Abstract

A study of optical aberrations for flat lenses based on phase discontinuities is reported. The wave aberration function and the analytical expression of the aberrations up to the 4th order are derived to describe the performance of both ideal and practical flat lenses. We find that aberration-free focusing is possible under axial illumination but off-axis aberrations appear when the excitation is not normal to the interface. An alternative design for an aplanatic metasurface on a curved substrate is proposed to focus light without coma and spherical aberrations.

© 2013 Optical Society of America

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2013 (10)

N. Yu, P. Genevet, F. Aieta, M. A. Kats, R. Blanchard, G. Aoust, J.-P. Tetienne, Z. Gaburro, and F. Capasso, “Flat optics: controlling wavefronts with optical antenna metasurfaces,” IEEE J. Sel. Top. Quantum Electron.19(3), 4700423 (2013).
[CrossRef]

A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science339(6125), 1232009 (2013).
[CrossRef] [PubMed]

C. Pfeiffer and A. Grbic, “Metamaterial huygens’ surfaces: tailoring wave fronts with reflectionless sheets,” Phys. Rev. Lett.110(19), 197401 (2013).
[CrossRef] [PubMed]

A. Pors, M. G. Nielsen, R. L. Eriksen, and S. I. Bozhevolnyi, “Broadband focusing flat mirrors based on plasmonic gradient metasurfaces,” Nano Lett.13(2), 829–834 (2013).
[CrossRef] [PubMed]

X. Ni, S. Ishii, A. V. Kildishev, and V. M. Shalaev, “Ultra-thin, planar, Babinet-inverted plasmonic metalenses,” Light Sci. Appl.2(4), e72 (2013).
[CrossRef]

C. Pfeiffer and A. Grbic, “Cascaded metasurfaces for complete phase and polarization control,” Appl. Phys. Lett.102(23), 231116 (2013).
[CrossRef]

F. Zhou, Y. Liu, and W. Cai, “Plasmonic holographic imaging with V-shaped nanoantenna array,” Opt. Express21(4), 4348–4354 (2013).
[CrossRef] [PubMed]

B. Yang, W. M. Ye, X. D. Yuan, Z. H. Zhu, and C. Zeng, “Design of ultrathin plasmonic quarter-wave plate based on period coupling,” Opt. Lett.38(5), 679–681 (2013).
[CrossRef] [PubMed]

Z. Wei, Y. Cao, X. Su, Z. Gong, Y. Long, and H. Li, “Highly efficient beam steering with a transparent metasurface,” Opt. Express21(9), 10739–10745 (2013).
[CrossRef] [PubMed]

J. He, X. Wang, D. Hu, J. Ye, S. Feng, Q. Kan, and Y. Zhang, “Generation and evolution of the terahertz vortex beam,” Opt. Express21(17), 20230–20239 (2013).
[CrossRef] [PubMed]

2012 (14)

S. Larouche and D. R. Smith, “Reconciliation of generalized refraction with diffraction theory,” Opt. Lett.37(12), 2391–2393 (2012).
[CrossRef] [PubMed]

M. Kang, T. Feng, H.-T. Wang, and J. Li, “Wave front engineering from an array of thin aperture antennas,” Opt. Express20(14), 15882–15890 (2012).
[CrossRef] [PubMed]

X. Li, S. Xiao, B. Cai, Q. He, T. J. Cui, and L. Zhou, “Flat metasurfaces to focus electromagnetic waves in reflection geometry,” Opt. Lett.37(23), 4940–4942 (2012).
[CrossRef] [PubMed]

F. Aieta, P. Genevet, N. Yu, M. A. Kats, Z. Gaburro, and F. Capasso, “Out-of-plane reflection and refraction of light by anisotropic optical antenna metasurfaces with phase discontinuities,” Nano Lett.12(3), 1702–1706 (2012).
[CrossRef] [PubMed]

S. K.-Y. Sun, K. Y. Yang, C. M. Wang, T. K. Juan, W. T. Chen, C. Y. Liao, Q. He, S. Xiao, W. T. Kung, G. Y. Guo, L. Zhou, and D. P. Tsai, “High-efficiency broadband anomalous reflection by gradient meta-surfaces,” Nano Lett.12(12), 6223–6229 (2012).
[CrossRef] [PubMed]

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science335(6067), 427 (2012).
[CrossRef] [PubMed]

P. Genevet, N. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett.100(1), 013101 (2012).
[CrossRef]

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett.12(12), 6328–6333 (2012).
[CrossRef] [PubMed]

Y. Zhao, M. A. Belkin, and A. Alù, “Twisted optical metamaterials for planarized ultrathin broadband circular polarizers,” Nat. Commun.3, 870 (2012).
[CrossRef] [PubMed]

M. Kats, P. Genevet, G. Aoust, N. Yu, R. Blanchard, F. Aieta, Z. Gaburro, and F. Capasso, “Giant birefringence in optical antenna arrays with widely tailorable optical anisotropy,” Proc. Natl. Acad. Sci. U.S.A.109(31), 12364–12368 (2012).
[CrossRef]

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett.12(9), 4932–4936 (2012).
[CrossRef] [PubMed]

X. Chen, L. Huang, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C.-W. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commun.3, 1198 (2012).
[CrossRef] [PubMed]

S. Q. Sun, Q. He, S. Xiao, Q. Xu, X. Li, and L. Zhou, “Gradient-index meta-surfaces as a bridge linking propagating waves and surface waves,” Nat. Mater.11(5), 426–431 (2012).
[CrossRef] [PubMed]

F. Aieta, A. Kabiri, P. Genevet, N. Yu, M. A. Kats, Z. Gaburro, and F. Capasso, “Reflection and refraction of light from metasurfaces with phase discontinuities,” J. Nanophotonics6, 063532 (2012).
[PubMed]

2011 (3)

J. Tetienne, R. Blanchard, N. Yu, P. Genevet, M. A. Kats, J. A. Fan, T. Edamura, S. Furuta, M. Yamanishi, and F. Capasso, “Dipolar modeling and experimental demonstration of multi-beam plasmonic collimators,” New J. Phys.13(5), 053057 (2011).
[CrossRef]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science334(6054), 333–337 (2011).
[CrossRef] [PubMed]

B. Memarzadeh and H. Mosallaei, “Array of planar plasmonic scatterers functioning as light concentrator,” Opt. Lett.36(13), 2569–2571 (2011).
[CrossRef] [PubMed]

2010 (1)

M. Lombardo and G. Lombardo, “Wave aberration of human eyes and new descriptors of image optical quality and visual performance,” J. Cataract Refract. Surg.36(2), 313–331 (2010).
[CrossRef] [PubMed]

2009 (4)

B. Päivänranta, M. Pudas, O. Pitkänen, K. Leinonen, M. Kuittinen, P.-Y. Baroni, T. Scharf, and H.-P. Herzig, “Liquid phase deposition of polymers on arbitrary shaped surfaces and their suitability for e-beam patterning,” Nanotechnology20(22), 225305 (2009).
[CrossRef] [PubMed]

E. J. Smythe, M. D. Dickey, G. M. Whitesides, and F. Capasso, “A Technique to transfer metallic nanoscale patterns to small and non-planar surfaces,” ACS Nano3(1), 59–65 (2009).
[CrossRef] [PubMed]

E. J. Smythe, M. D. Dickey, J. Bao, G. M. Whitesides, and F. Capasso, “Optical antenna arrays on a fiber facet for in situ surface-enhanced Raman scattering detection,” Nano Lett.9(3), 1132–1138 (2009).
[CrossRef] [PubMed]

C. L. Holloway, A. Dienstfrey, E. F. Kuester, J. F. O’Hara, A. K. Azad, and A. J. Taylor, “A discussion on the interpretation and characterization of metafilms/metasurfaces: The two-dimensional equivalent of metamaterials,” Metamaterials (Amst.)3(2), 100–112 (2009).
[CrossRef]

2007 (1)

2005 (1)

B. D. Gates, Q. Xu, M. Stewart, D. Ryan, C. G. Willson, and G. M. Whitesides, “New approaches to nanofabrication: molding, printing, and other techniques,” Chem. Rev.105(4), 1171–1196 (2005).
[CrossRef] [PubMed]

2003 (3)

K. E. Paul, M. Prentiss, and G. M. Whitesides, “Patterning spherical surfaces at the two-hundred-nanometer scale using soft lithography,” Adv. Funct. Mater.13(4), 259–263 (2003).
[CrossRef]

F. Hosokawa, T. Tomita, M. Naruse, T. Honda, P. Hartel, and M. Haider, “A spherical aberration-corrected 200 kV TEM,” J. Electron Microsc. (Tokyo)52(1), 3–10 (2003).
[CrossRef] [PubMed]

A. Papakostas, A. Potts, D. M. Bagnall, S. L. Prosvirnin, H. J. Coles, and N. I. Zheludev, “Optical manifestations of planar chirality,” Phys. Rev. Lett.90(10), 107404 (2003).
[CrossRef] [PubMed]

1999 (1)

P. Ruchhoeft, M. Colburn, B. Choi, H. Nounu, S. Johnson, T. Bailey, S. Damle, M. Stewart, J. Ekerdt, S. V. Sreenivasan, J. C. Wolfe, and C. G. Willson, “Patterning curved surfaces: template generation by ion beam proximity lithography and relief transfer by step and flash imprint lithography,” J. Vac. Sci. Technol. B17, 2965–2969 (1999).

1993 (1)

1992 (1)

W. Coene, G. Janssen, M. O. de Beek, and D. Van Dyck, “Phase retrieval through focus variation for ultra-resolution in field-emission transmission electron microscopy,” Phys. Rev. Lett.69(26), 3743–3746 (1992).
[CrossRef] [PubMed]

1988 (1)

1972 (1)

M. Young, “Zone plates and their aberrations,” J. Opt. Soc. Am. A62(8), 972 (1972).
[CrossRef]

1960 (1)

1947 (1)

Aieta, F.

N. Yu, P. Genevet, F. Aieta, M. A. Kats, R. Blanchard, G. Aoust, J.-P. Tetienne, Z. Gaburro, and F. Capasso, “Flat optics: controlling wavefronts with optical antenna metasurfaces,” IEEE J. Sel. Top. Quantum Electron.19(3), 4700423 (2013).
[CrossRef]

F. Aieta, P. Genevet, N. Yu, M. A. Kats, Z. Gaburro, and F. Capasso, “Out-of-plane reflection and refraction of light by anisotropic optical antenna metasurfaces with phase discontinuities,” Nano Lett.12(3), 1702–1706 (2012).
[CrossRef] [PubMed]

F. Aieta, A. Kabiri, P. Genevet, N. Yu, M. A. Kats, Z. Gaburro, and F. Capasso, “Reflection and refraction of light from metasurfaces with phase discontinuities,” J. Nanophotonics6, 063532 (2012).
[PubMed]

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett.12(9), 4932–4936 (2012).
[CrossRef] [PubMed]

M. Kats, P. Genevet, G. Aoust, N. Yu, R. Blanchard, F. Aieta, Z. Gaburro, and F. Capasso, “Giant birefringence in optical antenna arrays with widely tailorable optical anisotropy,” Proc. Natl. Acad. Sci. U.S.A.109(31), 12364–12368 (2012).
[CrossRef]

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett.12(12), 6328–6333 (2012).
[CrossRef] [PubMed]

P. Genevet, N. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett.100(1), 013101 (2012).
[CrossRef]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science334(6054), 333–337 (2011).
[CrossRef] [PubMed]

Alù, A.

Y. Zhao, M. A. Belkin, and A. Alù, “Twisted optical metamaterials for planarized ultrathin broadband circular polarizers,” Nat. Commun.3, 870 (2012).
[CrossRef] [PubMed]

Aoust, G.

N. Yu, P. Genevet, F. Aieta, M. A. Kats, R. Blanchard, G. Aoust, J.-P. Tetienne, Z. Gaburro, and F. Capasso, “Flat optics: controlling wavefronts with optical antenna metasurfaces,” IEEE J. Sel. Top. Quantum Electron.19(3), 4700423 (2013).
[CrossRef]

M. Kats, P. Genevet, G. Aoust, N. Yu, R. Blanchard, F. Aieta, Z. Gaburro, and F. Capasso, “Giant birefringence in optical antenna arrays with widely tailorable optical anisotropy,” Proc. Natl. Acad. Sci. U.S.A.109(31), 12364–12368 (2012).
[CrossRef]

Artal, P.

Azad, A. K.

C. L. Holloway, A. Dienstfrey, E. F. Kuester, J. F. O’Hara, A. K. Azad, and A. J. Taylor, “A discussion on the interpretation and characterization of metafilms/metasurfaces: The two-dimensional equivalent of metamaterials,” Metamaterials (Amst.)3(2), 100–112 (2009).
[CrossRef]

Bagnall, D. M.

A. Papakostas, A. Potts, D. M. Bagnall, S. L. Prosvirnin, H. J. Coles, and N. I. Zheludev, “Optical manifestations of planar chirality,” Phys. Rev. Lett.90(10), 107404 (2003).
[CrossRef] [PubMed]

Bai, B.

X. Chen, L. Huang, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C.-W. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commun.3, 1198 (2012).
[CrossRef] [PubMed]

Bailey, T.

P. Ruchhoeft, M. Colburn, B. Choi, H. Nounu, S. Johnson, T. Bailey, S. Damle, M. Stewart, J. Ekerdt, S. V. Sreenivasan, J. C. Wolfe, and C. G. Willson, “Patterning curved surfaces: template generation by ion beam proximity lithography and relief transfer by step and flash imprint lithography,” J. Vac. Sci. Technol. B17, 2965–2969 (1999).

Bao, J.

E. J. Smythe, M. D. Dickey, J. Bao, G. M. Whitesides, and F. Capasso, “Optical antenna arrays on a fiber facet for in situ surface-enhanced Raman scattering detection,” Nano Lett.9(3), 1132–1138 (2009).
[CrossRef] [PubMed]

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B. Päivänranta, M. Pudas, O. Pitkänen, K. Leinonen, M. Kuittinen, P.-Y. Baroni, T. Scharf, and H.-P. Herzig, “Liquid phase deposition of polymers on arbitrary shaped surfaces and their suitability for e-beam patterning,” Nanotechnology20(22), 225305 (2009).
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Y. Zhao, M. A. Belkin, and A. Alù, “Twisted optical metamaterials for planarized ultrathin broadband circular polarizers,” Nat. Commun.3, 870 (2012).
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N. Yu, P. Genevet, F. Aieta, M. A. Kats, R. Blanchard, G. Aoust, J.-P. Tetienne, Z. Gaburro, and F. Capasso, “Flat optics: controlling wavefronts with optical antenna metasurfaces,” IEEE J. Sel. Top. Quantum Electron.19(3), 4700423 (2013).
[CrossRef]

M. Kats, P. Genevet, G. Aoust, N. Yu, R. Blanchard, F. Aieta, Z. Gaburro, and F. Capasso, “Giant birefringence in optical antenna arrays with widely tailorable optical anisotropy,” Proc. Natl. Acad. Sci. U.S.A.109(31), 12364–12368 (2012).
[CrossRef]

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett.12(9), 4932–4936 (2012).
[CrossRef] [PubMed]

P. Genevet, N. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett.100(1), 013101 (2012).
[CrossRef]

J. Tetienne, R. Blanchard, N. Yu, P. Genevet, M. A. Kats, J. A. Fan, T. Edamura, S. Furuta, M. Yamanishi, and F. Capasso, “Dipolar modeling and experimental demonstration of multi-beam plasmonic collimators,” New J. Phys.13(5), 053057 (2011).
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A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science339(6125), 1232009 (2013).
[CrossRef] [PubMed]

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science335(6067), 427 (2012).
[CrossRef] [PubMed]

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A. Pors, M. G. Nielsen, R. L. Eriksen, and S. I. Bozhevolnyi, “Broadband focusing flat mirrors based on plasmonic gradient metasurfaces,” Nano Lett.13(2), 829–834 (2013).
[CrossRef] [PubMed]

Cai, B.

Cai, W.

Cao, Y.

Capasso, F.

N. Yu, P. Genevet, F. Aieta, M. A. Kats, R. Blanchard, G. Aoust, J.-P. Tetienne, Z. Gaburro, and F. Capasso, “Flat optics: controlling wavefronts with optical antenna metasurfaces,” IEEE J. Sel. Top. Quantum Electron.19(3), 4700423 (2013).
[CrossRef]

F. Aieta, P. Genevet, N. Yu, M. A. Kats, Z. Gaburro, and F. Capasso, “Out-of-plane reflection and refraction of light by anisotropic optical antenna metasurfaces with phase discontinuities,” Nano Lett.12(3), 1702–1706 (2012).
[CrossRef] [PubMed]

F. Aieta, A. Kabiri, P. Genevet, N. Yu, M. A. Kats, Z. Gaburro, and F. Capasso, “Reflection and refraction of light from metasurfaces with phase discontinuities,” J. Nanophotonics6, 063532 (2012).
[PubMed]

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett.12(9), 4932–4936 (2012).
[CrossRef] [PubMed]

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett.12(12), 6328–6333 (2012).
[CrossRef] [PubMed]

M. Kats, P. Genevet, G. Aoust, N. Yu, R. Blanchard, F. Aieta, Z. Gaburro, and F. Capasso, “Giant birefringence in optical antenna arrays with widely tailorable optical anisotropy,” Proc. Natl. Acad. Sci. U.S.A.109(31), 12364–12368 (2012).
[CrossRef]

P. Genevet, N. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett.100(1), 013101 (2012).
[CrossRef]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science334(6054), 333–337 (2011).
[CrossRef] [PubMed]

J. Tetienne, R. Blanchard, N. Yu, P. Genevet, M. A. Kats, J. A. Fan, T. Edamura, S. Furuta, M. Yamanishi, and F. Capasso, “Dipolar modeling and experimental demonstration of multi-beam plasmonic collimators,” New J. Phys.13(5), 053057 (2011).
[CrossRef]

E. J. Smythe, M. D. Dickey, G. M. Whitesides, and F. Capasso, “A Technique to transfer metallic nanoscale patterns to small and non-planar surfaces,” ACS Nano3(1), 59–65 (2009).
[CrossRef] [PubMed]

E. J. Smythe, M. D. Dickey, J. Bao, G. M. Whitesides, and F. Capasso, “Optical antenna arrays on a fiber facet for in situ surface-enhanced Raman scattering detection,” Nano Lett.9(3), 1132–1138 (2009).
[CrossRef] [PubMed]

Chen, W. T.

S. K.-Y. Sun, K. Y. Yang, C. M. Wang, T. K. Juan, W. T. Chen, C. Y. Liao, Q. He, S. Xiao, W. T. Kung, G. Y. Guo, L. Zhou, and D. P. Tsai, “High-efficiency broadband anomalous reflection by gradient meta-surfaces,” Nano Lett.12(12), 6223–6229 (2012).
[CrossRef] [PubMed]

Chen, X.

X. Chen, L. Huang, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C.-W. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commun.3, 1198 (2012).
[CrossRef] [PubMed]

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P. Ruchhoeft, M. Colburn, B. Choi, H. Nounu, S. Johnson, T. Bailey, S. Damle, M. Stewart, J. Ekerdt, S. V. Sreenivasan, J. C. Wolfe, and C. G. Willson, “Patterning curved surfaces: template generation by ion beam proximity lithography and relief transfer by step and flash imprint lithography,” J. Vac. Sci. Technol. B17, 2965–2969 (1999).

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W. Coene, G. Janssen, M. O. de Beek, and D. Van Dyck, “Phase retrieval through focus variation for ultra-resolution in field-emission transmission electron microscopy,” Phys. Rev. Lett.69(26), 3743–3746 (1992).
[CrossRef] [PubMed]

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P. Ruchhoeft, M. Colburn, B. Choi, H. Nounu, S. Johnson, T. Bailey, S. Damle, M. Stewart, J. Ekerdt, S. V. Sreenivasan, J. C. Wolfe, and C. G. Willson, “Patterning curved surfaces: template generation by ion beam proximity lithography and relief transfer by step and flash imprint lithography,” J. Vac. Sci. Technol. B17, 2965–2969 (1999).

Coles, H. J.

A. Papakostas, A. Potts, D. M. Bagnall, S. L. Prosvirnin, H. J. Coles, and N. I. Zheludev, “Optical manifestations of planar chirality,” Phys. Rev. Lett.90(10), 107404 (2003).
[CrossRef] [PubMed]

Cui, T. J.

Damle, S.

P. Ruchhoeft, M. Colburn, B. Choi, H. Nounu, S. Johnson, T. Bailey, S. Damle, M. Stewart, J. Ekerdt, S. V. Sreenivasan, J. C. Wolfe, and C. G. Willson, “Patterning curved surfaces: template generation by ion beam proximity lithography and relief transfer by step and flash imprint lithography,” J. Vac. Sci. Technol. B17, 2965–2969 (1999).

de Beek, M. O.

W. Coene, G. Janssen, M. O. de Beek, and D. Van Dyck, “Phase retrieval through focus variation for ultra-resolution in field-emission transmission electron microscopy,” Phys. Rev. Lett.69(26), 3743–3746 (1992).
[CrossRef] [PubMed]

Dickey, M. D.

E. J. Smythe, M. D. Dickey, G. M. Whitesides, and F. Capasso, “A Technique to transfer metallic nanoscale patterns to small and non-planar surfaces,” ACS Nano3(1), 59–65 (2009).
[CrossRef] [PubMed]

E. J. Smythe, M. D. Dickey, J. Bao, G. M. Whitesides, and F. Capasso, “Optical antenna arrays on a fiber facet for in situ surface-enhanced Raman scattering detection,” Nano Lett.9(3), 1132–1138 (2009).
[CrossRef] [PubMed]

Dienstfrey, A.

C. L. Holloway, A. Dienstfrey, E. F. Kuester, J. F. O’Hara, A. K. Azad, and A. J. Taylor, “A discussion on the interpretation and characterization of metafilms/metasurfaces: The two-dimensional equivalent of metamaterials,” Metamaterials (Amst.)3(2), 100–112 (2009).
[CrossRef]

Edamura, T.

J. Tetienne, R. Blanchard, N. Yu, P. Genevet, M. A. Kats, J. A. Fan, T. Edamura, S. Furuta, M. Yamanishi, and F. Capasso, “Dipolar modeling and experimental demonstration of multi-beam plasmonic collimators,” New J. Phys.13(5), 053057 (2011).
[CrossRef]

Ekerdt, J.

P. Ruchhoeft, M. Colburn, B. Choi, H. Nounu, S. Johnson, T. Bailey, S. Damle, M. Stewart, J. Ekerdt, S. V. Sreenivasan, J. C. Wolfe, and C. G. Willson, “Patterning curved surfaces: template generation by ion beam proximity lithography and relief transfer by step and flash imprint lithography,” J. Vac. Sci. Technol. B17, 2965–2969 (1999).

Emani, N. K.

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science335(6067), 427 (2012).
[CrossRef] [PubMed]

Eriksen, R. L.

A. Pors, M. G. Nielsen, R. L. Eriksen, and S. I. Bozhevolnyi, “Broadband focusing flat mirrors based on plasmonic gradient metasurfaces,” Nano Lett.13(2), 829–834 (2013).
[CrossRef] [PubMed]

Fan, J. A.

J. Tetienne, R. Blanchard, N. Yu, P. Genevet, M. A. Kats, J. A. Fan, T. Edamura, S. Furuta, M. Yamanishi, and F. Capasso, “Dipolar modeling and experimental demonstration of multi-beam plasmonic collimators,” New J. Phys.13(5), 053057 (2011).
[CrossRef]

Feng, S.

Feng, T.

Furuta, S.

J. Tetienne, R. Blanchard, N. Yu, P. Genevet, M. A. Kats, J. A. Fan, T. Edamura, S. Furuta, M. Yamanishi, and F. Capasso, “Dipolar modeling and experimental demonstration of multi-beam plasmonic collimators,” New J. Phys.13(5), 053057 (2011).
[CrossRef]

Gaburro, Z.

N. Yu, P. Genevet, F. Aieta, M. A. Kats, R. Blanchard, G. Aoust, J.-P. Tetienne, Z. Gaburro, and F. Capasso, “Flat optics: controlling wavefronts with optical antenna metasurfaces,” IEEE J. Sel. Top. Quantum Electron.19(3), 4700423 (2013).
[CrossRef]

F. Aieta, P. Genevet, N. Yu, M. A. Kats, Z. Gaburro, and F. Capasso, “Out-of-plane reflection and refraction of light by anisotropic optical antenna metasurfaces with phase discontinuities,” Nano Lett.12(3), 1702–1706 (2012).
[CrossRef] [PubMed]

F. Aieta, A. Kabiri, P. Genevet, N. Yu, M. A. Kats, Z. Gaburro, and F. Capasso, “Reflection and refraction of light from metasurfaces with phase discontinuities,” J. Nanophotonics6, 063532 (2012).
[PubMed]

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett.12(12), 6328–6333 (2012).
[CrossRef] [PubMed]

M. Kats, P. Genevet, G. Aoust, N. Yu, R. Blanchard, F. Aieta, Z. Gaburro, and F. Capasso, “Giant birefringence in optical antenna arrays with widely tailorable optical anisotropy,” Proc. Natl. Acad. Sci. U.S.A.109(31), 12364–12368 (2012).
[CrossRef]

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett.12(9), 4932–4936 (2012).
[CrossRef] [PubMed]

P. Genevet, N. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett.100(1), 013101 (2012).
[CrossRef]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science334(6054), 333–337 (2011).
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N. Yu, P. Genevet, F. Aieta, M. A. Kats, R. Blanchard, G. Aoust, J.-P. Tetienne, Z. Gaburro, and F. Capasso, “Flat optics: controlling wavefronts with optical antenna metasurfaces,” IEEE J. Sel. Top. Quantum Electron.19(3), 4700423 (2013).
[CrossRef]

F. Aieta, P. Genevet, N. Yu, M. A. Kats, Z. Gaburro, and F. Capasso, “Out-of-plane reflection and refraction of light by anisotropic optical antenna metasurfaces with phase discontinuities,” Nano Lett.12(3), 1702–1706 (2012).
[CrossRef] [PubMed]

F. Aieta, A. Kabiri, P. Genevet, N. Yu, M. A. Kats, Z. Gaburro, and F. Capasso, “Reflection and refraction of light from metasurfaces with phase discontinuities,” J. Nanophotonics6, 063532 (2012).
[PubMed]

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett.12(9), 4932–4936 (2012).
[CrossRef] [PubMed]

M. Kats, P. Genevet, G. Aoust, N. Yu, R. Blanchard, F. Aieta, Z. Gaburro, and F. Capasso, “Giant birefringence in optical antenna arrays with widely tailorable optical anisotropy,” Proc. Natl. Acad. Sci. U.S.A.109(31), 12364–12368 (2012).
[CrossRef]

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett.12(12), 6328–6333 (2012).
[CrossRef] [PubMed]

P. Genevet, N. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett.100(1), 013101 (2012).
[CrossRef]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science334(6054), 333–337 (2011).
[CrossRef] [PubMed]

J. Tetienne, R. Blanchard, N. Yu, P. Genevet, M. A. Kats, J. A. Fan, T. Edamura, S. Furuta, M. Yamanishi, and F. Capasso, “Dipolar modeling and experimental demonstration of multi-beam plasmonic collimators,” New J. Phys.13(5), 053057 (2011).
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S. K.-Y. Sun, K. Y. Yang, C. M. Wang, T. K. Juan, W. T. Chen, C. Y. Liao, Q. He, S. Xiao, W. T. Kung, G. Y. Guo, L. Zhou, and D. P. Tsai, “High-efficiency broadband anomalous reflection by gradient meta-surfaces,” Nano Lett.12(12), 6223–6229 (2012).
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F. Hosokawa, T. Tomita, M. Naruse, T. Honda, P. Hartel, and M. Haider, “A spherical aberration-corrected 200 kV TEM,” J. Electron Microsc. (Tokyo)52(1), 3–10 (2003).
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Hartel, P.

F. Hosokawa, T. Tomita, M. Naruse, T. Honda, P. Hartel, and M. Haider, “A spherical aberration-corrected 200 kV TEM,” J. Electron Microsc. (Tokyo)52(1), 3–10 (2003).
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He, Q.

S. Q. Sun, Q. He, S. Xiao, Q. Xu, X. Li, and L. Zhou, “Gradient-index meta-surfaces as a bridge linking propagating waves and surface waves,” Nat. Mater.11(5), 426–431 (2012).
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[CrossRef] [PubMed]

Herzig, H.-P.

B. Päivänranta, M. Pudas, O. Pitkänen, K. Leinonen, M. Kuittinen, P.-Y. Baroni, T. Scharf, and H.-P. Herzig, “Liquid phase deposition of polymers on arbitrary shaped surfaces and their suitability for e-beam patterning,” Nanotechnology20(22), 225305 (2009).
[CrossRef] [PubMed]

Holloway, C. L.

C. L. Holloway, A. Dienstfrey, E. F. Kuester, J. F. O’Hara, A. K. Azad, and A. J. Taylor, “A discussion on the interpretation and characterization of metafilms/metasurfaces: The two-dimensional equivalent of metamaterials,” Metamaterials (Amst.)3(2), 100–112 (2009).
[CrossRef]

Honda, T.

F. Hosokawa, T. Tomita, M. Naruse, T. Honda, P. Hartel, and M. Haider, “A spherical aberration-corrected 200 kV TEM,” J. Electron Microsc. (Tokyo)52(1), 3–10 (2003).
[CrossRef] [PubMed]

Hosokawa, F.

F. Hosokawa, T. Tomita, M. Naruse, T. Honda, P. Hartel, and M. Haider, “A spherical aberration-corrected 200 kV TEM,” J. Electron Microsc. (Tokyo)52(1), 3–10 (2003).
[CrossRef] [PubMed]

Hu, D.

Huang, L.

X. Chen, L. Huang, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C.-W. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commun.3, 1198 (2012).
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W. Coene, G. Janssen, M. O. de Beek, and D. Van Dyck, “Phase retrieval through focus variation for ultra-resolution in field-emission transmission electron microscopy,” Phys. Rev. Lett.69(26), 3743–3746 (1992).
[CrossRef] [PubMed]

Jin, G.

X. Chen, L. Huang, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C.-W. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commun.3, 1198 (2012).
[CrossRef] [PubMed]

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P. Ruchhoeft, M. Colburn, B. Choi, H. Nounu, S. Johnson, T. Bailey, S. Damle, M. Stewart, J. Ekerdt, S. V. Sreenivasan, J. C. Wolfe, and C. G. Willson, “Patterning curved surfaces: template generation by ion beam proximity lithography and relief transfer by step and flash imprint lithography,” J. Vac. Sci. Technol. B17, 2965–2969 (1999).

Juan, T. K.

S. K.-Y. Sun, K. Y. Yang, C. M. Wang, T. K. Juan, W. T. Chen, C. Y. Liao, Q. He, S. Xiao, W. T. Kung, G. Y. Guo, L. Zhou, and D. P. Tsai, “High-efficiency broadband anomalous reflection by gradient meta-surfaces,” Nano Lett.12(12), 6223–6229 (2012).
[CrossRef] [PubMed]

Kabiri, A.

F. Aieta, A. Kabiri, P. Genevet, N. Yu, M. A. Kats, Z. Gaburro, and F. Capasso, “Reflection and refraction of light from metasurfaces with phase discontinuities,” J. Nanophotonics6, 063532 (2012).
[PubMed]

Kan, Q.

Kang, M.

Kats, M.

M. Kats, P. Genevet, G. Aoust, N. Yu, R. Blanchard, F. Aieta, Z. Gaburro, and F. Capasso, “Giant birefringence in optical antenna arrays with widely tailorable optical anisotropy,” Proc. Natl. Acad. Sci. U.S.A.109(31), 12364–12368 (2012).
[CrossRef]

Kats, M. A.

N. Yu, P. Genevet, F. Aieta, M. A. Kats, R. Blanchard, G. Aoust, J.-P. Tetienne, Z. Gaburro, and F. Capasso, “Flat optics: controlling wavefronts with optical antenna metasurfaces,” IEEE J. Sel. Top. Quantum Electron.19(3), 4700423 (2013).
[CrossRef]

F. Aieta, P. Genevet, N. Yu, M. A. Kats, Z. Gaburro, and F. Capasso, “Out-of-plane reflection and refraction of light by anisotropic optical antenna metasurfaces with phase discontinuities,” Nano Lett.12(3), 1702–1706 (2012).
[CrossRef] [PubMed]

F. Aieta, A. Kabiri, P. Genevet, N. Yu, M. A. Kats, Z. Gaburro, and F. Capasso, “Reflection and refraction of light from metasurfaces with phase discontinuities,” J. Nanophotonics6, 063532 (2012).
[PubMed]

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett.12(12), 6328–6333 (2012).
[CrossRef] [PubMed]

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett.12(9), 4932–4936 (2012).
[CrossRef] [PubMed]

P. Genevet, N. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett.100(1), 013101 (2012).
[CrossRef]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science334(6054), 333–337 (2011).
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ACS Nano (1)

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C. Pfeiffer and A. Grbic, “Cascaded metasurfaces for complete phase and polarization control,” Appl. Phys. Lett.102(23), 231116 (2013).
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IEEE J. Sel. Top. Quantum Electron. (1)

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Nano Lett. (6)

F. Aieta, P. Genevet, N. Yu, M. A. Kats, Z. Gaburro, and F. Capasso, “Out-of-plane reflection and refraction of light by anisotropic optical antenna metasurfaces with phase discontinuities,” Nano Lett.12(3), 1702–1706 (2012).
[CrossRef] [PubMed]

S. K.-Y. Sun, K. Y. Yang, C. M. Wang, T. K. Juan, W. T. Chen, C. Y. Liao, Q. He, S. Xiao, W. T. Kung, G. Y. Guo, L. Zhou, and D. P. Tsai, “High-efficiency broadband anomalous reflection by gradient meta-surfaces,” Nano Lett.12(12), 6223–6229 (2012).
[CrossRef] [PubMed]

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett.12(9), 4932–4936 (2012).
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Nanotechnology (1)

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Figures (4)

Fig. 1
Fig. 1

(a) The wavefront scattered by a flat lens based on a metasurface is given by the envelope of the secondary spherical waves emitted by the antennas with subwavelength separation. For a very dense distribution of antennas, the phase function φ(x,y) can be assumed continuous leading to a perfect spherical wavefront. (b) If a flat lens is designed using a limited set of phase elements, the continuous phase function is replaced with a discrete distribution that introduces aberrations (the yellow region corresponds to the wave aberration function (WAF)). (c) The effect of the discretization of the phase function is evaluated by calculating the root mean square of the wave aberration function (WAFrms) and the Strehl ratio for an increasing number of phase levels.

Fig. 2
Fig. 2

(a) A flat lens is illuminated with parallel light incident at angle α with the optical axis. An axial ray (chief ray) and a marginal ray are refracted at an angle α* in the substrate (with refractive index n). φ(r) is the phase shift at point r, with respect to the center of the lens (r = 0). (b) Point Spread Function (PSF) calculated from the WAF for a flat lens with radius 1 mm, NA = 0.5 illuminated with parallel monochromatic light at λ = 1.55 μm incident at an angle α = 10°. x and y are the spatial coordinates in the focal plane. (c) Modulation Transfer Function (MTF) (blue curve) for the same lens. The MTF for an aberration-free lens with the same NA is shown for comparison.

Fig. 3
Fig. 3

(a) Schematic of the aplanatic metasurface patterned on a spherical interface with center in O and with radius f. According to the definition of Apollonius, the locus of points that have a specified ratio of the distances between two fixed points (A and A’) known as foci, is a circle. A ray incident on the substrate at an angle U* is refracted and hits the metasurface in point P. We derived the expression of the phase gradient which imposes at the point P the proper phase such that a ray forming an angle U with the optical axis is redirected to form an angle U with the optical axis. (b) Point Spread Function (PSF) and (c) Modulation Transfer Function (MTF) for an aplanatic metasurface with NA = 0.5 illuminated with parallel monochromatic light at λ = 1.55 μm incident at an angle α = 10°.

Fig. 4
Fig. 4

Ray tracing plot for a plano-convex refractive lens (a), flat lens (b), and an aplanatic metasurface (c). The yellow-shaded areas represent the dielectric substrate (n = 3.5) and the green lines represent the metasurfaces. The parallel illumination forms an angle α = 10° with respect to the optical axis, NA = 0.5.

Equations (8)

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

R( t x , t y )= λ 2π φ( t x , t y )= t x 2 + t y 2 + f 2 f
F(x,y,z, t x , t y )= (x t x ) 2 + (y t y ) 2 + z 2 R ( t x , t y ) 2
x 2 + y 2 + (zf) 2 = f 2
OPD= 1 4f r 2 α 2 5 4f r 2 α 2 1 4 f 2 r 3 α+higherorderterms
nsinγ+sin γ = λ 2π dφ dθ
{ sinγ= Lf AP ¯ sinθ sin γ = f L A P ¯ sinθ
sinU=sin U * /n, AP ¯ =n A * P ¯ ,L= L * + AP ¯ ( ncosUcos U * )
dφ dθ =n 2π λ sinθ

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