (2008).
[CrossRef] [PubMed]

Yu, Z.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses Based on Nanoscale Slit Arrays in a metallic film,” Nano Lett.9(1), 235–238 (2009).
[CrossRef] [PubMed]

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett.103(3), 033902 (2009).
[CrossRef] [PubMed]

Ziolkowski, R. W.

R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.70(4), 046608 (2004).
[CrossRef] [PubMed]

Appl. Phys. Lett. (2)

Z. Sun and H. K. Kim, “Refractive transmission of light and beam shaping with metallic nano-optic lenses,” Appl. Phys. Lett.85(4), 642–644 (2004).
[CrossRef]

C. Ma and Z. Liu, “A super resolution metalens with phase compensation mechanism,” Appl. Phys. Lett.96(18), 183103 (2010).
[CrossRef]

IEEE T. Microw. Theory (1)

D. Filipovic, S. Gearhart, and G. Rebeiz, “Double-slot antennas on extended hemispherical and elliptical silicon dielectric lenses,” IEEE T. Microw. Theory41(10), 1738–1749 (1993).
[CrossRef]

IEEE Trans. Antenn. Propag. (3)

N. Llombart, G. Chattopadhyay, A. Skalare, and I. Mehdi, “Novel terahertz antenna based on a silicon lens fed by a leaky wave enhanced waveguide,” IEEE Trans. Antenn. Propag.59(6), 2160–2168 (2011).
[CrossRef]

M. Beruete, I. Campillo, M. Navarro-Cia, F. Falcone, and M. Sorolla Ayza, “Molding left- or right-handed metamaterials by stacked cutoff metallic hole arrays,” IEEE Trans. Antenn. Propag.55(6), 1514–1521 (2007).
[CrossRef]

M. Navarro-Cía, M. Beruete, I. Campillo, and M. Sorolla Ayza, “Beamforming by left-handed extraordinary transmission metamaterial bi- and plano-concave lens at millimeter-waves,” IEEE Trans. Antenn. Propag.59(6), 2141–2151 (2011).
[CrossRef]

Laser Phys. Lett. (1)

S. Ishii, A. V. Kildishev, V. M. Shalaev, and V. P. Drachev, “Controlling the wave focal structure of metallic nanoslit lenses with liquid crystals,” Laser Phys. Lett.8(11), 828–832 (2011).
[CrossRef]

Nano Lett. (2)

S. Ishii, V. M. Shalaev, and A. V. Kildishev, “Holey-metal lenses: sieving single modes with proper phases,” Nano Lett.13(1), 159–163 (2013).
[CrossRef] [PubMed]

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses Based on Nanoscale Slit Arrays in a metallic film,” Nano Lett.9(1), 235–238 (2009).
[CrossRef] [PubMed]

Opt. Express (2)

Opt. Lett. (1)

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[CrossRef]

C. Ma, M. Escobar, and Z. Liu, “Extraordinary light focusing and Fourier transform properties of gradient-index metalenses,” Phys. Rev. B84(19), 195142 (2011).
[CrossRef]

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: tailoring the radiation phase pattern,” Phys. Rev. B75(15), 155410 (2007).
[CrossRef]

M. G. Silveirinha and N. Engheta, “Theory of supercoupling, squeezing wave energy, and field confinement in narrow channels and tight bends using ε near-zero metamaterials,” Phys. Rev. B76(24), 245109 (2007).
[CrossRef]

M. Navarro-Cía, M. Beruete, I. Campillo, and M. Sorolla, “Enhanced lens by ε and μ near-zero metamaterial boosted by extraordinary optical transmission,” Phys. Rev. B83(11), 115112 (2011).
[CrossRef]

M. Navarro-Cía, M. Beruete, M. Sorolla, and N. Engheta, “Lensing system and Fourier transformation using epsilon-near-zero metamaterials,” Phys. Rev. B86(16), 165130 (2012).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (2)

R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.70(4), 046608 (2004).
[CrossRef] [PubMed]

A. Alù, M. G. Silveirinha, and N. Engheta, “Transmission-line analysis of ε -near-zero-filled narrow channels,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.78(1), 016604 (2008).
[CrossRef] [PubMed]

Phys. Rev. Lett. (4)

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett.103(3), 033902 (2009).
[CrossRef] [PubMed]

M. G. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using ε-near-zero materials,” Phys. Rev. Lett.97(15), 157403 (2006).
[CrossRef] [PubMed]

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett.100(3), 033903 (2008).
[CrossRef] [PubMed]

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(18), 4184–4187 (2000).
[CrossRef] [PubMed]

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[CrossRef]

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[CrossRef]

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L. Solymar and E. Shamonina, Waves in Metamaterials (Oxford, 2009).

N. Engheta and R. W. Ziolkowski, Metamaterials: Physics and Engineering Explorations (Wiley, 2006).

H. D. Hristov, Fresnel Zones in Wireless Links, Zone Plate Lenses and Antennas (Artech House, 2000).

R. E. Collin, Foundations for Microwave Engineering (Wiley, 2000).

D. M. Pozar, Microwave Engineering (Wiley, 2005).

Microtech Instruments Inc, http://mtinstruments.com

Thorlabs Inc, http://www.thorlabs.com

J. W. Goodman, Introduction to Fourier Optics (Roberts & Company Publishers, 2004).

C. Bohren and D. Huffmann, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

J. D. Jackson, Classical Electrodynamics (Wiley, 1999).

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Figures (6)

Fig. 1
Fig. 1

(a) Schematic of a plane wave with TM-polarization impinging on an arrangement of metallic waveguides of constant length L. For each waveguide, width (hx) and height (hy) are determined in order to achieve the required circular wave front with focal length r0. The values Δθw and Δθa are the phase delay inside the waveguide and the phase delay in the air, respectively. (b) Perspective view and unit cell detail of dimensions dx and dy.

Fig. 2
Fig. 2

(a) Dimensions of the waveguide width hx, and height hy and phase variation Δθw of each waveguide for a 2D graded-index lens of total width 3.06 mm and focal length 1.5 mm. (b) Comparison between the relative effective permittivity of each ENZ waveguide obtained with simulation (open square) and analytical formulation (solid rhombus).

Fig. 3
Fig. 3

(a) Top view (xz-plane) of the magnetic field distribution Hy on a system composed of a flat metallic lens made of arrangement of ENZ waveguides illuminated by a normally incident plane wave. (b) Magnetic field distribution Hy and electric field distribution Ex along the optical axis, z-direction; and (c) along the x-direction at the focal length.

Fig. 4
Fig. 4

Cross section of the power along x-direction at the focal plane when the input signal is an obliquely incident plane wave. It is represented from 0 to 20 degrees of angle of incidence in steps of 5 degrees. (inset) Top view (xz-plane) of the magnetic field distribution Hy along the focal plane for an input wave with an angle of incidence of 20 degrees.

Fig. 5
Fig. 5

(a) Sketch of the proposed 3D planar graded index lens, made of arrangement of ENZ waveguides, of total dimensions Lx and Ly and thickness Lz. (b) Power distribution along the xz- and yz-planes, and (inset) along the x-direction and y-direction when the structure is excited with a plane wave

Fig. 6
Fig. 6

(a) Top view (xz-plane) and (b) side view (yz-plane) of the magnetic field distribution Hy on a system composed of a three dimensional ENZ lens illuminated by a Gaussian beam. (c) xz-plane and (d) yz-plane of the power distribution on the same system. Scale on panel (b) and (d) is also valid in (a) and (c) respectively.

Tables (2)

Tables Icon

Table 1 Feature summary for a two-dimensional lens with different total widths

Tables Icon

Table 2 Feature Summary for a Two-dimensional Lens at Different Operation Frequencies

Equations (7)

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β= k 0 1 ( f c T E 01 f ) 2 = k 0 1 ( π k 0 h y ) 2 ,
ε w_eff =1 ( f c T E 01 f ) 2 =1 ( π k 0 h y ) 2 ,
Δ θ w =βL=( k 0 1 ( π k 0 h y ) 2 )L,
Δ θ w ( x i )=2πiΔ θ a ( x i )Δ θ w ( x i =0)=2πi k 0 ( r i r 0 )Δ θ w ( x i =0),
h y ( x i )= π k 0 2 ( Δ θ w ( x i ) L ) 2 .
d x d y μ 0 ε 0 = η air = η w = h x ( x i ) h y ( x i ) μ 0 ε 0 ε w_eff .
h x ( x i )= Δ θ w ( x i ) k 0 L d x d y h y ( x i ).

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