Abstract

In this paper, we present a design strategy for single layer metasurface lenses based on dielectric resonators. This strategy is based on a robust optimization procedure for the resonator distribution in order to meet required performances (e.g. encircled energy, bandwidth, field of view, etc.). Possible deviations due to manufacturing errors are taken into account in the design procedure. This is applied to the design of array of microlenses for maskless lithography applications. The final design shows more uniform focusing performances (bandwidth 20 nm at 395 nm – 415 nm, field of view ±60 mrad) and increased robustness against manufacturing errors, compared to designs based on analytic phase projections.

© 2016 Optical Society of America

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A. Zhan, S. Colburn, R. Trivedi, T.K. Fryett, C.M. Dodson, and A. Majumdar, “Low-Contrast Dielectric Metasurface Optics,” ACS Phot. 3(2), 209–214 (2016).
[Crossref]

Z. L. Deng, S. Zhang, and G. P. Wang, “A facile grating approach towards broadband, wide-angle and high efficiency holographic metasurfaces,” Nanos. 8, 1588–1594 (2016)
[Crossref]

D. Headland, E. Carrasco, S. Nirantar, W. Withayachumnankul, P. Gutruf, J. Schwarz, D. Abbott, M. Bhaskaran, S. Sriram, J. Perruisseau-Carrier, and C. Fumeaux, “Dielectric resonator reflectarray as high-efficiency nonuniform terahertz metasurface,” ACS Photonics 3(6), 1019–1026 (2016).
[Crossref]

E. Arbabi, A. Arbabi, S.M. Kamali, Y. Horie, and A. Faraon, “Multiwavelength polarization-insensitive lenses based on dielectric metasurfaces with meta-molecules,” Optica 3(6), 628–633 (2016).
[Crossref]

Z. L. Deng, S. Zhang, and G. P. Wang, “Wide-angled off-axis achromatic metasurfaces for visible light,” Opt. Express 24(20), 23118–23128 (2016).
[Crossref] [PubMed]

2015 (4)

M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, “High-efficiency dielectric Huygens’ surfaces,” Adv. Opt. Mat. 3(6), 813–820 (2015).
[Crossref]

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6, 7069 (2015).
[Crossref] [PubMed]

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nano. 10, 937–943 (2015).
[Crossref]

F. Aieta, M.A. Kats, P. Genevet, and F. Capasso, “Multiwavelength achromatic metasurfaces by dispersive phase compensation,” Science 347(6228), 1342–1345 (2015).
[Crossref] [PubMed]

2014 (2)

2013 (1)

1993 (1)

G. Vuye, S. Fisson, V. Nguyen Van, Y. Wang, J. Rivory, and F. Abelès, “Temperature dependence of the dielectric function of silicon using in situ spectroscopic ellipsometry,” Thin Solid Films 233(1–2), 166–170, (1993).
[Crossref]

1973 (1)

A.S. Barker and M. Ilegems, “Infrared lattice vibrations and free-electron dispersion in GaN,” Phys. Rev. B 7, 743 (1973).
[Crossref]

1965 (1)

Abbott, D.

D. Headland, E. Carrasco, S. Nirantar, W. Withayachumnankul, P. Gutruf, J. Schwarz, D. Abbott, M. Bhaskaran, S. Sriram, J. Perruisseau-Carrier, and C. Fumeaux, “Dielectric resonator reflectarray as high-efficiency nonuniform terahertz metasurface,” ACS Photonics 3(6), 1019–1026 (2016).
[Crossref]

Abelès, F.

G. Vuye, S. Fisson, V. Nguyen Van, Y. Wang, J. Rivory, and F. Abelès, “Temperature dependence of the dielectric function of silicon using in situ spectroscopic ellipsometry,” Thin Solid Films 233(1–2), 166–170, (1993).
[Crossref]

Aieta, F.

F. Aieta, M.A. Kats, P. Genevet, and F. Capasso, “Multiwavelength achromatic metasurfaces by dispersive phase compensation,” Science 347(6228), 1342–1345 (2015).
[Crossref] [PubMed]

Arbabi, A.

E. Arbabi, A. Arbabi, S.M. Kamali, Y. Horie, and A. Faraon, “Multiwavelength polarization-insensitive lenses based on dielectric metasurfaces with meta-molecules,” Optica 3(6), 628–633 (2016).
[Crossref]

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6, 7069 (2015).
[Crossref] [PubMed]

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nano. 10, 937–943 (2015).
[Crossref]

Arbabi, E.

Bagheri, M.

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nano. 10, 937–943 (2015).
[Crossref]

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6, 7069 (2015).
[Crossref] [PubMed]

Barker, A.S.

A.S. Barker and M. Ilegems, “Infrared lattice vibrations and free-electron dispersion in GaN,” Phys. Rev. B 7, 743 (1973).
[Crossref]

Bäumer, S. M. B.

F. Silvestri, F. Bernal Arango, K. J. A. Vendel, G. Gerini, S. M. B. Bäumer, and A. F. Koenderink, “Optical antennas for far and near field metrology,” in Proceedings 10th European Conference on Antennas and Propagation, Davos 2016 (2016), pp. 1–4.
[Crossref]

Beausoleil, R. G.

S. Vo, D. Fattal, W. V. Sorin, Z. Peng, T. Tran, and R. G. Beausoleil, “Sub-wavelength grating lenses with a twist,” IEEE Phot. Tech. Lett. 26(13), 1375–1378 (2014).
[Crossref]

Bernal Arango, F.

F. Silvestri, F. Bernal Arango, K. J. A. Vendel, G. Gerini, S. M. B. Bäumer, and A. F. Koenderink, “Optical antennas for far and near field metrology,” in Proceedings 10th European Conference on Antennas and Propagation, Davos 2016 (2016), pp. 1–4.
[Crossref]

Bhaskaran, M.

D. Headland, E. Carrasco, S. Nirantar, W. Withayachumnankul, P. Gutruf, J. Schwarz, D. Abbott, M. Bhaskaran, S. Sriram, J. Perruisseau-Carrier, and C. Fumeaux, “Dielectric resonator reflectarray as high-efficiency nonuniform terahertz metasurface,” ACS Photonics 3(6), 1019–1026 (2016).
[Crossref]

L. Zou, W. Withayachumnankul, C.M. Shah, A. Mitchell, M. Bhaskaran, S. Sriram, and C. Fumeaux, “Dielectric resonator nanoantennas at visible frequencies,” Opt. Express 21(1), 1344–1352 (2013).
[Crossref] [PubMed]

Brener, I.

M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, “High-efficiency dielectric Huygens’ surfaces,” Adv. Opt. Mat. 3(6), 813–820 (2015).
[Crossref]

Byren, R.

Capasso, F.

F. Aieta, M.A. Kats, P. Genevet, and F. Capasso, “Multiwavelength achromatic metasurfaces by dispersive phase compensation,” Science 347(6228), 1342–1345 (2015).
[Crossref] [PubMed]

Carrasco, E.

D. Headland, E. Carrasco, S. Nirantar, W. Withayachumnankul, P. Gutruf, J. Schwarz, D. Abbott, M. Bhaskaran, S. Sriram, J. Perruisseau-Carrier, and C. Fumeaux, “Dielectric resonator reflectarray as high-efficiency nonuniform terahertz metasurface,” ACS Photonics 3(6), 1019–1026 (2016).
[Crossref]

Colburn, S.

A. Zhan, S. Colburn, R. Trivedi, T.K. Fryett, C.M. Dodson, and A. Majumdar, “Low-Contrast Dielectric Metasurface Optics,” ACS Phot. 3(2), 209–214 (2016).
[Crossref]

De Jager, P. W. H.

P. W. H. De Jager, C. Q. Gui, J. F. F. Klinkhamer, and E. Hoeberichts, “Scanning lithographic apparatus and device manufacturing method,” US Patent 7,609,362 (2009).

Decker, M.

M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, “High-efficiency dielectric Huygens’ surfaces,” Adv. Opt. Mat. 3(6), 813–820 (2015).
[Crossref]

Deng, Z. L.

Z. L. Deng, S. Zhang, and G. P. Wang, “Wide-angled off-axis achromatic metasurfaces for visible light,” Opt. Express 24(20), 23118–23128 (2016).
[Crossref] [PubMed]

Z. L. Deng, S. Zhang, and G. P. Wang, “A facile grating approach towards broadband, wide-angle and high efficiency holographic metasurfaces,” Nanos. 8, 1588–1594 (2016)
[Crossref]

Dodds, R.K.

Dodson, C.M.

A. Zhan, S. Colburn, R. Trivedi, T.K. Fryett, C.M. Dodson, and A. Majumdar, “Low-Contrast Dielectric Metasurface Optics,” ACS Phot. 3(2), 209–214 (2016).
[Crossref]

Dominguez, J.

M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, “High-efficiency dielectric Huygens’ surfaces,” Adv. Opt. Mat. 3(6), 813–820 (2015).
[Crossref]

Encinar, J. A.

J. Huang and J. A. Encinar, Reflectarray antennas (IEEE Press, 2008).

Falkner, M.

M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, “High-efficiency dielectric Huygens’ surfaces,” Adv. Opt. Mat. 3(6), 813–820 (2015).
[Crossref]

Faraon, A.

E. Arbabi, A. Arbabi, S.M. Kamali, Y. Horie, and A. Faraon, “Multiwavelength polarization-insensitive lenses based on dielectric metasurfaces with meta-molecules,” Optica 3(6), 628–633 (2016).
[Crossref]

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nano. 10, 937–943 (2015).
[Crossref]

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6, 7069 (2015).
[Crossref] [PubMed]

Fattal, D.

S. Vo, D. Fattal, W. V. Sorin, Z. Peng, T. Tran, and R. G. Beausoleil, “Sub-wavelength grating lenses with a twist,” IEEE Phot. Tech. Lett. 26(13), 1375–1378 (2014).
[Crossref]

Fisson, S.

G. Vuye, S. Fisson, V. Nguyen Van, Y. Wang, J. Rivory, and F. Abelès, “Temperature dependence of the dielectric function of silicon using in situ spectroscopic ellipsometry,” Thin Solid Films 233(1–2), 166–170, (1993).
[Crossref]

Fryett, T.K.

A. Zhan, S. Colburn, R. Trivedi, T.K. Fryett, C.M. Dodson, and A. Majumdar, “Low-Contrast Dielectric Metasurface Optics,” ACS Phot. 3(2), 209–214 (2016).
[Crossref]

Fumeaux, C.

D. Headland, E. Carrasco, S. Nirantar, W. Withayachumnankul, P. Gutruf, J. Schwarz, D. Abbott, M. Bhaskaran, S. Sriram, J. Perruisseau-Carrier, and C. Fumeaux, “Dielectric resonator reflectarray as high-efficiency nonuniform terahertz metasurface,” ACS Photonics 3(6), 1019–1026 (2016).
[Crossref]

L. Zou, W. Withayachumnankul, C.M. Shah, A. Mitchell, M. Bhaskaran, S. Sriram, and C. Fumeaux, “Dielectric resonator nanoantennas at visible frequencies,” Opt. Express 21(1), 1344–1352 (2013).
[Crossref] [PubMed]

Galdi, V.

F. Silvestri, E. Pisano, G. Gerini, V. Lancellotti, and V. Galdi, “Nanoresonator based dielectric surfaces for light manipulation,” Proceedings of European Microwave Conference EuMC 2015, Paris 2015 (2015), pp. 1240–1243.

Genevet, P.

F. Aieta, M.A. Kats, P. Genevet, and F. Capasso, “Multiwavelength achromatic metasurfaces by dispersive phase compensation,” Science 347(6228), 1342–1345 (2015).
[Crossref] [PubMed]

Gerini, G.

F. Silvestri, E. Pisano, G. Gerini, V. Lancellotti, and V. Galdi, “Nanoresonator based dielectric surfaces for light manipulation,” Proceedings of European Microwave Conference EuMC 2015, Paris 2015 (2015), pp. 1240–1243.

F. Silvestri, F. Bernal Arango, K. J. A. Vendel, G. Gerini, S. M. B. Bäumer, and A. F. Koenderink, “Optical antennas for far and near field metrology,” in Proceedings 10th European Conference on Antennas and Propagation, Davos 2016 (2016), pp. 1–4.
[Crossref]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw Hill Inc., 1996).

Gui, C. Q.

P. W. H. De Jager, C. Q. Gui, J. F. F. Klinkhamer, and E. Hoeberichts, “Scanning lithographic apparatus and device manufacturing method,” US Patent 7,609,362 (2009).

Gutruf, P.

D. Headland, E. Carrasco, S. Nirantar, W. Withayachumnankul, P. Gutruf, J. Schwarz, D. Abbott, M. Bhaskaran, S. Sriram, J. Perruisseau-Carrier, and C. Fumeaux, “Dielectric resonator reflectarray as high-efficiency nonuniform terahertz metasurface,” ACS Photonics 3(6), 1019–1026 (2016).
[Crossref]

Headland, D.

D. Headland, E. Carrasco, S. Nirantar, W. Withayachumnankul, P. Gutruf, J. Schwarz, D. Abbott, M. Bhaskaran, S. Sriram, J. Perruisseau-Carrier, and C. Fumeaux, “Dielectric resonator reflectarray as high-efficiency nonuniform terahertz metasurface,” ACS Photonics 3(6), 1019–1026 (2016).
[Crossref]

Hoeberichts, E.

P. W. H. De Jager, C. Q. Gui, J. F. F. Klinkhamer, and E. Hoeberichts, “Scanning lithographic apparatus and device manufacturing method,” US Patent 7,609,362 (2009).

Horie, Y.

E. Arbabi, A. Arbabi, S.M. Kamali, Y. Horie, and A. Faraon, “Multiwavelength polarization-insensitive lenses based on dielectric metasurfaces with meta-molecules,” Optica 3(6), 628–633 (2016).
[Crossref]

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6, 7069 (2015).
[Crossref] [PubMed]

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nano. 10, 937–943 (2015).
[Crossref]

Huang, J.

J. Huang and J. A. Encinar, Reflectarray antennas (IEEE Press, 2008).

Ilegems, M.

A.S. Barker and M. Ilegems, “Infrared lattice vibrations and free-electron dispersion in GaN,” Phys. Rev. B 7, 743 (1973).
[Crossref]

Kamali, S.M.

Kats, M.A.

F. Aieta, M.A. Kats, P. Genevet, and F. Capasso, “Multiwavelength achromatic metasurfaces by dispersive phase compensation,” Science 347(6228), 1342–1345 (2015).
[Crossref] [PubMed]

Kildishev, A.V.

Kivshar, Y. S.

M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, “High-efficiency dielectric Huygens’ surfaces,” Adv. Opt. Mat. 3(6), 813–820 (2015).
[Crossref]

Klinkhamer, J. F. F.

P. W. H. De Jager, C. Q. Gui, J. F. F. Klinkhamer, and E. Hoeberichts, “Scanning lithographic apparatus and device manufacturing method,” US Patent 7,609,362 (2009).

Koenderink, A. F.

F. Silvestri, F. Bernal Arango, K. J. A. Vendel, G. Gerini, S. M. B. Bäumer, and A. F. Koenderink, “Optical antennas for far and near field metrology,” in Proceedings 10th European Conference on Antennas and Propagation, Davos 2016 (2016), pp. 1–4.
[Crossref]

Kress, B. C.

B. C. Kress and P. Meyrueis, Applied Digital Optics (John Wiley and Sons, 2009).

Lancellotti, V.

F. Silvestri, E. Pisano, G. Gerini, V. Lancellotti, and V. Galdi, “Nanoresonator based dielectric surfaces for light manipulation,” Proceedings of European Microwave Conference EuMC 2015, Paris 2015 (2015), pp. 1240–1243.

Lee, J.J.

J.J. Lee, “Lens antennas,” in Antenna Handbook: Theory, Applications and Design, Y.T. Lo and J.J. Lee, eds. (Springer, 1988).
[Crossref]

Majumdar, A.

A. Zhan, S. Colburn, R. Trivedi, T.K. Fryett, C.M. Dodson, and A. Majumdar, “Low-Contrast Dielectric Metasurface Optics,” ACS Phot. 3(2), 209–214 (2016).
[Crossref]

Malitson, I.H.

Meyrueis, P.

B. C. Kress and P. Meyrueis, Applied Digital Optics (John Wiley and Sons, 2009).

Mitchell, A.

Neshev, D. N.

M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, “High-efficiency dielectric Huygens’ surfaces,” Adv. Opt. Mat. 3(6), 813–820 (2015).
[Crossref]

Nguyen Van, V.

G. Vuye, S. Fisson, V. Nguyen Van, Y. Wang, J. Rivory, and F. Abelès, “Temperature dependence of the dielectric function of silicon using in situ spectroscopic ellipsometry,” Thin Solid Films 233(1–2), 166–170, (1993).
[Crossref]

Nirantar, S.

D. Headland, E. Carrasco, S. Nirantar, W. Withayachumnankul, P. Gutruf, J. Schwarz, D. Abbott, M. Bhaskaran, S. Sriram, J. Perruisseau-Carrier, and C. Fumeaux, “Dielectric resonator reflectarray as high-efficiency nonuniform terahertz metasurface,” ACS Photonics 3(6), 1019–1026 (2016).
[Crossref]

Peng, Z.

S. Vo, D. Fattal, W. V. Sorin, Z. Peng, T. Tran, and R. G. Beausoleil, “Sub-wavelength grating lenses with a twist,” IEEE Phot. Tech. Lett. 26(13), 1375–1378 (2014).
[Crossref]

Perruisseau-Carrier, J.

D. Headland, E. Carrasco, S. Nirantar, W. Withayachumnankul, P. Gutruf, J. Schwarz, D. Abbott, M. Bhaskaran, S. Sriram, J. Perruisseau-Carrier, and C. Fumeaux, “Dielectric resonator reflectarray as high-efficiency nonuniform terahertz metasurface,” ACS Photonics 3(6), 1019–1026 (2016).
[Crossref]

Pertsch, T.

M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, “High-efficiency dielectric Huygens’ surfaces,” Adv. Opt. Mat. 3(6), 813–820 (2015).
[Crossref]

Pisano, E.

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D. Headland, E. Carrasco, S. Nirantar, W. Withayachumnankul, P. Gutruf, J. Schwarz, D. Abbott, M. Bhaskaran, S. Sriram, J. Perruisseau-Carrier, and C. Fumeaux, “Dielectric resonator reflectarray as high-efficiency nonuniform terahertz metasurface,” ACS Photonics 3(6), 1019–1026 (2016).
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L. Zou, W. Withayachumnankul, C.M. Shah, A. Mitchell, M. Bhaskaran, S. Sriram, and C. Fumeaux, “Dielectric resonator nanoantennas at visible frequencies,” Opt. Express 21(1), 1344–1352 (2013).
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S. Vo, D. Fattal, W. V. Sorin, Z. Peng, T. Tran, and R. G. Beausoleil, “Sub-wavelength grating lenses with a twist,” IEEE Phot. Tech. Lett. 26(13), 1375–1378 (2014).
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G. Vuye, S. Fisson, V. Nguyen Van, Y. Wang, J. Rivory, and F. Abelès, “Temperature dependence of the dielectric function of silicon using in situ spectroscopic ellipsometry,” Thin Solid Films 233(1–2), 166–170, (1993).
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D. Headland, E. Carrasco, S. Nirantar, W. Withayachumnankul, P. Gutruf, J. Schwarz, D. Abbott, M. Bhaskaran, S. Sriram, J. Perruisseau-Carrier, and C. Fumeaux, “Dielectric resonator reflectarray as high-efficiency nonuniform terahertz metasurface,” ACS Photonics 3(6), 1019–1026 (2016).
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Zhan, A.

A. Zhan, S. Colburn, R. Trivedi, T.K. Fryett, C.M. Dodson, and A. Majumdar, “Low-Contrast Dielectric Metasurface Optics,” ACS Phot. 3(2), 209–214 (2016).
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Z. L. Deng, S. Zhang, and G. P. Wang, “Wide-angled off-axis achromatic metasurfaces for visible light,” Opt. Express 24(20), 23118–23128 (2016).
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ACS Phot. (1)

A. Zhan, S. Colburn, R. Trivedi, T.K. Fryett, C.M. Dodson, and A. Majumdar, “Low-Contrast Dielectric Metasurface Optics,” ACS Phot. 3(2), 209–214 (2016).
[Crossref]

ACS Photonics (1)

D. Headland, E. Carrasco, S. Nirantar, W. Withayachumnankul, P. Gutruf, J. Schwarz, D. Abbott, M. Bhaskaran, S. Sriram, J. Perruisseau-Carrier, and C. Fumeaux, “Dielectric resonator reflectarray as high-efficiency nonuniform terahertz metasurface,” ACS Photonics 3(6), 1019–1026 (2016).
[Crossref]

Adv. Opt. Mat. (1)

M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, “High-efficiency dielectric Huygens’ surfaces,” Adv. Opt. Mat. 3(6), 813–820 (2015).
[Crossref]

IEEE Phot. Tech. Lett. (1)

S. Vo, D. Fattal, W. V. Sorin, Z. Peng, T. Tran, and R. G. Beausoleil, “Sub-wavelength grating lenses with a twist,” IEEE Phot. Tech. Lett. 26(13), 1375–1378 (2014).
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J. Opt. Soc. Am. (1)

Nanos. (1)

Z. L. Deng, S. Zhang, and G. P. Wang, “A facile grating approach towards broadband, wide-angle and high efficiency holographic metasurfaces,” Nanos. 8, 1588–1594 (2016)
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A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6, 7069 (2015).
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A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nano. 10, 937–943 (2015).
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F. Aieta, M.A. Kats, P. Genevet, and F. Capasso, “Multiwavelength achromatic metasurfaces by dispersive phase compensation,” Science 347(6228), 1342–1345 (2015).
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Thin Solid Films (1)

G. Vuye, S. Fisson, V. Nguyen Van, Y. Wang, J. Rivory, and F. Abelès, “Temperature dependence of the dielectric function of silicon using in situ spectroscopic ellipsometry,” Thin Solid Films 233(1–2), 166–170, (1993).
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[Crossref]

F. Silvestri, E. Pisano, G. Gerini, V. Lancellotti, and V. Galdi, “Nanoresonator based dielectric surfaces for light manipulation,” Proceedings of European Microwave Conference EuMC 2015, Paris 2015 (2015), pp. 1240–1243.

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Figures (11)

Fig. 1
Fig. 1 (a) Artistic impression of a dielectric resonators metasurface lens applied in maskless lithography, (b) unit cell of the designed metasurface lens with dimensions. For the sake of clarity the 500 μm thick back layer of fused Silica is not shown in both pictures.
Fig. 2
Fig. 2 Transmission characteristics of the array of resonators vs. resonators radius, for different wavelengths and angles of incidence: (a,b,c) transmittance, (d,e,f) transmission coefficient phase.
Fig. 3
Fig. 3 Focal plane intensity distribution of the theoretical phase surface for different wavelengths and angles of FOV: (a,b,c) wavelength λ = 395 nm, FOV = 0, 30, 60 mrad; (d,e,f) wavelength λ = 405 nm, FOV = 0, 30, 60 mrad; (g,h,i) wavelength λ = 415 nm, FOV = 0, 30, 60 mrad; (j) per cent energy in the central disk for different wavelengths with the respect to the FOV angles.
Fig. 4
Fig. 4 a) Per cent energy vs. field angles of the theoretical phase profile mapped into dispersive (wavelength and angular) resonators; b) zoom of the plot in a) in the range of energies related to the extreme wavelengths in the BW.
Fig. 5
Fig. 5 Optimized phase profile of the dielectric resonator metasurface lens.
Fig. 6
Fig. 6 Transmittance and phase distributions on the optimized metasurface for different angles of FOV at 405 nm. (a,b) transmittance and phase distribution for on axis excitation; (c,d) 30 mrad,; (e,f) 60 mrad. The distributions at the other wavelengths show similar behaviors. The shift of the beam for off axis angles is explained by the telecentric aperture stop placed at the front focal plane of the lens.
Fig. 7
Fig. 7 Focal plane intensity distributions for different wavelengths and angles of FOV for the dielectric resonator metasurface lens optimized with the robust optimization procedure considering the manufacturing tolerances: (a,b,c) wavelength λ = 395 nm, FOV = 0, 30, 60 mrad; (d,e,f) wavelength λ = 405 nm, FOV = 0, 30, 60 mrad; (g,h,i) wavelength λ = 415 nm, FOV = 0, 30, 60 mrad; (j) per cent energy in the central disk for different wavelengths with the respect to the FOV angle.
Fig. 8
Fig. 8 Per cent energy in the central disk for nominal designs vs. the average behaviour out from a Monte Carlo analysis with manufacturing tolerances with σ2 = 5 nm, for different wavelengths: a), b), c) nominal design derived from the phase distribution of the theoretical phase surface (same design as Fig. 4): a) 395 nm, b) 405 nm, c) 415 nm; d), e), f) nominal design derived from the robust optimization procedure (same design as Fig. 7 d) 395 nm, e) 405 nm, f) 415 nm. The arrows in each plot show the maximum per cent variation between the nominal design and the Monte Carlo average behaviours for each wavelength.
Fig. 9
Fig. 9 Transmission characteristics of the array of resonators with respect to resonators radius for different wavelengths and angles of incidence: (a,b,c) transmittance, (d,e,f) transmission coefficient phase.
Fig. 10
Fig. 10 Transmittance and phase distributions on the metasurface for different angles of FOV at 635 nm. (a,b) transmittance and phase distribution for on axis excitation; (c,d) 30 mrad,; (e,f) 60 mrad. The distributions at the other wavelengths show similar behaviors. The shift of the beam for off axis angles is explained by the telecentric aperture stop placed at the front focal plane of the lens.
Fig. 11
Fig. 11 Focal plane intensity distribution of the optimized dielectric resonator metasurface lens for different wavelengths and angles of FOV: (a,b,c) wavelength λ = 625 nm, FOV = 0, 30, 60 mrad; (d,e,f) wavelength λ = 635 nm, FOV = 0, 30, 60 mrad; (g,h,i) wavelength λ = 645 nm, FOV = 0, 30, 60 mrad; (j) per cent energy in the central disk for different wavelengths with the respect to the FOV angles.

Tables (2)

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Table 1 Characteristic parameters of designed telecentric metasurface lens

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Table 2 Characteristic parameters of designed telecentric metasurface lens

Equations (5)

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a < λ / ( 1 + NA )
CF = n λ = 1 N λ n FOV = 1 N FOV [ x x GIP ( n FOV ) ] 8 [ I ( x ; n λ , n FOV ) I Airy ( x ; n λ , n FOV ) ] 2
ϕ ( r ) = 2 π λ 0 ( Cr 2 1 + [ 1 ( 1 + K ) C 2 r 2 ] 1 / 2 + i = 1 6 C i r 2 ( i + 1 ) )
ϕ ( r ; λ ) = λ 0 λ ϕ ( r ; λ 0 )
max [ ϕ ( r ) ] δ < < 360 °

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