Abstract

In this paper we theoretically and experimentally demonstrate a stepped-refractive-index convergent lens made of a parallel stack of metallic plates for terahertz frequencies based on artificial dielectrics. The lens consist of a non-uniformly spaced stack of metallic plates, forming a mirror-symmetric array of parallel-plate waveguides (PPWGs). The operation of the device is based on the TE1 mode of the PPWG. The effective refractive index of the TE1 mode is a function of the frequency of operation and the spacing between the plates of the PPWG. By varying the spacing between the plates, we can modify the local refractive index of the structure in every individual PPWG that constitutes the lens producing a stepped refractive index profile across the multi stack structure. The theoretical and experimental results show that this structure is capable of focusing a 1 cm diameter beam to a line focus of less than 4 mm for the design frequency of 0.18 THz. This structure shows that this artificial-dielectric concept is an important technology for the fabrication of next generation terahertz devices.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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Corrections

27 February 2018: A typographical correction was made to the author affiliations.


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References

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  1. S. Dhillon, M. Vitiello, E. Linfield, A. Davies, M. C. Hoffmann, J. Booske, C. Paoloni, M. Gensch, P. Weightman, G. Williams, and et al., “The 2017 terahertz science and technology roadmap,” J. Phys. D: Appl. Phys. 50, 043001 (2017).
    [Crossref]
  2. A. Squires, E. Constable, and R. A. Lewis, “3d printed terahertz diffraction gratings and lenses,” J. Infrared Millim. Terahertz Waves. 36, 72–80 (2015).
    [Crossref]
  3. S. Busch, M. Weidenbach, M. Fey, F. Schäfer, T. Probst, and M. Koch, “Optical properties of 3d printable plastics in the thz regime and their application for 3d printed thz optics,” J. Infrared Millim. Terahertz Waves. 35, 993–997 (2014).
    [Crossref]
  4. A. Hernandez-Serrano, M. Weidenbach, S. Busch, M. Koch, and E. Castro-Camus, “Fabrication of gradient-refractive-index lenses for terahertz applications by three-dimensional printing,” J. Opt. Soc. Am. B. 33, 928–931 (2016).
    [Crossref]
  5. S. F. Busch, J. C. Balzer, G. Bastian, G. E. Town, and M. Koch, “Extending the alvarez-lens concept to arbitrary optical devices: Tunable gratings, lenses, and spiral phase plates,” IEEE Trans. THz Sci. Technol. 7, 320–325 (2017).
    [Crossref]
  6. B. Scherger, M. Scheller, C. Jansen, M. Koch, and K. Wiesauer, “Terahertz lenses made by compression molding of micropowders,” Appl. Opt. 50, 2256–2262 (2011).
    [Crossref] [PubMed]
  7. 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]
  8. D. Smith, J. Mock, A. Starr, and D. Schurig, “Gradient index metamaterials,” Phys. Rev. E. 71, 036609 (2005).
    [Crossref]
  9. 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] [PubMed]
  10. O. Paul, B. Reinhard, B. Krolla, R. Beigang, and M. Rahm, “Gradient index metamaterial based on slot elements,” Appl. Phys. Lett. 96, 241110 (2010).
    [Crossref]
  11. R. Mendis and D. M. Mittleman, “A 2-d artificial dielectric with 0≤n<1 for the terahertz region,” IEEE Trans. Microw. Theory Techn. 58, 1993–1998 (2010).
    [Crossref]
  12. R. Mendis, M. Nagai, Y. Wang, N. Karl, and D. M. Mittleman, “Terahertz artificial dielectric lens,” Sci. Rep. 6, 23023 (2016).
    [Crossref]
  13. S. Jones and J. Brown, “Metallic delay lenses,” Nature 163, 324–325 (1949).
    [Crossref]
  14. W. E. Kock, “Metal-lens antennas,” Proc. IRE 34, 828–836 (1946).
    [Crossref]
  15. J. Brown, “Artificial dielectrics having refractive indices less than unity,” Proc IEE 100, 51–62 (1953).
  16. V. Torres, V. Pacheco-Peña, P. Rodríguez-Ulibarri, M. Navarro-Cía, M. Beruete, M. Sorolla, and N. Engheta, “Terahertz epsilon-near-zero graded-index lens,” Opt. Express. 21, 9156–9166 (2013).
    [Crossref] [PubMed]
  17. R. Mendis and D. M. Mittleman, “Comparison of the lowest-order transverse-electric (TE1) and transverse-magnetic (TEM) modes of the parallel-plate waveguide for terahertz pulse applications,” Opt. Express. 17, 14839–14850 (2009).
    [Crossref] [PubMed]
  18. R. Mendis, M. Nagai, W. Zhang, and D. M. Mittleman, “Artificial dielectric polarizing-beamsplitter and isolator for the terahertz region,” Sci. Rep. 7, 5909 (2017).
    [Crossref] [PubMed]
  19. R. Mendis, J. Liu, and D. M. Mittleman, “Terahertz mirage: Deflecting terahertz beams in an inhomogeneous artificial dielectric based on a parallel-plate waveguide,” Appl. Phys. Lett. 101, 111108 (2012).
    [Crossref]
  20. C. A. Balanis, Advanced engineering electromagnetics (John Wiley & Sons, 1999).
  21. D. G. Voelz, Computational fourier optics: a MATLAB tutorial (SPIE press, 2011).

2017 (3)

R. Mendis, M. Nagai, W. Zhang, and D. M. Mittleman, “Artificial dielectric polarizing-beamsplitter and isolator for the terahertz region,” Sci. Rep. 7, 5909 (2017).
[Crossref] [PubMed]

S. Dhillon, M. Vitiello, E. Linfield, A. Davies, M. C. Hoffmann, J. Booske, C. Paoloni, M. Gensch, P. Weightman, G. Williams, and et al., “The 2017 terahertz science and technology roadmap,” J. Phys. D: Appl. Phys. 50, 043001 (2017).
[Crossref]

S. F. Busch, J. C. Balzer, G. Bastian, G. E. Town, and M. Koch, “Extending the alvarez-lens concept to arbitrary optical devices: Tunable gratings, lenses, and spiral phase plates,” IEEE Trans. THz Sci. Technol. 7, 320–325 (2017).
[Crossref]

2016 (2)

R. Mendis, M. Nagai, Y. Wang, N. Karl, and D. M. Mittleman, “Terahertz artificial dielectric lens,” Sci. Rep. 6, 23023 (2016).
[Crossref]

A. Hernandez-Serrano, M. Weidenbach, S. Busch, M. Koch, and E. Castro-Camus, “Fabrication of gradient-refractive-index lenses for terahertz applications by three-dimensional printing,” J. Opt. Soc. Am. B. 33, 928–931 (2016).
[Crossref]

2015 (1)

A. Squires, E. Constable, and R. A. Lewis, “3d printed terahertz diffraction gratings and lenses,” J. Infrared Millim. Terahertz Waves. 36, 72–80 (2015).
[Crossref]

2014 (1)

S. Busch, M. Weidenbach, M. Fey, F. Schäfer, T. Probst, and M. Koch, “Optical properties of 3d printable plastics in the thz regime and their application for 3d printed thz optics,” J. Infrared Millim. Terahertz Waves. 35, 993–997 (2014).
[Crossref]

2013 (1)

V. Torres, V. Pacheco-Peña, P. Rodríguez-Ulibarri, M. Navarro-Cía, M. Beruete, M. Sorolla, and N. Engheta, “Terahertz epsilon-near-zero graded-index lens,” Opt. Express. 21, 9156–9166 (2013).
[Crossref] [PubMed]

2012 (1)

R. Mendis, J. Liu, and D. M. Mittleman, “Terahertz mirage: Deflecting terahertz beams in an inhomogeneous artificial dielectric based on a parallel-plate waveguide,” Appl. Phys. Lett. 101, 111108 (2012).
[Crossref]

2011 (1)

2010 (3)

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]

O. Paul, B. Reinhard, B. Krolla, R. Beigang, and M. Rahm, “Gradient index metamaterial based on slot elements,” Appl. Phys. Lett. 96, 241110 (2010).
[Crossref]

R. Mendis and D. M. Mittleman, “A 2-d artificial dielectric with 0≤n<1 for the terahertz region,” IEEE Trans. Microw. Theory Techn. 58, 1993–1998 (2010).
[Crossref]

2009 (2)

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] [PubMed]

R. Mendis and D. M. Mittleman, “Comparison of the lowest-order transverse-electric (TE1) and transverse-magnetic (TEM) modes of the parallel-plate waveguide for terahertz pulse applications,” Opt. Express. 17, 14839–14850 (2009).
[Crossref] [PubMed]

2005 (1)

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

1953 (1)

J. Brown, “Artificial dielectrics having refractive indices less than unity,” Proc IEE 100, 51–62 (1953).

1949 (1)

S. Jones and J. Brown, “Metallic delay lenses,” Nature 163, 324–325 (1949).
[Crossref]

1946 (1)

W. E. Kock, “Metal-lens antennas,” Proc. IRE 34, 828–836 (1946).
[Crossref]

Balanis, C. A.

C. A. Balanis, Advanced engineering electromagnetics (John Wiley & Sons, 1999).

Balzer, J. C.

S. F. Busch, J. C. Balzer, G. Bastian, G. E. Town, and M. Koch, “Extending the alvarez-lens concept to arbitrary optical devices: Tunable gratings, lenses, and spiral phase plates,” IEEE Trans. THz Sci. Technol. 7, 320–325 (2017).
[Crossref]

Bastian, G.

S. F. Busch, J. C. Balzer, G. Bastian, G. E. Town, and M. Koch, “Extending the alvarez-lens concept to arbitrary optical devices: Tunable gratings, lenses, and spiral phase plates,” IEEE Trans. THz Sci. Technol. 7, 320–325 (2017).
[Crossref]

Beigang, R.

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]

O. Paul, B. Reinhard, B. Krolla, R. Beigang, and M. Rahm, “Gradient index metamaterial based on slot elements,” Appl. Phys. Lett. 96, 241110 (2010).
[Crossref]

Beruete, M.

V. Torres, V. Pacheco-Peña, P. Rodríguez-Ulibarri, M. Navarro-Cía, M. Beruete, M. Sorolla, and N. Engheta, “Terahertz epsilon-near-zero graded-index lens,” Opt. Express. 21, 9156–9166 (2013).
[Crossref] [PubMed]

Booske, J.

S. Dhillon, M. Vitiello, E. Linfield, A. Davies, M. C. Hoffmann, J. Booske, C. Paoloni, M. Gensch, P. Weightman, G. Williams, and et al., “The 2017 terahertz science and technology roadmap,” J. Phys. D: Appl. Phys. 50, 043001 (2017).
[Crossref]

Brown, J.

J. Brown, “Artificial dielectrics having refractive indices less than unity,” Proc IEE 100, 51–62 (1953).

S. Jones and J. Brown, “Metallic delay lenses,” Nature 163, 324–325 (1949).
[Crossref]

Busch, S.

A. Hernandez-Serrano, M. Weidenbach, S. Busch, M. Koch, and E. Castro-Camus, “Fabrication of gradient-refractive-index lenses for terahertz applications by three-dimensional printing,” J. Opt. Soc. Am. B. 33, 928–931 (2016).
[Crossref]

S. Busch, M. Weidenbach, M. Fey, F. Schäfer, T. Probst, and M. Koch, “Optical properties of 3d printable plastics in the thz regime and their application for 3d printed thz optics,” J. Infrared Millim. Terahertz Waves. 35, 993–997 (2014).
[Crossref]

Busch, S. F.

S. F. Busch, J. C. Balzer, G. Bastian, G. E. Town, and M. Koch, “Extending the alvarez-lens concept to arbitrary optical devices: Tunable gratings, lenses, and spiral phase plates,” IEEE Trans. THz Sci. Technol. 7, 320–325 (2017).
[Crossref]

Castro-Camus, E.

A. Hernandez-Serrano, M. Weidenbach, S. Busch, M. Koch, and E. Castro-Camus, “Fabrication of gradient-refractive-index lenses for terahertz applications by three-dimensional printing,” J. Opt. Soc. Am. B. 33, 928–931 (2016).
[Crossref]

Cheng, Q.

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] [PubMed]

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] [PubMed]

Constable, E.

A. Squires, E. Constable, and R. A. Lewis, “3d printed terahertz diffraction gratings and lenses,” J. Infrared Millim. Terahertz Waves. 36, 72–80 (2015).
[Crossref]

Cui, T. 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] [PubMed]

Davies, A.

S. Dhillon, M. Vitiello, E. Linfield, A. Davies, M. C. Hoffmann, J. Booske, C. Paoloni, M. Gensch, P. Weightman, G. Williams, and et al., “The 2017 terahertz science and technology roadmap,” J. Phys. D: Appl. Phys. 50, 043001 (2017).
[Crossref]

Dhillon, S.

S. Dhillon, M. Vitiello, E. Linfield, A. Davies, M. C. Hoffmann, J. Booske, C. Paoloni, M. Gensch, P. Weightman, G. Williams, and et al., “The 2017 terahertz science and technology roadmap,” J. Phys. D: Appl. Phys. 50, 043001 (2017).
[Crossref]

Engheta, N.

V. Torres, V. Pacheco-Peña, P. Rodríguez-Ulibarri, M. Navarro-Cía, M. Beruete, M. Sorolla, and N. Engheta, “Terahertz epsilon-near-zero graded-index lens,” Opt. Express. 21, 9156–9166 (2013).
[Crossref] [PubMed]

Fey, M.

S. Busch, M. Weidenbach, M. Fey, F. Schäfer, T. Probst, and M. Koch, “Optical properties of 3d printable plastics in the thz regime and their application for 3d printed thz optics,” J. Infrared Millim. Terahertz Waves. 35, 993–997 (2014).
[Crossref]

Gensch, M.

S. Dhillon, M. Vitiello, E. Linfield, A. Davies, M. C. Hoffmann, J. Booske, C. Paoloni, M. Gensch, P. Weightman, G. Williams, and et al., “The 2017 terahertz science and technology roadmap,” J. Phys. D: Appl. Phys. 50, 043001 (2017).
[Crossref]

Hernandez-Serrano, A.

A. Hernandez-Serrano, M. Weidenbach, S. Busch, M. Koch, and E. Castro-Camus, “Fabrication of gradient-refractive-index lenses for terahertz applications by three-dimensional printing,” J. Opt. Soc. Am. B. 33, 928–931 (2016).
[Crossref]

Hoffmann, M. C.

S. Dhillon, M. Vitiello, E. Linfield, A. Davies, M. C. Hoffmann, J. Booske, C. Paoloni, M. Gensch, P. Weightman, G. Williams, and et al., “The 2017 terahertz science and technology roadmap,” J. Phys. D: Appl. Phys. 50, 043001 (2017).
[Crossref]

Jansen, C.

Jones, S.

S. Jones and J. Brown, “Metallic delay lenses,” Nature 163, 324–325 (1949).
[Crossref]

Karl, N.

R. Mendis, M. Nagai, Y. Wang, N. Karl, and D. M. Mittleman, “Terahertz artificial dielectric lens,” Sci. Rep. 6, 23023 (2016).
[Crossref]

Koch, M.

S. F. Busch, J. C. Balzer, G. Bastian, G. E. Town, and M. Koch, “Extending the alvarez-lens concept to arbitrary optical devices: Tunable gratings, lenses, and spiral phase plates,” IEEE Trans. THz Sci. Technol. 7, 320–325 (2017).
[Crossref]

A. Hernandez-Serrano, M. Weidenbach, S. Busch, M. Koch, and E. Castro-Camus, “Fabrication of gradient-refractive-index lenses for terahertz applications by three-dimensional printing,” J. Opt. Soc. Am. B. 33, 928–931 (2016).
[Crossref]

S. Busch, M. Weidenbach, M. Fey, F. Schäfer, T. Probst, and M. Koch, “Optical properties of 3d printable plastics in the thz regime and their application for 3d printed thz optics,” J. Infrared Millim. Terahertz Waves. 35, 993–997 (2014).
[Crossref]

B. Scherger, M. Scheller, C. Jansen, M. Koch, and K. Wiesauer, “Terahertz lenses made by compression molding of micropowders,” Appl. Opt. 50, 2256–2262 (2011).
[Crossref] [PubMed]

Kock, W. E.

W. E. Kock, “Metal-lens antennas,” Proc. IRE 34, 828–836 (1946).
[Crossref]

Krolla, B.

O. Paul, B. Reinhard, B. Krolla, R. Beigang, and M. Rahm, “Gradient index metamaterial based on slot elements,” Appl. Phys. Lett. 96, 241110 (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]

Lewis, R. A.

A. Squires, E. Constable, and R. A. Lewis, “3d printed terahertz diffraction gratings and lenses,” J. Infrared Millim. Terahertz Waves. 36, 72–80 (2015).
[Crossref]

Linfield, E.

S. Dhillon, M. Vitiello, E. Linfield, A. Davies, M. C. Hoffmann, J. Booske, C. Paoloni, M. Gensch, P. Weightman, G. Williams, and et al., “The 2017 terahertz science and technology roadmap,” J. Phys. D: Appl. Phys. 50, 043001 (2017).
[Crossref]

Liu, J.

R. Mendis, J. Liu, and D. M. Mittleman, “Terahertz mirage: Deflecting terahertz beams in an inhomogeneous artificial dielectric based on a parallel-plate waveguide,” Appl. Phys. Lett. 101, 111108 (2012).
[Crossref]

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] [PubMed]

Mendis, R.

R. Mendis, M. Nagai, W. Zhang, and D. M. Mittleman, “Artificial dielectric polarizing-beamsplitter and isolator for the terahertz region,” Sci. Rep. 7, 5909 (2017).
[Crossref] [PubMed]

R. Mendis, M. Nagai, Y. Wang, N. Karl, and D. M. Mittleman, “Terahertz artificial dielectric lens,” Sci. Rep. 6, 23023 (2016).
[Crossref]

R. Mendis, J. Liu, and D. M. Mittleman, “Terahertz mirage: Deflecting terahertz beams in an inhomogeneous artificial dielectric based on a parallel-plate waveguide,” Appl. Phys. Lett. 101, 111108 (2012).
[Crossref]

R. Mendis and D. M. Mittleman, “A 2-d artificial dielectric with 0≤n<1 for the terahertz region,” IEEE Trans. Microw. Theory Techn. 58, 1993–1998 (2010).
[Crossref]

R. Mendis and D. M. Mittleman, “Comparison of the lowest-order transverse-electric (TE1) and transverse-magnetic (TEM) modes of the parallel-plate waveguide for terahertz pulse applications,” Opt. Express. 17, 14839–14850 (2009).
[Crossref] [PubMed]

Mittleman, D. M.

R. Mendis, M. Nagai, W. Zhang, and D. M. Mittleman, “Artificial dielectric polarizing-beamsplitter and isolator for the terahertz region,” Sci. Rep. 7, 5909 (2017).
[Crossref] [PubMed]

R. Mendis, M. Nagai, Y. Wang, N. Karl, and D. M. Mittleman, “Terahertz artificial dielectric lens,” Sci. Rep. 6, 23023 (2016).
[Crossref]

R. Mendis, J. Liu, and D. M. Mittleman, “Terahertz mirage: Deflecting terahertz beams in an inhomogeneous artificial dielectric based on a parallel-plate waveguide,” Appl. Phys. Lett. 101, 111108 (2012).
[Crossref]

R. Mendis and D. M. Mittleman, “A 2-d artificial dielectric with 0≤n<1 for the terahertz region,” IEEE Trans. Microw. Theory Techn. 58, 1993–1998 (2010).
[Crossref]

R. Mendis and D. M. Mittleman, “Comparison of the lowest-order transverse-electric (TE1) and transverse-magnetic (TEM) modes of the parallel-plate waveguide for terahertz pulse applications,” Opt. Express. 17, 14839–14850 (2009).
[Crossref] [PubMed]

Mock, J.

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

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] [PubMed]

Nagai, M.

R. Mendis, M. Nagai, W. Zhang, and D. M. Mittleman, “Artificial dielectric polarizing-beamsplitter and isolator for the terahertz region,” Sci. Rep. 7, 5909 (2017).
[Crossref] [PubMed]

R. Mendis, M. Nagai, Y. Wang, N. Karl, and D. M. Mittleman, “Terahertz artificial dielectric lens,” Sci. Rep. 6, 23023 (2016).
[Crossref]

Navarro-Cía, M.

V. Torres, V. Pacheco-Peña, P. Rodríguez-Ulibarri, M. Navarro-Cía, M. Beruete, M. Sorolla, and N. Engheta, “Terahertz epsilon-near-zero graded-index lens,” Opt. Express. 21, 9156–9166 (2013).
[Crossref] [PubMed]

Neu, J.

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]

Pacheco-Peña, V.

V. Torres, V. Pacheco-Peña, P. Rodríguez-Ulibarri, M. Navarro-Cía, M. Beruete, M. Sorolla, and N. Engheta, “Terahertz epsilon-near-zero graded-index lens,” Opt. Express. 21, 9156–9166 (2013).
[Crossref] [PubMed]

Paoloni, C.

S. Dhillon, M. Vitiello, E. Linfield, A. Davies, M. C. Hoffmann, J. Booske, C. Paoloni, M. Gensch, P. Weightman, G. Williams, and et al., “The 2017 terahertz science and technology roadmap,” J. Phys. D: Appl. Phys. 50, 043001 (2017).
[Crossref]

Paul, O.

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]

O. Paul, B. Reinhard, B. Krolla, R. Beigang, and M. Rahm, “Gradient index metamaterial based on slot elements,” Appl. Phys. Lett. 96, 241110 (2010).
[Crossref]

Probst, T.

S. Busch, M. Weidenbach, M. Fey, F. Schäfer, T. Probst, and M. Koch, “Optical properties of 3d printable plastics in the thz regime and their application for 3d printed thz optics,” J. Infrared Millim. Terahertz Waves. 35, 993–997 (2014).
[Crossref]

Rahm, M.

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]

O. Paul, B. Reinhard, B. Krolla, R. Beigang, and M. Rahm, “Gradient index metamaterial based on slot elements,” Appl. Phys. Lett. 96, 241110 (2010).
[Crossref]

Reinhard, B.

O. Paul, B. Reinhard, B. Krolla, R. Beigang, and M. Rahm, “Gradient index metamaterial based on slot elements,” Appl. Phys. Lett. 96, 241110 (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]

Rodríguez-Ulibarri, P.

V. Torres, V. Pacheco-Peña, P. Rodríguez-Ulibarri, M. Navarro-Cía, M. Beruete, M. Sorolla, and N. Engheta, “Terahertz epsilon-near-zero graded-index lens,” Opt. Express. 21, 9156–9166 (2013).
[Crossref] [PubMed]

Schäfer, F.

S. Busch, M. Weidenbach, M. Fey, F. Schäfer, T. Probst, and M. Koch, “Optical properties of 3d printable plastics in the thz regime and their application for 3d printed thz optics,” J. Infrared Millim. Terahertz Waves. 35, 993–997 (2014).
[Crossref]

Scheller, M.

Scherger, B.

Schurig, D.

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

Smith, D.

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

Smith, D. 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] [PubMed]

Sorolla, M.

V. Torres, V. Pacheco-Peña, P. Rodríguez-Ulibarri, M. Navarro-Cía, M. Beruete, M. Sorolla, and N. Engheta, “Terahertz epsilon-near-zero graded-index lens,” Opt. Express. 21, 9156–9166 (2013).
[Crossref] [PubMed]

Squires, A.

A. Squires, E. Constable, and R. A. Lewis, “3d printed terahertz diffraction gratings and lenses,” J. Infrared Millim. Terahertz Waves. 36, 72–80 (2015).
[Crossref]

Starr, A.

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

Torres, V.

V. Torres, V. Pacheco-Peña, P. Rodríguez-Ulibarri, M. Navarro-Cía, M. Beruete, M. Sorolla, and N. Engheta, “Terahertz epsilon-near-zero graded-index lens,” Opt. Express. 21, 9156–9166 (2013).
[Crossref] [PubMed]

Town, G. E.

S. F. Busch, J. C. Balzer, G. Bastian, G. E. Town, and M. Koch, “Extending the alvarez-lens concept to arbitrary optical devices: Tunable gratings, lenses, and spiral phase plates,” IEEE Trans. THz Sci. Technol. 7, 320–325 (2017).
[Crossref]

Vitiello, M.

S. Dhillon, M. Vitiello, E. Linfield, A. Davies, M. C. Hoffmann, J. Booske, C. Paoloni, M. Gensch, P. Weightman, G. Williams, and et al., “The 2017 terahertz science and technology roadmap,” J. Phys. D: Appl. Phys. 50, 043001 (2017).
[Crossref]

Voelz, D. G.

D. G. Voelz, Computational fourier optics: a MATLAB tutorial (SPIE press, 2011).

Wang, Y.

R. Mendis, M. Nagai, Y. Wang, N. Karl, and D. M. Mittleman, “Terahertz artificial dielectric lens,” Sci. Rep. 6, 23023 (2016).
[Crossref]

Weidenbach, M.

A. Hernandez-Serrano, M. Weidenbach, S. Busch, M. Koch, and E. Castro-Camus, “Fabrication of gradient-refractive-index lenses for terahertz applications by three-dimensional printing,” J. Opt. Soc. Am. B. 33, 928–931 (2016).
[Crossref]

S. Busch, M. Weidenbach, M. Fey, F. Schäfer, T. Probst, and M. Koch, “Optical properties of 3d printable plastics in the thz regime and their application for 3d printed thz optics,” J. Infrared Millim. Terahertz Waves. 35, 993–997 (2014).
[Crossref]

Weightman, P.

S. Dhillon, M. Vitiello, E. Linfield, A. Davies, M. C. Hoffmann, J. Booske, C. Paoloni, M. Gensch, P. Weightman, G. Williams, and et al., “The 2017 terahertz science and technology roadmap,” J. Phys. D: Appl. Phys. 50, 043001 (2017).
[Crossref]

Wiesauer, K.

Williams, G.

S. Dhillon, M. Vitiello, E. Linfield, A. Davies, M. C. Hoffmann, J. Booske, C. Paoloni, M. Gensch, P. Weightman, G. Williams, and et al., “The 2017 terahertz science and technology roadmap,” J. Phys. D: Appl. Phys. 50, 043001 (2017).
[Crossref]

Zhang, W.

R. Mendis, M. Nagai, W. Zhang, and D. M. Mittleman, “Artificial dielectric polarizing-beamsplitter and isolator for the terahertz region,” Sci. Rep. 7, 5909 (2017).
[Crossref] [PubMed]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

O. Paul, B. Reinhard, B. Krolla, R. Beigang, and M. Rahm, “Gradient index metamaterial based on slot elements,” Appl. Phys. Lett. 96, 241110 (2010).
[Crossref]

R. Mendis, J. Liu, and D. M. Mittleman, “Terahertz mirage: Deflecting terahertz beams in an inhomogeneous artificial dielectric based on a parallel-plate waveguide,” Appl. Phys. Lett. 101, 111108 (2012).
[Crossref]

IEEE Trans. Microw. Theory Techn. (1)

R. Mendis and D. M. Mittleman, “A 2-d artificial dielectric with 0≤n<1 for the terahertz region,” IEEE Trans. Microw. Theory Techn. 58, 1993–1998 (2010).
[Crossref]

IEEE Trans. THz Sci. Technol. (1)

S. F. Busch, J. C. Balzer, G. Bastian, G. E. Town, and M. Koch, “Extending the alvarez-lens concept to arbitrary optical devices: Tunable gratings, lenses, and spiral phase plates,” IEEE Trans. THz Sci. Technol. 7, 320–325 (2017).
[Crossref]

J. Infrared Millim. Terahertz Waves. (2)

A. Squires, E. Constable, and R. A. Lewis, “3d printed terahertz diffraction gratings and lenses,” J. Infrared Millim. Terahertz Waves. 36, 72–80 (2015).
[Crossref]

S. Busch, M. Weidenbach, M. Fey, F. Schäfer, T. Probst, and M. Koch, “Optical properties of 3d printable plastics in the thz regime and their application for 3d printed thz optics,” J. Infrared Millim. Terahertz Waves. 35, 993–997 (2014).
[Crossref]

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

A. Hernandez-Serrano, M. Weidenbach, S. Busch, M. Koch, and E. Castro-Camus, “Fabrication of gradient-refractive-index lenses for terahertz applications by three-dimensional printing,” J. Opt. Soc. Am. B. 33, 928–931 (2016).
[Crossref]

J. Phys. D: Appl. Phys. (1)

S. Dhillon, M. Vitiello, E. Linfield, A. Davies, M. C. Hoffmann, J. Booske, C. Paoloni, M. Gensch, P. Weightman, G. Williams, and et al., “The 2017 terahertz science and technology roadmap,” J. Phys. D: Appl. Phys. 50, 043001 (2017).
[Crossref]

Nature (1)

S. Jones and J. Brown, “Metallic delay lenses,” Nature 163, 324–325 (1949).
[Crossref]

Opt. Express. (4)

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] [PubMed]

V. Torres, V. Pacheco-Peña, P. Rodríguez-Ulibarri, M. Navarro-Cía, M. Beruete, M. Sorolla, and N. Engheta, “Terahertz epsilon-near-zero graded-index lens,” Opt. Express. 21, 9156–9166 (2013).
[Crossref] [PubMed]

R. Mendis and D. M. Mittleman, “Comparison of the lowest-order transverse-electric (TE1) and transverse-magnetic (TEM) modes of the parallel-plate waveguide for terahertz pulse applications,” Opt. Express. 17, 14839–14850 (2009).
[Crossref] [PubMed]

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]

Phys. Rev. E. (1)

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

Proc IEE (1)

J. Brown, “Artificial dielectrics having refractive indices less than unity,” Proc IEE 100, 51–62 (1953).

Proc. IRE (1)

W. E. Kock, “Metal-lens antennas,” Proc. IRE 34, 828–836 (1946).
[Crossref]

Sci. Rep. (2)

R. Mendis, M. Nagai, W. Zhang, and D. M. Mittleman, “Artificial dielectric polarizing-beamsplitter and isolator for the terahertz region,” Sci. Rep. 7, 5909 (2017).
[Crossref] [PubMed]

R. Mendis, M. Nagai, Y. Wang, N. Karl, and D. M. Mittleman, “Terahertz artificial dielectric lens,” Sci. Rep. 6, 23023 (2016).
[Crossref]

Other (2)

C. A. Balanis, Advanced engineering electromagnetics (John Wiley & Sons, 1999).

D. G. Voelz, Computational fourier optics: a MATLAB tutorial (SPIE press, 2011).

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Figures (5)

Fig. 1
Fig. 1 Schematic diagram of the device. (a) lateral view, (b) front view (the aspect ratio of the device was exaggerated for clarity). (c) refractive index of a typical PPWG operating in the TE1 mode as function of the plate spacing for frequencies from 0.15 THz to 0.20 THz (d) Photograph of the fabricated device. The dotted circle denotes the incident beam. e) Index profile of the structure at 0.18 THz along the red dotted line in (d). In (e) the red dashed line is a parabolic fit to the refractive index profile.
Fig. 2
Fig. 2 Numerical simulation results. (a) Instantaneous electric field and (b) normalized electric field at 0.18 THz. (c) longitudinal cross-section along the dotted line in Fig (b) for the same simulation but for frequencies from 0.17 THz to 0.21 THz in steps of 0.01 THz. In (a) and (b) the focus is clearly identified at approximately 10 mm from the front face of the lens. This distance is confirmed in (c) where the maximum amplitude is at approximately 10 mm for f = 0.18 THz. Figure (d) shows the predicted wavefront position after 4.3 ps (red lines) using eq. (2).
Fig. 3
Fig. 3 Schematic of the experimental setup for the experimental characterization of the focusing properties for the artificial dielectric stepped-index device.
Fig. 4
Fig. 4 Cross sectional profile for the input and output beams for a) 0.15 THz, b) 0.18 THz and c) 0.20 THz. The data were recorded at 18 mm from the front surface of the device. In the same figures Gaussian fits are shown.
Fig. 5
Fig. 5 Comparison between cross section of the beam for the numerical simulation (blue line), experimental result (red line) and theoretical result (yellow line) at 180 GHz. It is observed that the beam waist for the experimental result is larger than the theoretical and the simulation one. This is most likely due the imperfections on the device.

Equations (3)

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

n = 1 c 2 4 h 2 f 2 ,
E ( t ) = e i ω t ,
U 2 ( x , y ) = z j λ Σ U 1 ( ξ , η ) exp ( jkr 12 ) r 12 2 d ξ d η ,

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