Abstract

Topology-optimized metasurfaces are thin film optical devices that have received much interest because they support ultra-high diffraction efficiencies. An important design consideration is ensuring that devices are insensitive to imperfections arising from realistic fabrication processing. We show that topology-optimized metasurfaces can be made robust by incorporating the performance of geometrically eroded and dilated devices directly into the iterative optimization algorithm. We additionally apply topology optimization to refine conventional designs and make them more robust. Unexpectedly, we find that devices robust to systematic erosion and dilation variations are also robust to random periodic perturbations. An analysis of the optical modes of robust devices indicates that robustness is enforced via highly complex and non-intuitive interactions between these modes and cannot be enforced using simple design rules. These concepts can more generally address other fabrication imperfections, such as thickness and refractive index variation, and can extend to other diffractive and nanophotonic platforms.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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References

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2018 (9)

S. Colburn, A. Zhan, and A. Majumdar, “Metasurface optics for full-color computational imaging,” Sci. Adv. 4(2), r2114 (2018).
[Crossref] [PubMed]

E. Arbabi, S. M. Kamali, A. Arbabi, and A. Faraon, “Full-Stokes Imaging Polarimetry Using Dielectric Metasurfaces,” ACS Photonics 5(8), 3132–3140 (2018).
[Crossref]

A. Tittl, A. Leitis, M. Liu, F. Yesilkoy, D. Y. Choi, D. N. Neshev, Y. S. Kivshar, and H. Altug, “Imaging-based molecular barcoding with pixelated dielectric metasurfaces,” Science 360(6393), 1105–1109 (2018).
[Crossref] [PubMed]

S. Doshay, D. Sell, J. Yang, R. Yang, and J. A. Fan, “High-performance axicon lenses based on high-contrast, multilayer gratings,” APL Photonics 3(1), 011302 (2018).
[Crossref]

D. Sell, J. Yang, E. W. Wang, T. Phan, S. Doshay, and J. A. Fan, “Ultra-High-Efficiency Anomalous Refraction with Dielectric Metasurfaces,” ACS Photonics 5(6), 2402–2407 (2018).
[Crossref]

Z. Lin, B. Groever, F. Capasso, A. W. Rodriguez, and M. Loncar, “Topology-Optimized Multilayered Metaoptics,” Phys. Rev. Appl. 9(4), 044030 (2018).
[Crossref]

J. Yang, D. Sell, and J. A. Fan, “Freeform metagratings based on complex light scattering dynamics for extreme, high efficiency beam steering,” Ann. Phys. 530(1), 1700302 (2018).
[Crossref]

A. Zhan, T. K. Fryett, S. Colburn, and A. Majumdar, “Inverse design of optical elements based on arrays of dielectric spheres,” Appl. Opt. 57(6), 1437–1446 (2018).
[Crossref] [PubMed]

V.-C. Su, C. H. Chu, G. Sun, and D. P. Tsai, “Advances in optical metasurfaces: fabrication and applications [Invited],” Opt. Express 26(10), 13148–13182 (2018).
[Crossref] [PubMed]

2017 (5)

P. Genevet, F. Capasso, F. Aieta, M. Khorasaninejad, and R. Devlin, “Recent advances in planar optics: from plasmonic to dielectric metasurfaces,” Optica 4(1), 139–152 (2017).
[Crossref]

J. Yang and J. A. Fan, “Topology-optimized metasurfaces: impact of initial geometric layout,” Opt. Lett. 42(16), 3161–3164 (2017).
[Crossref] [PubMed]

J. Yang and J. A. Fan, “Analysis of material selection on dielectric metasurface performance,” Opt. Express 25(20), 23899–23909 (2017).
[Crossref] [PubMed]

D. Sell, J. Yang, S. Doshay, R. Yang, and J. A. Fan, “Large-Angle, Multifunctional Metagratings Based on Freeform Multimode Geometries,” Nano Lett. 17(6), 3752–3757 (2017).
[Crossref] [PubMed]

D. Sell, J. Yang, S. Doshay, and J. A. Fan, “Periodic Dielectric Metasurfaces with High-Efficiency, Multiwavelength Functionalities,” Adv. Opt. Mater. 5(23), 1700645 (2017).
[Crossref]

2016 (5)

R. C. Devlin, M. Khorasaninejad, W. T. Chen, J. Oh, and F. Capasso, “Broadband high-efficiency dielectric metasurfaces for the visible spectrum,” Proc. Natl. Acad. Sci. U.S.A. 113(38), 10473–10478 (2016).
[Crossref] [PubMed]

H. T. Chen, A. J. Taylor, and N. Yu, “A review of metasurfaces: physics and applications,” Rep. Prog. Phys. 79(7), 076401 (2016).
[Crossref] [PubMed]

D. Sell, J. Yang, S. Doshay, K. Zhang, and J. A. Fan, “Visible light metasurfaces based on single-crystal silicon,” ACS Photonics 3(10), 1919–1925 (2016).
[Crossref]

M. Khorasaninejad, A. Y. Zhu, C. Roques-Carmes, W. T. Chen, J. Oh, I. Mishra, R. C. Devlin, and F. Capasso, “Polarization-Insensitive Metalenses at Visible Wavelengths,” Nano Lett. 16(11), 7229–7234 (2016).
[Crossref] [PubMed]

L. Wang, S. Kruk, H. Tang, T. Li, I. Kravchenko, D. N. Neshev, and Y. S. Kivshar, “Grayscale transparent metasurface holograms,” Optica 3(12), 1504–1505 (2016).
[Crossref] [PubMed]

2015 (4)

A. Pors, M. G. Nielsen, and S. I. Bozhevolnyi, “Plasmonic metagratings for simultaneous determination of Stokes parameters,” Optica 2(8), 716–723 (2015).
[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. Nanotechnol. 10(11), 937–943 (2015).
[Crossref] [PubMed]

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

A. Piggott, J. Lu, K. G. Lagoudakis, J. Petykiewicz, T. M. Babinec, and J. Vuckovic, “Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer,” Nat. Photonics 9(6), 374–377 (2015).
[Crossref]

2014 (2)

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
[Crossref] [PubMed]

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345(6194), 298–302 (2014).
[Crossref] [PubMed]

2013 (3)

C. M. Lalau-Keraly, S. Bhargava, O. D. Miller, and E. Yablonovitch, “Adjoint shape optimization applied to electromagnetic design,” Opt. Express 21(18), 21693–21701 (2013).
[Crossref] [PubMed]

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

A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science 339(6125), 1232009 (2013).
[Crossref] [PubMed]

2011 (3)

M. Schevenels, B. S. Lazaroz, and O. Sigmund, “Robust topology optimization accounting for spatially varying manufacturing errors,” Comput. Methods Appl. Math. 200, 3613–3627 (2011).

J. Jensen and O. Sigmund, “Topology optimization for nanophotonics,” Laser Photonics Rev. 5(2), 308–321 (2011).
[Crossref]

F. Wang, J. Jensen, and O. Sigmund, “Robust topology optimization of photonic crystal waveguides with tailored dispersion properties,” J. Opt. Soc. Am. B 28(3), 387–397 (2011).
[Crossref]

1999 (1)

1997 (1)

J. Aarik, A. Aidla, A.-A. Kiisler, T. Uustare, and V. Sammelselg, “Effect of crystal structure on optical properties of TiO2 films grown by atomic layer deposition,” Thin Solid Films 305(1–2), 270–273 (1997).
[Crossref]

Aarik, J.

J. Aarik, A. Aidla, A.-A. Kiisler, T. Uustare, and V. Sammelselg, “Effect of crystal structure on optical properties of TiO2 films grown by atomic layer deposition,” Thin Solid Films 305(1–2), 270–273 (1997).
[Crossref]

Aidla, A.

J. Aarik, A. Aidla, A.-A. Kiisler, T. Uustare, and V. Sammelselg, “Effect of crystal structure on optical properties of TiO2 films grown by atomic layer deposition,” Thin Solid Films 305(1–2), 270–273 (1997).
[Crossref]

Aieta, F.

Altug, H.

A. Tittl, A. Leitis, M. Liu, F. Yesilkoy, D. Y. Choi, D. N. Neshev, Y. S. Kivshar, and H. Altug, “Imaging-based molecular barcoding with pixelated dielectric metasurfaces,” Science 360(6393), 1105–1109 (2018).
[Crossref] [PubMed]

Arbabi, A.

E. Arbabi, S. M. Kamali, A. Arbabi, and A. Faraon, “Full-Stokes Imaging Polarimetry Using Dielectric Metasurfaces,” ACS Photonics 5(8), 3132–3140 (2018).
[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. Nanotechnol. 10(11), 937–943 (2015).
[Crossref] [PubMed]

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

Arbabi, E.

E. Arbabi, S. M. Kamali, A. Arbabi, and A. Faraon, “Full-Stokes Imaging Polarimetry Using Dielectric Metasurfaces,” ACS Photonics 5(8), 3132–3140 (2018).
[Crossref]

Astilean, S.

Babinec, T. M.

A. Piggott, J. Lu, K. G. Lagoudakis, J. Petykiewicz, T. M. Babinec, and J. Vuckovic, “Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer,” Nat. Photonics 9(6), 374–377 (2015).
[Crossref]

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. Nanotechnol. 10(11), 937–943 (2015).
[Crossref] [PubMed]

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

Ball, A. J.

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

Bhargava, S.

Boltasseva, A.

A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science 339(6125), 1232009 (2013).
[Crossref] [PubMed]

Bozhevolnyi, S. I.

Brongersma, M. L.

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345(6194), 298–302 (2014).
[Crossref] [PubMed]

Cambril, E.

Capasso, F.

Z. Lin, B. Groever, F. Capasso, A. W. Rodriguez, and M. Loncar, “Topology-Optimized Multilayered Metaoptics,” Phys. Rev. Appl. 9(4), 044030 (2018).
[Crossref]

P. Genevet, F. Capasso, F. Aieta, M. Khorasaninejad, and R. Devlin, “Recent advances in planar optics: from plasmonic to dielectric metasurfaces,” Optica 4(1), 139–152 (2017).
[Crossref]

R. C. Devlin, M. Khorasaninejad, W. T. Chen, J. Oh, and F. Capasso, “Broadband high-efficiency dielectric metasurfaces for the visible spectrum,” Proc. Natl. Acad. Sci. U.S.A. 113(38), 10473–10478 (2016).
[Crossref] [PubMed]

M. Khorasaninejad, A. Y. Zhu, C. Roques-Carmes, W. T. Chen, J. Oh, I. Mishra, R. C. Devlin, and F. Capasso, “Polarization-Insensitive Metalenses at Visible Wavelengths,” Nano Lett. 16(11), 7229–7234 (2016).
[Crossref] [PubMed]

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
[Crossref] [PubMed]

Chavel, P.

Chen, H. T.

H. T. Chen, A. J. Taylor, and N. Yu, “A review of metasurfaces: physics and applications,” Rep. Prog. Phys. 79(7), 076401 (2016).
[Crossref] [PubMed]

Chen, W. T.

M. Khorasaninejad, A. Y. Zhu, C. Roques-Carmes, W. T. Chen, J. Oh, I. Mishra, R. C. Devlin, and F. Capasso, “Polarization-Insensitive Metalenses at Visible Wavelengths,” Nano Lett. 16(11), 7229–7234 (2016).
[Crossref] [PubMed]

R. C. Devlin, M. Khorasaninejad, W. T. Chen, J. Oh, and F. Capasso, “Broadband high-efficiency dielectric metasurfaces for the visible spectrum,” Proc. Natl. Acad. Sci. U.S.A. 113(38), 10473–10478 (2016).
[Crossref] [PubMed]

Choi, D. Y.

A. Tittl, A. Leitis, M. Liu, F. Yesilkoy, D. Y. Choi, D. N. Neshev, Y. S. Kivshar, and H. Altug, “Imaging-based molecular barcoding with pixelated dielectric metasurfaces,” Science 360(6393), 1105–1109 (2018).
[Crossref] [PubMed]

Chu, C. H.

Colburn, S.

Devlin, R.

Devlin, R. C.

M. Khorasaninejad, A. Y. Zhu, C. Roques-Carmes, W. T. Chen, J. Oh, I. Mishra, R. C. Devlin, and F. Capasso, “Polarization-Insensitive Metalenses at Visible Wavelengths,” Nano Lett. 16(11), 7229–7234 (2016).
[Crossref] [PubMed]

R. C. Devlin, M. Khorasaninejad, W. T. Chen, J. Oh, and F. Capasso, “Broadband high-efficiency dielectric metasurfaces for the visible spectrum,” Proc. Natl. Acad. Sci. U.S.A. 113(38), 10473–10478 (2016).
[Crossref] [PubMed]

Doshay, S.

S. Doshay, D. Sell, J. Yang, R. Yang, and J. A. Fan, “High-performance axicon lenses based on high-contrast, multilayer gratings,” APL Photonics 3(1), 011302 (2018).
[Crossref]

D. Sell, J. Yang, E. W. Wang, T. Phan, S. Doshay, and J. A. Fan, “Ultra-High-Efficiency Anomalous Refraction with Dielectric Metasurfaces,” ACS Photonics 5(6), 2402–2407 (2018).
[Crossref]

D. Sell, J. Yang, S. Doshay, and J. A. Fan, “Periodic Dielectric Metasurfaces with High-Efficiency, Multiwavelength Functionalities,” Adv. Opt. Mater. 5(23), 1700645 (2017).
[Crossref]

D. Sell, J. Yang, S. Doshay, R. Yang, and J. A. Fan, “Large-Angle, Multifunctional Metagratings Based on Freeform Multimode Geometries,” Nano Lett. 17(6), 3752–3757 (2017).
[Crossref] [PubMed]

D. Sell, J. Yang, S. Doshay, K. Zhang, and J. A. Fan, “Visible light metasurfaces based on single-crystal silicon,” ACS Photonics 3(10), 1919–1925 (2016).
[Crossref]

Fan, J. A.

D. Sell, J. Yang, E. W. Wang, T. Phan, S. Doshay, and J. A. Fan, “Ultra-High-Efficiency Anomalous Refraction with Dielectric Metasurfaces,” ACS Photonics 5(6), 2402–2407 (2018).
[Crossref]

S. Doshay, D. Sell, J. Yang, R. Yang, and J. A. Fan, “High-performance axicon lenses based on high-contrast, multilayer gratings,” APL Photonics 3(1), 011302 (2018).
[Crossref]

J. Yang, D. Sell, and J. A. Fan, “Freeform metagratings based on complex light scattering dynamics for extreme, high efficiency beam steering,” Ann. Phys. 530(1), 1700302 (2018).
[Crossref]

J. Yang and J. A. Fan, “Topology-optimized metasurfaces: impact of initial geometric layout,” Opt. Lett. 42(16), 3161–3164 (2017).
[Crossref] [PubMed]

J. Yang and J. A. Fan, “Analysis of material selection on dielectric metasurface performance,” Opt. Express 25(20), 23899–23909 (2017).
[Crossref] [PubMed]

D. Sell, J. Yang, S. Doshay, and J. A. Fan, “Periodic Dielectric Metasurfaces with High-Efficiency, Multiwavelength Functionalities,” Adv. Opt. Mater. 5(23), 1700645 (2017).
[Crossref]

D. Sell, J. Yang, S. Doshay, R. Yang, and J. A. Fan, “Large-Angle, Multifunctional Metagratings Based on Freeform Multimode Geometries,” Nano Lett. 17(6), 3752–3757 (2017).
[Crossref] [PubMed]

D. Sell, J. Yang, S. Doshay, K. Zhang, and J. A. Fan, “Visible light metasurfaces based on single-crystal silicon,” ACS Photonics 3(10), 1919–1925 (2016).
[Crossref]

Fan, P.

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345(6194), 298–302 (2014).
[Crossref] [PubMed]

Faraon, A.

E. Arbabi, S. M. Kamali, A. Arbabi, and A. Faraon, “Full-Stokes Imaging Polarimetry Using Dielectric Metasurfaces,” ACS Photonics 5(8), 3132–3140 (2018).
[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. Nanotechnol. 10(11), 937–943 (2015).
[Crossref] [PubMed]

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

Fryett, T. K.

Genevet, P.

Grbic, A.

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

Groever, B.

Z. Lin, B. Groever, F. Capasso, A. W. Rodriguez, and M. Loncar, “Topology-Optimized Multilayered Metaoptics,” Phys. Rev. Appl. 9(4), 044030 (2018).
[Crossref]

Hasman, E.

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345(6194), 298–302 (2014).
[Crossref] [PubMed]

Horie, Y.

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. Nanotechnol. 10(11), 937–943 (2015).
[Crossref] [PubMed]

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

Jensen, J.

Kamali, S. M.

E. Arbabi, S. M. Kamali, A. Arbabi, and A. Faraon, “Full-Stokes Imaging Polarimetry Using Dielectric Metasurfaces,” ACS Photonics 5(8), 3132–3140 (2018).
[Crossref]

Khorasaninejad, M.

P. Genevet, F. Capasso, F. Aieta, M. Khorasaninejad, and R. Devlin, “Recent advances in planar optics: from plasmonic to dielectric metasurfaces,” Optica 4(1), 139–152 (2017).
[Crossref]

M. Khorasaninejad, A. Y. Zhu, C. Roques-Carmes, W. T. Chen, J. Oh, I. Mishra, R. C. Devlin, and F. Capasso, “Polarization-Insensitive Metalenses at Visible Wavelengths,” Nano Lett. 16(11), 7229–7234 (2016).
[Crossref] [PubMed]

R. C. Devlin, M. Khorasaninejad, W. T. Chen, J. Oh, and F. Capasso, “Broadband high-efficiency dielectric metasurfaces for the visible spectrum,” Proc. Natl. Acad. Sci. U.S.A. 113(38), 10473–10478 (2016).
[Crossref] [PubMed]

Kiisler, A.-A.

J. Aarik, A. Aidla, A.-A. Kiisler, T. Uustare, and V. Sammelselg, “Effect of crystal structure on optical properties of TiO2 films grown by atomic layer deposition,” Thin Solid Films 305(1–2), 270–273 (1997).
[Crossref]

Kildishev, A. V.

A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science 339(6125), 1232009 (2013).
[Crossref] [PubMed]

Kivshar, Y. S.

A. Tittl, A. Leitis, M. Liu, F. Yesilkoy, D. Y. Choi, D. N. Neshev, Y. S. Kivshar, and H. Altug, “Imaging-based molecular barcoding with pixelated dielectric metasurfaces,” Science 360(6393), 1105–1109 (2018).
[Crossref] [PubMed]

L. Wang, S. Kruk, H. Tang, T. Li, I. Kravchenko, D. N. Neshev, and Y. S. Kivshar, “Grayscale transparent metasurface holograms,” Optica 3(12), 1504–1505 (2016).
[Crossref] [PubMed]

Kravchenko, I.

Kruk, S.

Lagoudakis, K. G.

A. Piggott, J. Lu, K. G. Lagoudakis, J. Petykiewicz, T. M. Babinec, and J. Vuckovic, “Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer,” Nat. Photonics 9(6), 374–377 (2015).
[Crossref]

Lalanne, P.

Lalau-Keraly, C. M.

Launois, H.

Lazaroz, B. S.

M. Schevenels, B. S. Lazaroz, and O. Sigmund, “Robust topology optimization accounting for spatially varying manufacturing errors,” Comput. Methods Appl. Math. 200, 3613–3627 (2011).

Leitis, A.

A. Tittl, A. Leitis, M. Liu, F. Yesilkoy, D. Y. Choi, D. N. Neshev, Y. S. Kivshar, and H. Altug, “Imaging-based molecular barcoding with pixelated dielectric metasurfaces,” Science 360(6393), 1105–1109 (2018).
[Crossref] [PubMed]

Li, T.

Lin, D.

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345(6194), 298–302 (2014).
[Crossref] [PubMed]

Lin, Z.

Z. Lin, B. Groever, F. Capasso, A. W. Rodriguez, and M. Loncar, “Topology-Optimized Multilayered Metaoptics,” Phys. Rev. Appl. 9(4), 044030 (2018).
[Crossref]

Liu, M.

A. Tittl, A. Leitis, M. Liu, F. Yesilkoy, D. Y. Choi, D. N. Neshev, Y. S. Kivshar, and H. Altug, “Imaging-based molecular barcoding with pixelated dielectric metasurfaces,” Science 360(6393), 1105–1109 (2018).
[Crossref] [PubMed]

Loncar, M.

Z. Lin, B. Groever, F. Capasso, A. W. Rodriguez, and M. Loncar, “Topology-Optimized Multilayered Metaoptics,” Phys. Rev. Appl. 9(4), 044030 (2018).
[Crossref]

Lu, J.

A. Piggott, J. Lu, K. G. Lagoudakis, J. Petykiewicz, T. M. Babinec, and J. Vuckovic, “Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer,” Nat. Photonics 9(6), 374–377 (2015).
[Crossref]

Majumdar, A.

Miller, O. D.

Mishra, I.

M. Khorasaninejad, A. Y. Zhu, C. Roques-Carmes, W. T. Chen, J. Oh, I. Mishra, R. C. Devlin, and F. Capasso, “Polarization-Insensitive Metalenses at Visible Wavelengths,” Nano Lett. 16(11), 7229–7234 (2016).
[Crossref] [PubMed]

Neshev, D. N.

A. Tittl, A. Leitis, M. Liu, F. Yesilkoy, D. Y. Choi, D. N. Neshev, Y. S. Kivshar, and H. Altug, “Imaging-based molecular barcoding with pixelated dielectric metasurfaces,” Science 360(6393), 1105–1109 (2018).
[Crossref] [PubMed]

L. Wang, S. Kruk, H. Tang, T. Li, I. Kravchenko, D. N. Neshev, and Y. S. Kivshar, “Grayscale transparent metasurface holograms,” Optica 3(12), 1504–1505 (2016).
[Crossref] [PubMed]

Nielsen, M. G.

Oh, J.

R. C. Devlin, M. Khorasaninejad, W. T. Chen, J. Oh, and F. Capasso, “Broadband high-efficiency dielectric metasurfaces for the visible spectrum,” Proc. Natl. Acad. Sci. U.S.A. 113(38), 10473–10478 (2016).
[Crossref] [PubMed]

M. Khorasaninejad, A. Y. Zhu, C. Roques-Carmes, W. T. Chen, J. Oh, I. Mishra, R. C. Devlin, and F. Capasso, “Polarization-Insensitive Metalenses at Visible Wavelengths,” Nano Lett. 16(11), 7229–7234 (2016).
[Crossref] [PubMed]

Petykiewicz, J.

A. Piggott, J. Lu, K. G. Lagoudakis, J. Petykiewicz, T. M. Babinec, and J. Vuckovic, “Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer,” Nat. Photonics 9(6), 374–377 (2015).
[Crossref]

Pfeiffer, C.

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

Phan, T.

D. Sell, J. Yang, E. W. Wang, T. Phan, S. Doshay, and J. A. Fan, “Ultra-High-Efficiency Anomalous Refraction with Dielectric Metasurfaces,” ACS Photonics 5(6), 2402–2407 (2018).
[Crossref]

Piggott, A.

A. Piggott, J. Lu, K. G. Lagoudakis, J. Petykiewicz, T. M. Babinec, and J. Vuckovic, “Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer,” Nat. Photonics 9(6), 374–377 (2015).
[Crossref]

Platt, J. C.

P. Simard, D. Steinkraud, and J. C. Platt, “Best Practices for Convolutional Neural Networks Applied to Visual Document Analysis,” in Proc. of the International Conference on Document Analysis and Recognition, 2003.
[Crossref]

Pors, A.

Rodriguez, A. W.

Z. Lin, B. Groever, F. Capasso, A. W. Rodriguez, and M. Loncar, “Topology-Optimized Multilayered Metaoptics,” Phys. Rev. Appl. 9(4), 044030 (2018).
[Crossref]

Roques-Carmes, C.

M. Khorasaninejad, A. Y. Zhu, C. Roques-Carmes, W. T. Chen, J. Oh, I. Mishra, R. C. Devlin, and F. Capasso, “Polarization-Insensitive Metalenses at Visible Wavelengths,” Nano Lett. 16(11), 7229–7234 (2016).
[Crossref] [PubMed]

Sammelselg, V.

J. Aarik, A. Aidla, A.-A. Kiisler, T. Uustare, and V. Sammelselg, “Effect of crystal structure on optical properties of TiO2 films grown by atomic layer deposition,” Thin Solid Films 305(1–2), 270–273 (1997).
[Crossref]

Schevenels, M.

M. Schevenels, B. S. Lazaroz, and O. Sigmund, “Robust topology optimization accounting for spatially varying manufacturing errors,” Comput. Methods Appl. Math. 200, 3613–3627 (2011).

Sell, D.

J. Yang, D. Sell, and J. A. Fan, “Freeform metagratings based on complex light scattering dynamics for extreme, high efficiency beam steering,” Ann. Phys. 530(1), 1700302 (2018).
[Crossref]

D. Sell, J. Yang, E. W. Wang, T. Phan, S. Doshay, and J. A. Fan, “Ultra-High-Efficiency Anomalous Refraction with Dielectric Metasurfaces,” ACS Photonics 5(6), 2402–2407 (2018).
[Crossref]

S. Doshay, D. Sell, J. Yang, R. Yang, and J. A. Fan, “High-performance axicon lenses based on high-contrast, multilayer gratings,” APL Photonics 3(1), 011302 (2018).
[Crossref]

D. Sell, J. Yang, S. Doshay, and J. A. Fan, “Periodic Dielectric Metasurfaces with High-Efficiency, Multiwavelength Functionalities,” Adv. Opt. Mater. 5(23), 1700645 (2017).
[Crossref]

D. Sell, J. Yang, S. Doshay, R. Yang, and J. A. Fan, “Large-Angle, Multifunctional Metagratings Based on Freeform Multimode Geometries,” Nano Lett. 17(6), 3752–3757 (2017).
[Crossref] [PubMed]

D. Sell, J. Yang, S. Doshay, K. Zhang, and J. A. Fan, “Visible light metasurfaces based on single-crystal silicon,” ACS Photonics 3(10), 1919–1925 (2016).
[Crossref]

Shalaev, V. M.

A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science 339(6125), 1232009 (2013).
[Crossref] [PubMed]

Sigmund, O.

J. Jensen and O. Sigmund, “Topology optimization for nanophotonics,” Laser Photonics Rev. 5(2), 308–321 (2011).
[Crossref]

M. Schevenels, B. S. Lazaroz, and O. Sigmund, “Robust topology optimization accounting for spatially varying manufacturing errors,” Comput. Methods Appl. Math. 200, 3613–3627 (2011).

F. Wang, J. Jensen, and O. Sigmund, “Robust topology optimization of photonic crystal waveguides with tailored dispersion properties,” J. Opt. Soc. Am. B 28(3), 387–397 (2011).
[Crossref]

Simard, P.

P. Simard, D. Steinkraud, and J. C. Platt, “Best Practices for Convolutional Neural Networks Applied to Visual Document Analysis,” in Proc. of the International Conference on Document Analysis and Recognition, 2003.
[Crossref]

Steinkraud, D.

P. Simard, D. Steinkraud, and J. C. Platt, “Best Practices for Convolutional Neural Networks Applied to Visual Document Analysis,” in Proc. of the International Conference on Document Analysis and Recognition, 2003.
[Crossref]

Su, V.-C.

Sun, G.

Tang, H.

Taylor, A. J.

H. T. Chen, A. J. Taylor, and N. Yu, “A review of metasurfaces: physics and applications,” Rep. Prog. Phys. 79(7), 076401 (2016).
[Crossref] [PubMed]

Tittl, A.

A. Tittl, A. Leitis, M. Liu, F. Yesilkoy, D. Y. Choi, D. N. Neshev, Y. S. Kivshar, and H. Altug, “Imaging-based molecular barcoding with pixelated dielectric metasurfaces,” Science 360(6393), 1105–1109 (2018).
[Crossref] [PubMed]

Tsai, D. P.

Uustare, T.

J. Aarik, A. Aidla, A.-A. Kiisler, T. Uustare, and V. Sammelselg, “Effect of crystal structure on optical properties of TiO2 films grown by atomic layer deposition,” Thin Solid Films 305(1–2), 270–273 (1997).
[Crossref]

Vuckovic, J.

A. Piggott, J. Lu, K. G. Lagoudakis, J. Petykiewicz, T. M. Babinec, and J. Vuckovic, “Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer,” Nat. Photonics 9(6), 374–377 (2015).
[Crossref]

Wang, E. W.

D. Sell, J. Yang, E. W. Wang, T. Phan, S. Doshay, and J. A. Fan, “Ultra-High-Efficiency Anomalous Refraction with Dielectric Metasurfaces,” ACS Photonics 5(6), 2402–2407 (2018).
[Crossref]

Wang, F.

Wang, L.

Yablonovitch, E.

Yang, J.

J. Yang, D. Sell, and J. A. Fan, “Freeform metagratings based on complex light scattering dynamics for extreme, high efficiency beam steering,” Ann. Phys. 530(1), 1700302 (2018).
[Crossref]

D. Sell, J. Yang, E. W. Wang, T. Phan, S. Doshay, and J. A. Fan, “Ultra-High-Efficiency Anomalous Refraction with Dielectric Metasurfaces,” ACS Photonics 5(6), 2402–2407 (2018).
[Crossref]

S. Doshay, D. Sell, J. Yang, R. Yang, and J. A. Fan, “High-performance axicon lenses based on high-contrast, multilayer gratings,” APL Photonics 3(1), 011302 (2018).
[Crossref]

D. Sell, J. Yang, S. Doshay, R. Yang, and J. A. Fan, “Large-Angle, Multifunctional Metagratings Based on Freeform Multimode Geometries,” Nano Lett. 17(6), 3752–3757 (2017).
[Crossref] [PubMed]

D. Sell, J. Yang, S. Doshay, and J. A. Fan, “Periodic Dielectric Metasurfaces with High-Efficiency, Multiwavelength Functionalities,” Adv. Opt. Mater. 5(23), 1700645 (2017).
[Crossref]

J. Yang and J. A. Fan, “Topology-optimized metasurfaces: impact of initial geometric layout,” Opt. Lett. 42(16), 3161–3164 (2017).
[Crossref] [PubMed]

J. Yang and J. A. Fan, “Analysis of material selection on dielectric metasurface performance,” Opt. Express 25(20), 23899–23909 (2017).
[Crossref] [PubMed]

D. Sell, J. Yang, S. Doshay, K. Zhang, and J. A. Fan, “Visible light metasurfaces based on single-crystal silicon,” ACS Photonics 3(10), 1919–1925 (2016).
[Crossref]

Yang, R.

S. Doshay, D. Sell, J. Yang, R. Yang, and J. A. Fan, “High-performance axicon lenses based on high-contrast, multilayer gratings,” APL Photonics 3(1), 011302 (2018).
[Crossref]

D. Sell, J. Yang, S. Doshay, R. Yang, and J. A. Fan, “Large-Angle, Multifunctional Metagratings Based on Freeform Multimode Geometries,” Nano Lett. 17(6), 3752–3757 (2017).
[Crossref] [PubMed]

Yesilkoy, F.

A. Tittl, A. Leitis, M. Liu, F. Yesilkoy, D. Y. Choi, D. N. Neshev, Y. S. Kivshar, and H. Altug, “Imaging-based molecular barcoding with pixelated dielectric metasurfaces,” Science 360(6393), 1105–1109 (2018).
[Crossref] [PubMed]

Yu, N.

H. T. Chen, A. J. Taylor, and N. Yu, “A review of metasurfaces: physics and applications,” Rep. Prog. Phys. 79(7), 076401 (2016).
[Crossref] [PubMed]

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
[Crossref] [PubMed]

Zhan, A.

Zhang, K.

D. Sell, J. Yang, S. Doshay, K. Zhang, and J. A. Fan, “Visible light metasurfaces based on single-crystal silicon,” ACS Photonics 3(10), 1919–1925 (2016).
[Crossref]

Zhu, A. Y.

M. Khorasaninejad, A. Y. Zhu, C. Roques-Carmes, W. T. Chen, J. Oh, I. Mishra, R. C. Devlin, and F. Capasso, “Polarization-Insensitive Metalenses at Visible Wavelengths,” Nano Lett. 16(11), 7229–7234 (2016).
[Crossref] [PubMed]

ACS Photonics (3)

D. Sell, J. Yang, S. Doshay, K. Zhang, and J. A. Fan, “Visible light metasurfaces based on single-crystal silicon,” ACS Photonics 3(10), 1919–1925 (2016).
[Crossref]

E. Arbabi, S. M. Kamali, A. Arbabi, and A. Faraon, “Full-Stokes Imaging Polarimetry Using Dielectric Metasurfaces,” ACS Photonics 5(8), 3132–3140 (2018).
[Crossref]

D. Sell, J. Yang, E. W. Wang, T. Phan, S. Doshay, and J. A. Fan, “Ultra-High-Efficiency Anomalous Refraction with Dielectric Metasurfaces,” ACS Photonics 5(6), 2402–2407 (2018).
[Crossref]

Adv. Opt. Mater. (1)

D. Sell, J. Yang, S. Doshay, and J. A. Fan, “Periodic Dielectric Metasurfaces with High-Efficiency, Multiwavelength Functionalities,” Adv. Opt. Mater. 5(23), 1700645 (2017).
[Crossref]

Ann. Phys. (1)

J. Yang, D. Sell, and J. A. Fan, “Freeform metagratings based on complex light scattering dynamics for extreme, high efficiency beam steering,” Ann. Phys. 530(1), 1700302 (2018).
[Crossref]

APL Photonics (1)

S. Doshay, D. Sell, J. Yang, R. Yang, and J. A. Fan, “High-performance axicon lenses based on high-contrast, multilayer gratings,” APL Photonics 3(1), 011302 (2018).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

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

Comput. Methods Appl. Math. (1)

M. Schevenels, B. S. Lazaroz, and O. Sigmund, “Robust topology optimization accounting for spatially varying manufacturing errors,” Comput. Methods Appl. Math. 200, 3613–3627 (2011).

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

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

Laser Photonics Rev. (1)

J. Jensen and O. Sigmund, “Topology optimization for nanophotonics,” Laser Photonics Rev. 5(2), 308–321 (2011).
[Crossref]

Nano Lett. (2)

D. Sell, J. Yang, S. Doshay, R. Yang, and J. A. Fan, “Large-Angle, Multifunctional Metagratings Based on Freeform Multimode Geometries,” Nano Lett. 17(6), 3752–3757 (2017).
[Crossref] [PubMed]

M. Khorasaninejad, A. Y. Zhu, C. Roques-Carmes, W. T. Chen, J. Oh, I. Mishra, R. C. Devlin, and F. Capasso, “Polarization-Insensitive Metalenses at Visible Wavelengths,” Nano Lett. 16(11), 7229–7234 (2016).
[Crossref] [PubMed]

Nat. Commun. (1)

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

Nat. Mater. (1)

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
[Crossref] [PubMed]

Nat. Nanotechnol. (1)

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. Nanotechnol. 10(11), 937–943 (2015).
[Crossref] [PubMed]

Nat. Photonics (1)

A. Piggott, J. Lu, K. G. Lagoudakis, J. Petykiewicz, T. M. Babinec, and J. Vuckovic, “Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer,” Nat. Photonics 9(6), 374–377 (2015).
[Crossref]

Opt. Express (3)

Opt. Lett. (1)

Optica (3)

Phys. Rev. Appl. (1)

Z. Lin, B. Groever, F. Capasso, A. W. Rodriguez, and M. Loncar, “Topology-Optimized Multilayered Metaoptics,” Phys. Rev. Appl. 9(4), 044030 (2018).
[Crossref]

Proc. Natl. Acad. Sci. U.S.A. (1)

R. C. Devlin, M. Khorasaninejad, W. T. Chen, J. Oh, and F. Capasso, “Broadband high-efficiency dielectric metasurfaces for the visible spectrum,” Proc. Natl. Acad. Sci. U.S.A. 113(38), 10473–10478 (2016).
[Crossref] [PubMed]

Rep. Prog. Phys. (1)

H. T. Chen, A. J. Taylor, and N. Yu, “A review of metasurfaces: physics and applications,” Rep. Prog. Phys. 79(7), 076401 (2016).
[Crossref] [PubMed]

Sci. Adv. (1)

S. Colburn, A. Zhan, and A. Majumdar, “Metasurface optics for full-color computational imaging,” Sci. Adv. 4(2), r2114 (2018).
[Crossref] [PubMed]

Science (3)

A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science 339(6125), 1232009 (2013).
[Crossref] [PubMed]

A. Tittl, A. Leitis, M. Liu, F. Yesilkoy, D. Y. Choi, D. N. Neshev, Y. S. Kivshar, and H. Altug, “Imaging-based molecular barcoding with pixelated dielectric metasurfaces,” Science 360(6393), 1105–1109 (2018).
[Crossref] [PubMed]

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345(6194), 298–302 (2014).
[Crossref] [PubMed]

Thin Solid Films (1)

J. Aarik, A. Aidla, A.-A. Kiisler, T. Uustare, and V. Sammelselg, “Effect of crystal structure on optical properties of TiO2 films grown by atomic layer deposition,” Thin Solid Films 305(1–2), 270–273 (1997).
[Crossref]

Other (2)

P. Simard, D. Steinkraud, and J. C. Platt, “Best Practices for Convolutional Neural Networks Applied to Visual Document Analysis,” in Proc. of the International Conference on Document Analysis and Recognition, 2003.
[Crossref]

R. Pestourie, C. Perez-Arancibia, Z. Lin, W. Shin, F. Capasso, and S. Johnson, “Inverse design of large-area metasurfaces,” arXiv preprint arXiv:1808.04215 (2018).
[Crossref]

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Figures (11)

Fig. 1
Fig. 1 (a) Top view of an ideal pattern of a representative topology-optimized metasurface section, with silicon in gray and air in blue. (b,c) SEM images of the device fabricated with (b) near-optimal and (c) strongly underexposed dosing. Differences in fine spatial features are noted. Scale bar: 500 nm.
Fig. 2
Fig. 2 Schematics of the metasurface from Fig. 1, in which the ideal pattern is eroded and dilated with edge deviations of −10 nm and +10 nm, respectively. Fig. shows silicon in gray and air in blue. The dashed red line in each panel represents an outline of the ideal device. Scale bar: 500 nm.
Fig. 3
Fig. 3 (a) Absolute efficiency as a function of geometric edge deviation for a topology-optimized silicon metagrating. (b) Top view SEM images showing devices patterned with near-optimal and suboptimal dosing. Top left insets: theoretical unit cells for the respective edge deviations. Scale bars: 500 nm.
Fig. 4
Fig. 4 (a) Flow chart of one topology optimization iteration with robustness enforcement. (b) Theoretical absolute efficiencies of robust and non-robust topology-optimized metagratings that deflect normally incident, TM-polarized light to 75°, for differing edge deviations.
Fig. 5
Fig. 5 (a) Absolute efficiency as a function of edge deviation for a topology-optimized silicon metagrating designed with robustness enforcement. (b) Top view SEM images showing devices patterned with near-optimal and suboptimal dosing. Top left inset: theoretical unit cells for the respective edge deviations. Scale bars: 500 nm.
Fig. 6
Fig. 6 (a) Absolute efficiency as a function of edge deviation for a conventionally designed 40° metagrating deflector. Inset: top-view of a unit cell. (b) Red: Top-view unit cell and corresponding absolute efficiency curve of a conventionally designed 75° metgrating deflector. Blue: Top-view unit cell and corresponding absolute efficiency curve of a topology-refined metagrating using the device in red as a starting point. Scale bars: 250 nm
Fig. 7
Fig. 7 (a) Schematic showing the incorporation of random local deformations on an ideal, linear edge. I. Random displacement field with an average displacement of 6 nm and Gaussian spread of 10 nm. II. Displacement field of interest along a semi-infinite edge. III. Resulting transformed edge. Dashed red lines indicate ±6 nm displacement values. (b) Representative random local deformations (red lines) of ideal circular shapes (black lines), for varying displacement values. (c) Histograms of absolute efficiencies of one hundred random local deformations of non-robust and robust devices. Insets: representative unit cells of deformed structures.
Fig. 8
Fig. 8 (a) Absolute efficiency for the robust metagrating decomposed by contribution from each Bloch mode as a function of edge deviation. Modes are sorted in descending order of effective index. (b) Effective indices of the Bloch modes from (a). (c) H-field profiles of the thirteen propagating Bloch modes of the ideal pattern.
Fig. 9
Fig. 9 (a) Absolute efficiency of all one hundred variants of the robust metagrating, deformed with 6 nm average displacement. Devices are sorted in increasing order of efficiency, and the efficiency contribution per Bloch mode is plotted. (b) Patterns of the twelve highest efficiency devices from Fig. 8(a). The absolute efficiencies of each device are displayed.
Fig. 10
Fig. 10 (a) Absolute efficiency as a function of refractive index for metasurfaces that are not robust (from Fig. 3, red) and robust (from Fig. 5, blue) to edge deviations. (b) Absolute efficiency as a function of refractive index for a device designed to be robust to refractive index variations. Inset: top view of a unit cell of the device. Scale bar is 250 nm. Black dashed line represents the target refractive index of n0 = 3.57.
Fig. 11
Fig. 11 (a) Absolute efficiency as a function of wavelength for both robust and non-robust metasurfaces from the main text. (b) Absolute efficiency as a function of incidence angle for both robust and non-robust metasurfaces from the main text. Incidence angle is given as the value in air.

Equations (10)

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ρ ˜ ( r j )= r j 1 α ρ( r j ) e (r r j ) 2 σ 2 ,
α= r j e (r r j ) 2 σ 2 .
ρ ¯ (r)={ 0,0 ρ ˜ η 1,η ρ ˜ 1 .
1 2 η=erf( Δ σ ).
G= FoM ρ .
ρ ¯ (r)={ η e β(η ρ ˜ ) η (η ρ ˜ ) e β ,0 ρ ˜ η 1(1η) e β( ρ ˜ η) 1η (η ρ ˜ ) e β ,η< ρ ˜ 1 .
G= q w q G ¯ q ρ ¯ q ρ ˜ ρ ˜ ρ .
G= t w t G ¯ t .
G= i w i G ¯ i n i n 0 .
G= i,j,k w ijk G ¯ ijk ρ ¯ ijk ρ .

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