Abstract

Metalenses have shown great promise in their ability to function as ultracompact optical systems for focusing and imaging. Remarkably, several designs have been recently demonstrated that operate over a large range of frequencies with minimized chromatic aberrations, potentially paving the way for ultrathin achromatic optics. Here, we derive fundamental bandwidth limits that apply to broadband optical metalenses regardless of their implementation. Specifically, we discuss how the product between achievable time delay and bandwidth is limited in any time-invariant system, and we apply well-established bounds on this product to a general focusing system. We then show that all metalenses designed thus far obey the appropriate bandwidth limit. The derived physical bounds provide a useful metric to compare and assess the performance of different devices, and they offer fundamental insight into how to design better broadband metalenses.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Khorasaninejad and F. Capasso, “Metalenses: versatile multifunctional photonic components,” Science 358, eaam8100 (2017).
    [Crossref]
  2. M. L. Tseng, H.-H. Hsiao, C. H. Chu, M. K. Chen, G. Sun, A.-Q. Liu, and D. P. Tsai, “Metalenses: Advances and applications,” Adv. Opt. Mater. 6, 1800554 (2018).
    [Crossref]
  3. P. Lalanne and P. Chavel, “Metalenses at visible wavelengths: past, present, perspectives,” Laser Photon. Rev. 11, 1600295 (2017).
    [Crossref]
  4. A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, “Performing mathematical operations with metamaterials,” Science 343, 160–163 (2014).
    [Crossref]
  5. A. Pors, M. G. Nielsen, and S. I. Bozhevolnyi, “Analog computing using reflective plasmonic metasurfaces,” Nano Lett. 15, 791–797 (2015).
    [Crossref]
  6. M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1980).
  7. W. T. Chen, A. Y. Zhu, V. Sanjeev, M. Khorasaninejad, Z. Shi, E. Lee, and F. Capasso, “A broadband achromatic metalens for focusing and imaging in the visible,” Nat. Nanotechnol. 13, 220–226 (2018).
    [Crossref]
  8. W. T. Chen, A. Y. Zhu, J. Sisler, Z. Bharwani, and F. Capasso, “A broadband achromatic polarization-insensitive metalens consisting of anisotropic nanostructures,” Nat. Commun. 10, 1–7 (2019).
    [Crossref]
  9. M. Khorasaninejad, Z. Shi, A. Y. Zhu, W. T. Chen, V. Sanjeev, A. Zaidi, and F. Capasso, “Achromatic metalens over 60  nm bandwidth in the visible and metalens with reverse chromatic dispersion,” Nano Lett. 17, 1819–1824 (2017).
    [Crossref]
  10. S. Shrestha, A. C. Overvig, M. Lu, A. Stein, and N. Yu, “Broadband achromatic dielectric metalenses,” Light: Sci. Appl. 7, 85 (2018).
    [Crossref]
  11. M. Ye, V. Ray, and Y. S. Yi, “Achromatic flat subwavelength grating lens over whole visible bandwidths,” IEEE Photon. Technol. Lett. 30, 955–958 (2018).
    [Crossref]
  12. R. J. Lin, V.-C. Su, S. Wang, M. K. Chen, T. L. Chung, Y. H. Chen, H. Y. Kuo, J.-W. Chen, J. Chen, Y.-T. Huang, J.-H. Wang, C. H. Chu, P. Chieh Wu, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “Achromatic metalens array for full-colour light-field imaging,” Nat. Nanotechnol. 14, 227–231 (2019).
    [Crossref]
  13. H. Chung and O. D. Miller, “High-NA, achromatic metalenses by inverse design,” Opt. Express 28, 6945–6965 (2019).
    [Crossref]
  14. N. Mohammad, M. Meem, P. Wang, and R. Menon, “Broadband imaging with one planar diffractive lens,” Sci. Rep. 8, 2799 (2018).
    [Crossref]
  15. S. Banerji, M. Meem, A. Majumder, F. G. Vasquez, B. Sensale-Rodriguez, and R. Menon, “Imaging with flat optics: metalenses or diffractive lenses?” Optica 6, 805–810 (2019).
    [Crossref]
  16. S. Zhang, A. Soibel, S. Keo, D. Wilson, S. Rafol, D. Z. Ting, A. She, S. D. Gunapala, and F. Capasso, “Solid-immersion metalenses for infrared focal plane arrays,” Appl. Phys. Lett. 113, 111104 (2018).
    [Crossref]
  17. S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, M.-K. Chen, H. Y. Kuo, B. H. Chen, Y. H. Chen, T.-T. Huang, J.-H. Wang, R.-M. Lin, C.-H. Kuan, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13, 227–232 (2018).
    [Crossref]
  18. F. Balli, M. A. Sultan, S. K. Lami, and J. T. Hastings, “A hybrid achromatic metalens,” arXiv:1909.07941 (2019).
  19. B. Yu, J. Wen, X. Chen, and D. Zhang, “An achromatic metalens in the near-infrared region with an array based on a single nano-rod unit,” Appl. Phys. Express 12, 092003 (2019).
    [Crossref]
  20. Q. Cheng, M. Ma, D. Yu, Z. Shen, J. Xie, J. Wang, N. Xu, H. Guo, W. Hu, S. Wang, T. Li, and S. Zhuang, “Broadband achromatic metalens in terahertz regime,” Sci. Bull. 64, 1525–1531 (2019).
    [Crossref]
  21. S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. Hung Chu, J.-W. Chen, S.-H. Lu, J. Chen, B. Xu, C.-H. Kuan, T. Li, S. Zhu, and D. P. Tsai, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8, 187 (2017).
    [Crossref]
  22. Z. Lin and S. G. Johnson, “Overlapping domains for topology optimization of large-area metasurfaces,” Opt. Express 27, 32445–32453 (2019).
    [Crossref]
  23. D. Werdehausen, S. Burger, I. Staude, T. Pertsch, and M. Decker, “General design formalism for highly efficient flat optics for broadband applications,” Opt. Express 28, 6452–6468 (2020).
    [Crossref]
  24. A. Ozer, N. Yilmaz, H. Kocer, and H. Kurt, “Polarization-insensitive beam splitters using all-dielectric phase gradient metasurfaces at visible wavelengths,” Opt. Lett. 43, 4350–4353 (2018).
    [Crossref]
  25. D. M. Pozar, “Flat lens antenna concept using aperture coupled microstrip patches,” Electron. Lett. 32, 2109–2111 (1996).
    [Crossref]
  26. D. A. B. Miller, “Fundamental limit to linear one-dimensional slow light structures,” Phys. Rev. Lett. 99, 203903 (2007).
    [Crossref]
  27. R. S. Tucker, P.-C. Ku, and C. J. Chang-Hasnain, “Slow-light optical buffers: capabilities and fundamental limitations,” J. Lightwave Technol. 23, 4046–4066 (2005).
    [Crossref]
  28. J. Khurgin, “Bandwidth limitation in slow light schemes,” in Slow Light: Science and Applications, J. Khurgin and R. S. Tucker, eds. (Taylor & Francis Group, 2008), chap. 15, pp. 293–320.
  29. A. A. Fathnan and D. A. Powell, “Bandwidth and size limits of achromatic printed-circuit metasurfaces,” Opt. Express 26, 29440–29450 (2018).
    [Crossref]
  30. A. A. Fathnan, A. E. Olk, and D. A. Powell, “Broadband anomalous reflection with dispersion controlled metasurfaces,” arXiv:1912.03936 (2019).
  31. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999).
  32. S. A. Mann, D. L. Sounas, and A. Alù, “Nonreciprocal cavities and the time-bandwidth limit,” Optica 6, 104–110 (2019).
    [Crossref]
  33. H. Liang, A. Martins, B.-H. V. Borges, J. Zhou, E. R. Martins, J. Li, and T. F. Krauss, “High performance metalenses: numerical aperture, aberrations, chromaticity, and trade-offs,” Optica 6, 1461–1470 (2019).
    [Crossref]
  34. E. Arbabi, A. Arbabi, S. M. Kamali, Y. Horie, and A. Faraon, “Controlling the sign of chromatic dispersion in diffractive optics with dielectric metasurfaces,” Optica 4, 625–632 (2017).
    [Crossref]
  35. C. Pfeiffer and A. Grbic, “Metamaterial Huygens’ surfaces: tailoring wave fronts with reflectionless sheets,” Phys. Rev. Lett. 110, 197401 (2013).
    [Crossref]
  36. F. Monticone, N. M. Estakhri, and A. Alù, “Full control of nanoscale optical transmission with a composite metascreen,” Phys. Rev. Lett. 110, 203903 (2013).
    [Crossref]
  37. A. Epstein and G. V. Eleftheriades, “Huygens’ metasurfaces via the equivalence principle: design and applications,” J. Opt. Soc. Am. B 33, A31–A50 (2016).
    [Crossref]
  38. J. C. Wyant and K. Creath, “Basic wavefront aberration theory for optical metrology,” in Applied Optics and Optical Engineering, Volume XI, R. R. Shannon and J. C. Wyant, eds. (Academic, 1992), Vol. 11.
  39. J. W. Hardy, “Adaptive optics for astronomical telescopes,” in Adaptive Optics for Astronomical Telescopes (Oxford University, 1998), chap. 4, p. 104–134.
  40. F. Aieta, P. Genevet, M. Kats, and F. Capasso, “Aberrations of flat lenses and aplanatic metasurfaces,” Opt. Express 21, 31530–31539 (2013).
    [Crossref]
  41. T. Siefke, S. Kroker, K. Pfeiffer, O. Puffky, K. Dietrich, D. Franta, I. Ohlídal, A. Szeghalmi, E.-B. Kley, and A. Tünnermann, “Materials pushing the application limits of wire grid polarizers further into the deep ultraviolet spectral range,” Adv. Opt. Mater. 4, 1780–1786 (2016).
    [Crossref]
  42. 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. USA 113, 10473–10478 (2016).
    [Crossref]
  43. E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1998), Vol. 3.
  44. R. Ferrini, M. Patrini, and S. Franchi, “Optical functions from 0.02 to 6  eV of AlxGa1-xSb/GaSb epitaxial layers,” J. Appl. Phys. 84, 4517–4524 (1998).
    [Crossref]
  45. R. Fano, “Theoretical limitations on the broadband matching of arbitrary impedances,” J. Franklin Inst. 249, 57–83 (1950).
    [Crossref]
  46. F. Monticone and A. Alù, “Invisibility exposed: physical bounds on passive cloaking,” Optica 3, 718–724 (2016).
    [Crossref]
  47. S. Abdollahramezani, O. Hemmatyar, H. Taghinejad, A. Krasnok, Y. Kiarashinejad, M. Zandehshahvar, A. Alu, and A. Adibi, “Tunable nanophotonics enabled by chalcogenide phase-change materials,” arXiv:2001.06335 (2020).
  48. S. A. Tretyakov, Analytical Modeling in Applied Electromagnetics (Artech House, 2003).
  49. J. M. Meem, S. Banerji, A. Majumder, J. C. Garcia, P. W. C. Hon, B. Sensale-Rodriquez, and R. Menon, “Imaging from the visible to the longwave infrared wavelengths via an inverse-designed flat lens,” https://arxiv.org/abs/2001.03684 (2020).
  50. S. Colburn, A. Zhan, and A. Majumdar, “Metasurface optics for full-color computational imaging,” Sci. Adv. 4, eaar2114 (2018).
    [Crossref]
  51. L. Huang, J. Whitehead, S. Colburn, and A. Majumdar, “Design and analysis of extended depth of focus metalenses for achromatic computational imaging,” arXiv:2003.09599 (2020).

2020 (1)

2019 (9)

S. A. Mann, D. L. Sounas, and A. Alù, “Nonreciprocal cavities and the time-bandwidth limit,” Optica 6, 104–110 (2019).
[Crossref]

H. Liang, A. Martins, B.-H. V. Borges, J. Zhou, E. R. Martins, J. Li, and T. F. Krauss, “High performance metalenses: numerical aperture, aberrations, chromaticity, and trade-offs,” Optica 6, 1461–1470 (2019).
[Crossref]

W. T. Chen, A. Y. Zhu, J. Sisler, Z. Bharwani, and F. Capasso, “A broadband achromatic polarization-insensitive metalens consisting of anisotropic nanostructures,” Nat. Commun. 10, 1–7 (2019).
[Crossref]

R. J. Lin, V.-C. Su, S. Wang, M. K. Chen, T. L. Chung, Y. H. Chen, H. Y. Kuo, J.-W. Chen, J. Chen, Y.-T. Huang, J.-H. Wang, C. H. Chu, P. Chieh Wu, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “Achromatic metalens array for full-colour light-field imaging,” Nat. Nanotechnol. 14, 227–231 (2019).
[Crossref]

H. Chung and O. D. Miller, “High-NA, achromatic metalenses by inverse design,” Opt. Express 28, 6945–6965 (2019).
[Crossref]

S. Banerji, M. Meem, A. Majumder, F. G. Vasquez, B. Sensale-Rodriguez, and R. Menon, “Imaging with flat optics: metalenses or diffractive lenses?” Optica 6, 805–810 (2019).
[Crossref]

B. Yu, J. Wen, X. Chen, and D. Zhang, “An achromatic metalens in the near-infrared region with an array based on a single nano-rod unit,” Appl. Phys. Express 12, 092003 (2019).
[Crossref]

Q. Cheng, M. Ma, D. Yu, Z. Shen, J. Xie, J. Wang, N. Xu, H. Guo, W. Hu, S. Wang, T. Li, and S. Zhuang, “Broadband achromatic metalens in terahertz regime,” Sci. Bull. 64, 1525–1531 (2019).
[Crossref]

Z. Lin and S. G. Johnson, “Overlapping domains for topology optimization of large-area metasurfaces,” Opt. Express 27, 32445–32453 (2019).
[Crossref]

2018 (10)

W. T. Chen, A. Y. Zhu, V. Sanjeev, M. Khorasaninejad, Z. Shi, E. Lee, and F. Capasso, “A broadband achromatic metalens for focusing and imaging in the visible,” Nat. Nanotechnol. 13, 220–226 (2018).
[Crossref]

S. Zhang, A. Soibel, S. Keo, D. Wilson, S. Rafol, D. Z. Ting, A. She, S. D. Gunapala, and F. Capasso, “Solid-immersion metalenses for infrared focal plane arrays,” Appl. Phys. Lett. 113, 111104 (2018).
[Crossref]

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, M.-K. Chen, H. Y. Kuo, B. H. Chen, Y. H. Chen, T.-T. Huang, J.-H. Wang, R.-M. Lin, C.-H. Kuan, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13, 227–232 (2018).
[Crossref]

N. Mohammad, M. Meem, P. Wang, and R. Menon, “Broadband imaging with one planar diffractive lens,” Sci. Rep. 8, 2799 (2018).
[Crossref]

S. Shrestha, A. C. Overvig, M. Lu, A. Stein, and N. Yu, “Broadband achromatic dielectric metalenses,” Light: Sci. Appl. 7, 85 (2018).
[Crossref]

M. Ye, V. Ray, and Y. S. Yi, “Achromatic flat subwavelength grating lens over whole visible bandwidths,” IEEE Photon. Technol. Lett. 30, 955–958 (2018).
[Crossref]

M. L. Tseng, H.-H. Hsiao, C. H. Chu, M. K. Chen, G. Sun, A.-Q. Liu, and D. P. Tsai, “Metalenses: Advances and applications,” Adv. Opt. Mater. 6, 1800554 (2018).
[Crossref]

A. Ozer, N. Yilmaz, H. Kocer, and H. Kurt, “Polarization-insensitive beam splitters using all-dielectric phase gradient metasurfaces at visible wavelengths,” Opt. Lett. 43, 4350–4353 (2018).
[Crossref]

A. A. Fathnan and D. A. Powell, “Bandwidth and size limits of achromatic printed-circuit metasurfaces,” Opt. Express 26, 29440–29450 (2018).
[Crossref]

S. Colburn, A. Zhan, and A. Majumdar, “Metasurface optics for full-color computational imaging,” Sci. Adv. 4, eaar2114 (2018).
[Crossref]

2017 (5)

E. Arbabi, A. Arbabi, S. M. Kamali, Y. Horie, and A. Faraon, “Controlling the sign of chromatic dispersion in diffractive optics with dielectric metasurfaces,” Optica 4, 625–632 (2017).
[Crossref]

P. Lalanne and P. Chavel, “Metalenses at visible wavelengths: past, present, perspectives,” Laser Photon. Rev. 11, 1600295 (2017).
[Crossref]

M. Khorasaninejad and F. Capasso, “Metalenses: versatile multifunctional photonic components,” Science 358, eaam8100 (2017).
[Crossref]

M. Khorasaninejad, Z. Shi, A. Y. Zhu, W. T. Chen, V. Sanjeev, A. Zaidi, and F. Capasso, “Achromatic metalens over 60  nm bandwidth in the visible and metalens with reverse chromatic dispersion,” Nano Lett. 17, 1819–1824 (2017).
[Crossref]

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. Hung Chu, J.-W. Chen, S.-H. Lu, J. Chen, B. Xu, C.-H. Kuan, T. Li, S. Zhu, and D. P. Tsai, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8, 187 (2017).
[Crossref]

2016 (4)

F. Monticone and A. Alù, “Invisibility exposed: physical bounds on passive cloaking,” Optica 3, 718–724 (2016).
[Crossref]

A. Epstein and G. V. Eleftheriades, “Huygens’ metasurfaces via the equivalence principle: design and applications,” J. Opt. Soc. Am. B 33, A31–A50 (2016).
[Crossref]

T. Siefke, S. Kroker, K. Pfeiffer, O. Puffky, K. Dietrich, D. Franta, I. Ohlídal, A. Szeghalmi, E.-B. Kley, and A. Tünnermann, “Materials pushing the application limits of wire grid polarizers further into the deep ultraviolet spectral range,” Adv. Opt. Mater. 4, 1780–1786 (2016).
[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. USA 113, 10473–10478 (2016).
[Crossref]

2015 (1)

A. Pors, M. G. Nielsen, and S. I. Bozhevolnyi, “Analog computing using reflective plasmonic metasurfaces,” Nano Lett. 15, 791–797 (2015).
[Crossref]

2014 (1)

A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, “Performing mathematical operations with metamaterials,” Science 343, 160–163 (2014).
[Crossref]

2013 (3)

F. Aieta, P. Genevet, M. Kats, and F. Capasso, “Aberrations of flat lenses and aplanatic metasurfaces,” Opt. Express 21, 31530–31539 (2013).
[Crossref]

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

F. Monticone, N. M. Estakhri, and A. Alù, “Full control of nanoscale optical transmission with a composite metascreen,” Phys. Rev. Lett. 110, 203903 (2013).
[Crossref]

2007 (1)

D. A. B. Miller, “Fundamental limit to linear one-dimensional slow light structures,” Phys. Rev. Lett. 99, 203903 (2007).
[Crossref]

2005 (1)

1998 (1)

R. Ferrini, M. Patrini, and S. Franchi, “Optical functions from 0.02 to 6  eV of AlxGa1-xSb/GaSb epitaxial layers,” J. Appl. Phys. 84, 4517–4524 (1998).
[Crossref]

1996 (1)

D. M. Pozar, “Flat lens antenna concept using aperture coupled microstrip patches,” Electron. Lett. 32, 2109–2111 (1996).
[Crossref]

1950 (1)

R. Fano, “Theoretical limitations on the broadband matching of arbitrary impedances,” J. Franklin Inst. 249, 57–83 (1950).
[Crossref]

Abdollahramezani, S.

S. Abdollahramezani, O. Hemmatyar, H. Taghinejad, A. Krasnok, Y. Kiarashinejad, M. Zandehshahvar, A. Alu, and A. Adibi, “Tunable nanophotonics enabled by chalcogenide phase-change materials,” arXiv:2001.06335 (2020).

Adibi, A.

S. Abdollahramezani, O. Hemmatyar, H. Taghinejad, A. Krasnok, Y. Kiarashinejad, M. Zandehshahvar, A. Alu, and A. Adibi, “Tunable nanophotonics enabled by chalcogenide phase-change materials,” arXiv:2001.06335 (2020).

Aieta, F.

Alu, A.

S. Abdollahramezani, O. Hemmatyar, H. Taghinejad, A. Krasnok, Y. Kiarashinejad, M. Zandehshahvar, A. Alu, and A. Adibi, “Tunable nanophotonics enabled by chalcogenide phase-change materials,” arXiv:2001.06335 (2020).

Alù, A.

S. A. Mann, D. L. Sounas, and A. Alù, “Nonreciprocal cavities and the time-bandwidth limit,” Optica 6, 104–110 (2019).
[Crossref]

F. Monticone and A. Alù, “Invisibility exposed: physical bounds on passive cloaking,” Optica 3, 718–724 (2016).
[Crossref]

A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, “Performing mathematical operations with metamaterials,” Science 343, 160–163 (2014).
[Crossref]

F. Monticone, N. M. Estakhri, and A. Alù, “Full control of nanoscale optical transmission with a composite metascreen,” Phys. Rev. Lett. 110, 203903 (2013).
[Crossref]

Arbabi, A.

Arbabi, E.

Balli, F.

F. Balli, M. A. Sultan, S. K. Lami, and J. T. Hastings, “A hybrid achromatic metalens,” arXiv:1909.07941 (2019).

Banerji, S.

S. Banerji, M. Meem, A. Majumder, F. G. Vasquez, B. Sensale-Rodriguez, and R. Menon, “Imaging with flat optics: metalenses or diffractive lenses?” Optica 6, 805–810 (2019).
[Crossref]

J. M. Meem, S. Banerji, A. Majumder, J. C. Garcia, P. W. C. Hon, B. Sensale-Rodriquez, and R. Menon, “Imaging from the visible to the longwave infrared wavelengths via an inverse-designed flat lens,” https://arxiv.org/abs/2001.03684 (2020).

Bharwani, Z.

W. T. Chen, A. Y. Zhu, J. Sisler, Z. Bharwani, and F. Capasso, “A broadband achromatic polarization-insensitive metalens consisting of anisotropic nanostructures,” Nat. Commun. 10, 1–7 (2019).
[Crossref]

Borges, B.-H. V.

Born, M.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1980).

Bozhevolnyi, S. I.

A. Pors, M. G. Nielsen, and S. I. Bozhevolnyi, “Analog computing using reflective plasmonic metasurfaces,” Nano Lett. 15, 791–797 (2015).
[Crossref]

Burger, S.

Capasso, F.

W. T. Chen, A. Y. Zhu, J. Sisler, Z. Bharwani, and F. Capasso, “A broadband achromatic polarization-insensitive metalens consisting of anisotropic nanostructures,” Nat. Commun. 10, 1–7 (2019).
[Crossref]

W. T. Chen, A. Y. Zhu, V. Sanjeev, M. Khorasaninejad, Z. Shi, E. Lee, and F. Capasso, “A broadband achromatic metalens for focusing and imaging in the visible,” Nat. Nanotechnol. 13, 220–226 (2018).
[Crossref]

S. Zhang, A. Soibel, S. Keo, D. Wilson, S. Rafol, D. Z. Ting, A. She, S. D. Gunapala, and F. Capasso, “Solid-immersion metalenses for infrared focal plane arrays,” Appl. Phys. Lett. 113, 111104 (2018).
[Crossref]

M. Khorasaninejad and F. Capasso, “Metalenses: versatile multifunctional photonic components,” Science 358, eaam8100 (2017).
[Crossref]

M. Khorasaninejad, Z. Shi, A. Y. Zhu, W. T. Chen, V. Sanjeev, A. Zaidi, and F. Capasso, “Achromatic metalens over 60  nm bandwidth in the visible and metalens with reverse chromatic dispersion,” Nano Lett. 17, 1819–1824 (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. USA 113, 10473–10478 (2016).
[Crossref]

F. Aieta, P. Genevet, M. Kats, and F. Capasso, “Aberrations of flat lenses and aplanatic metasurfaces,” Opt. Express 21, 31530–31539 (2013).
[Crossref]

Castaldi, G.

A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, “Performing mathematical operations with metamaterials,” Science 343, 160–163 (2014).
[Crossref]

Chang-Hasnain, C. J.

Chavel, P.

P. Lalanne and P. Chavel, “Metalenses at visible wavelengths: past, present, perspectives,” Laser Photon. Rev. 11, 1600295 (2017).
[Crossref]

Chen, B. H.

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, M.-K. Chen, H. Y. Kuo, B. H. Chen, Y. H. Chen, T.-T. Huang, J.-H. Wang, R.-M. Lin, C.-H. Kuan, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13, 227–232 (2018).
[Crossref]

Chen, J.

R. J. Lin, V.-C. Su, S. Wang, M. K. Chen, T. L. Chung, Y. H. Chen, H. Y. Kuo, J.-W. Chen, J. Chen, Y.-T. Huang, J.-H. Wang, C. H. Chu, P. Chieh Wu, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “Achromatic metalens array for full-colour light-field imaging,” Nat. Nanotechnol. 14, 227–231 (2019).
[Crossref]

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. Hung Chu, J.-W. Chen, S.-H. Lu, J. Chen, B. Xu, C.-H. Kuan, T. Li, S. Zhu, and D. P. Tsai, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8, 187 (2017).
[Crossref]

Chen, J.-W.

R. J. Lin, V.-C. Su, S. Wang, M. K. Chen, T. L. Chung, Y. H. Chen, H. Y. Kuo, J.-W. Chen, J. Chen, Y.-T. Huang, J.-H. Wang, C. H. Chu, P. Chieh Wu, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “Achromatic metalens array for full-colour light-field imaging,” Nat. Nanotechnol. 14, 227–231 (2019).
[Crossref]

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. Hung Chu, J.-W. Chen, S.-H. Lu, J. Chen, B. Xu, C.-H. Kuan, T. Li, S. Zhu, and D. P. Tsai, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8, 187 (2017).
[Crossref]

Chen, M. K.

R. J. Lin, V.-C. Su, S. Wang, M. K. Chen, T. L. Chung, Y. H. Chen, H. Y. Kuo, J.-W. Chen, J. Chen, Y.-T. Huang, J.-H. Wang, C. H. Chu, P. Chieh Wu, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “Achromatic metalens array for full-colour light-field imaging,” Nat. Nanotechnol. 14, 227–231 (2019).
[Crossref]

M. L. Tseng, H.-H. Hsiao, C. H. Chu, M. K. Chen, G. Sun, A.-Q. Liu, and D. P. Tsai, “Metalenses: Advances and applications,” Adv. Opt. Mater. 6, 1800554 (2018).
[Crossref]

Chen, M.-K.

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, M.-K. Chen, H. Y. Kuo, B. H. Chen, Y. H. Chen, T.-T. Huang, J.-H. Wang, R.-M. Lin, C.-H. Kuan, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13, 227–232 (2018).
[Crossref]

Chen, W. T.

W. T. Chen, A. Y. Zhu, J. Sisler, Z. Bharwani, and F. Capasso, “A broadband achromatic polarization-insensitive metalens consisting of anisotropic nanostructures,” Nat. Commun. 10, 1–7 (2019).
[Crossref]

W. T. Chen, A. Y. Zhu, V. Sanjeev, M. Khorasaninejad, Z. Shi, E. Lee, and F. Capasso, “A broadband achromatic metalens for focusing and imaging in the visible,” Nat. Nanotechnol. 13, 220–226 (2018).
[Crossref]

M. Khorasaninejad, Z. Shi, A. Y. Zhu, W. T. Chen, V. Sanjeev, A. Zaidi, and F. Capasso, “Achromatic metalens over 60  nm bandwidth in the visible and metalens with reverse chromatic dispersion,” Nano Lett. 17, 1819–1824 (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. USA 113, 10473–10478 (2016).
[Crossref]

Chen, X.

B. Yu, J. Wen, X. Chen, and D. Zhang, “An achromatic metalens in the near-infrared region with an array based on a single nano-rod unit,” Appl. Phys. Express 12, 092003 (2019).
[Crossref]

Chen, Y. H.

R. J. Lin, V.-C. Su, S. Wang, M. K. Chen, T. L. Chung, Y. H. Chen, H. Y. Kuo, J.-W. Chen, J. Chen, Y.-T. Huang, J.-H. Wang, C. H. Chu, P. Chieh Wu, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “Achromatic metalens array for full-colour light-field imaging,” Nat. Nanotechnol. 14, 227–231 (2019).
[Crossref]

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, M.-K. Chen, H. Y. Kuo, B. H. Chen, Y. H. Chen, T.-T. Huang, J.-H. Wang, R.-M. Lin, C.-H. Kuan, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13, 227–232 (2018).
[Crossref]

Cheng, Q.

Q. Cheng, M. Ma, D. Yu, Z. Shen, J. Xie, J. Wang, N. Xu, H. Guo, W. Hu, S. Wang, T. Li, and S. Zhuang, “Broadband achromatic metalens in terahertz regime,” Sci. Bull. 64, 1525–1531 (2019).
[Crossref]

Chieh Wu, P.

R. J. Lin, V.-C. Su, S. Wang, M. K. Chen, T. L. Chung, Y. H. Chen, H. Y. Kuo, J.-W. Chen, J. Chen, Y.-T. Huang, J.-H. Wang, C. H. Chu, P. Chieh Wu, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “Achromatic metalens array for full-colour light-field imaging,” Nat. Nanotechnol. 14, 227–231 (2019).
[Crossref]

Chu, C. H.

R. J. Lin, V.-C. Su, S. Wang, M. K. Chen, T. L. Chung, Y. H. Chen, H. Y. Kuo, J.-W. Chen, J. Chen, Y.-T. Huang, J.-H. Wang, C. H. Chu, P. Chieh Wu, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “Achromatic metalens array for full-colour light-field imaging,” Nat. Nanotechnol. 14, 227–231 (2019).
[Crossref]

M. L. Tseng, H.-H. Hsiao, C. H. Chu, M. K. Chen, G. Sun, A.-Q. Liu, and D. P. Tsai, “Metalenses: Advances and applications,” Adv. Opt. Mater. 6, 1800554 (2018).
[Crossref]

Chung, H.

Chung, T. L.

R. J. Lin, V.-C. Su, S. Wang, M. K. Chen, T. L. Chung, Y. H. Chen, H. Y. Kuo, J.-W. Chen, J. Chen, Y.-T. Huang, J.-H. Wang, C. H. Chu, P. Chieh Wu, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “Achromatic metalens array for full-colour light-field imaging,” Nat. Nanotechnol. 14, 227–231 (2019).
[Crossref]

Colburn, S.

S. Colburn, A. Zhan, and A. Majumdar, “Metasurface optics for full-color computational imaging,” Sci. Adv. 4, eaar2114 (2018).
[Crossref]

L. Huang, J. Whitehead, S. Colburn, and A. Majumdar, “Design and analysis of extended depth of focus metalenses for achromatic computational imaging,” arXiv:2003.09599 (2020).

Creath, K.

J. C. Wyant and K. Creath, “Basic wavefront aberration theory for optical metrology,” in Applied Optics and Optical Engineering, Volume XI, R. R. Shannon and J. C. Wyant, eds. (Academic, 1992), Vol. 11.

Decker, M.

Devlin, R. C.

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. USA 113, 10473–10478 (2016).
[Crossref]

Dietrich, K.

T. Siefke, S. Kroker, K. Pfeiffer, O. Puffky, K. Dietrich, D. Franta, I. Ohlídal, A. Szeghalmi, E.-B. Kley, and A. Tünnermann, “Materials pushing the application limits of wire grid polarizers further into the deep ultraviolet spectral range,” Adv. Opt. Mater. 4, 1780–1786 (2016).
[Crossref]

Eleftheriades, G. V.

Engheta, N.

A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, “Performing mathematical operations with metamaterials,” Science 343, 160–163 (2014).
[Crossref]

Epstein, A.

Estakhri, N. M.

F. Monticone, N. M. Estakhri, and A. Alù, “Full control of nanoscale optical transmission with a composite metascreen,” Phys. Rev. Lett. 110, 203903 (2013).
[Crossref]

Fano, R.

R. Fano, “Theoretical limitations on the broadband matching of arbitrary impedances,” J. Franklin Inst. 249, 57–83 (1950).
[Crossref]

Faraon, A.

Fathnan, A. A.

A. A. Fathnan and D. A. Powell, “Bandwidth and size limits of achromatic printed-circuit metasurfaces,” Opt. Express 26, 29440–29450 (2018).
[Crossref]

A. A. Fathnan, A. E. Olk, and D. A. Powell, “Broadband anomalous reflection with dispersion controlled metasurfaces,” arXiv:1912.03936 (2019).

Ferrini, R.

R. Ferrini, M. Patrini, and S. Franchi, “Optical functions from 0.02 to 6  eV of AlxGa1-xSb/GaSb epitaxial layers,” J. Appl. Phys. 84, 4517–4524 (1998).
[Crossref]

Franchi, S.

R. Ferrini, M. Patrini, and S. Franchi, “Optical functions from 0.02 to 6  eV of AlxGa1-xSb/GaSb epitaxial layers,” J. Appl. Phys. 84, 4517–4524 (1998).
[Crossref]

Franta, D.

T. Siefke, S. Kroker, K. Pfeiffer, O. Puffky, K. Dietrich, D. Franta, I. Ohlídal, A. Szeghalmi, E.-B. Kley, and A. Tünnermann, “Materials pushing the application limits of wire grid polarizers further into the deep ultraviolet spectral range,” Adv. Opt. Mater. 4, 1780–1786 (2016).
[Crossref]

Galdi, V.

A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, “Performing mathematical operations with metamaterials,” Science 343, 160–163 (2014).
[Crossref]

Garcia, J. C.

J. M. Meem, S. Banerji, A. Majumder, J. C. Garcia, P. W. C. Hon, B. Sensale-Rodriquez, and R. Menon, “Imaging from the visible to the longwave infrared wavelengths via an inverse-designed flat lens,” https://arxiv.org/abs/2001.03684 (2020).

Genevet, P.

Grbic, A.

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

Gunapala, S. D.

S. Zhang, A. Soibel, S. Keo, D. Wilson, S. Rafol, D. Z. Ting, A. She, S. D. Gunapala, and F. Capasso, “Solid-immersion metalenses for infrared focal plane arrays,” Appl. Phys. Lett. 113, 111104 (2018).
[Crossref]

Guo, H.

Q. Cheng, M. Ma, D. Yu, Z. Shen, J. Xie, J. Wang, N. Xu, H. Guo, W. Hu, S. Wang, T. Li, and S. Zhuang, “Broadband achromatic metalens in terahertz regime,” Sci. Bull. 64, 1525–1531 (2019).
[Crossref]

Hardy, J. W.

J. W. Hardy, “Adaptive optics for astronomical telescopes,” in Adaptive Optics for Astronomical Telescopes (Oxford University, 1998), chap. 4, p. 104–134.

Hastings, J. T.

F. Balli, M. A. Sultan, S. K. Lami, and J. T. Hastings, “A hybrid achromatic metalens,” arXiv:1909.07941 (2019).

Hemmatyar, O.

S. Abdollahramezani, O. Hemmatyar, H. Taghinejad, A. Krasnok, Y. Kiarashinejad, M. Zandehshahvar, A. Alu, and A. Adibi, “Tunable nanophotonics enabled by chalcogenide phase-change materials,” arXiv:2001.06335 (2020).

Hon, P. W. C.

J. M. Meem, S. Banerji, A. Majumder, J. C. Garcia, P. W. C. Hon, B. Sensale-Rodriquez, and R. Menon, “Imaging from the visible to the longwave infrared wavelengths via an inverse-designed flat lens,” https://arxiv.org/abs/2001.03684 (2020).

Horie, Y.

Hsiao, H.-H.

M. L. Tseng, H.-H. Hsiao, C. H. Chu, M. K. Chen, G. Sun, A.-Q. Liu, and D. P. Tsai, “Metalenses: Advances and applications,” Adv. Opt. Mater. 6, 1800554 (2018).
[Crossref]

Hu, W.

Q. Cheng, M. Ma, D. Yu, Z. Shen, J. Xie, J. Wang, N. Xu, H. Guo, W. Hu, S. Wang, T. Li, and S. Zhuang, “Broadband achromatic metalens in terahertz regime,” Sci. Bull. 64, 1525–1531 (2019).
[Crossref]

Huang, L.

L. Huang, J. Whitehead, S. Colburn, and A. Majumdar, “Design and analysis of extended depth of focus metalenses for achromatic computational imaging,” arXiv:2003.09599 (2020).

Huang, T.-T.

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, M.-K. Chen, H. Y. Kuo, B. H. Chen, Y. H. Chen, T.-T. Huang, J.-H. Wang, R.-M. Lin, C.-H. Kuan, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13, 227–232 (2018).
[Crossref]

Huang, Y.-T.

R. J. Lin, V.-C. Su, S. Wang, M. K. Chen, T. L. Chung, Y. H. Chen, H. Y. Kuo, J.-W. Chen, J. Chen, Y.-T. Huang, J.-H. Wang, C. H. Chu, P. Chieh Wu, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “Achromatic metalens array for full-colour light-field imaging,” Nat. Nanotechnol. 14, 227–231 (2019).
[Crossref]

Hung Chu, C.

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. Hung Chu, J.-W. Chen, S.-H. Lu, J. Chen, B. Xu, C.-H. Kuan, T. Li, S. Zhu, and D. P. Tsai, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8, 187 (2017).
[Crossref]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999).

Johnson, S. G.

Kamali, S. M.

Kats, M.

Keo, S.

S. Zhang, A. Soibel, S. Keo, D. Wilson, S. Rafol, D. Z. Ting, A. She, S. D. Gunapala, and F. Capasso, “Solid-immersion metalenses for infrared focal plane arrays,” Appl. Phys. Lett. 113, 111104 (2018).
[Crossref]

Khorasaninejad, M.

W. T. Chen, A. Y. Zhu, V. Sanjeev, M. Khorasaninejad, Z. Shi, E. Lee, and F. Capasso, “A broadband achromatic metalens for focusing and imaging in the visible,” Nat. Nanotechnol. 13, 220–226 (2018).
[Crossref]

M. Khorasaninejad, Z. Shi, A. Y. Zhu, W. T. Chen, V. Sanjeev, A. Zaidi, and F. Capasso, “Achromatic metalens over 60  nm bandwidth in the visible and metalens with reverse chromatic dispersion,” Nano Lett. 17, 1819–1824 (2017).
[Crossref]

M. Khorasaninejad and F. Capasso, “Metalenses: versatile multifunctional photonic components,” Science 358, eaam8100 (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. USA 113, 10473–10478 (2016).
[Crossref]

Khurgin, J.

J. Khurgin, “Bandwidth limitation in slow light schemes,” in Slow Light: Science and Applications, J. Khurgin and R. S. Tucker, eds. (Taylor & Francis Group, 2008), chap. 15, pp. 293–320.

Kiarashinejad, Y.

S. Abdollahramezani, O. Hemmatyar, H. Taghinejad, A. Krasnok, Y. Kiarashinejad, M. Zandehshahvar, A. Alu, and A. Adibi, “Tunable nanophotonics enabled by chalcogenide phase-change materials,” arXiv:2001.06335 (2020).

Kley, E.-B.

T. Siefke, S. Kroker, K. Pfeiffer, O. Puffky, K. Dietrich, D. Franta, I. Ohlídal, A. Szeghalmi, E.-B. Kley, and A. Tünnermann, “Materials pushing the application limits of wire grid polarizers further into the deep ultraviolet spectral range,” Adv. Opt. Mater. 4, 1780–1786 (2016).
[Crossref]

Kocer, H.

Krasnok, A.

S. Abdollahramezani, O. Hemmatyar, H. Taghinejad, A. Krasnok, Y. Kiarashinejad, M. Zandehshahvar, A. Alu, and A. Adibi, “Tunable nanophotonics enabled by chalcogenide phase-change materials,” arXiv:2001.06335 (2020).

Krauss, T. F.

Kroker, S.

T. Siefke, S. Kroker, K. Pfeiffer, O. Puffky, K. Dietrich, D. Franta, I. Ohlídal, A. Szeghalmi, E.-B. Kley, and A. Tünnermann, “Materials pushing the application limits of wire grid polarizers further into the deep ultraviolet spectral range,” Adv. Opt. Mater. 4, 1780–1786 (2016).
[Crossref]

Ku, P.-C.

Kuan, C.-H.

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, M.-K. Chen, H. Y. Kuo, B. H. Chen, Y. H. Chen, T.-T. Huang, J.-H. Wang, R.-M. Lin, C.-H. Kuan, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13, 227–232 (2018).
[Crossref]

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. Hung Chu, J.-W. Chen, S.-H. Lu, J. Chen, B. Xu, C.-H. Kuan, T. Li, S. Zhu, and D. P. Tsai, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8, 187 (2017).
[Crossref]

Kuo, H. Y.

R. J. Lin, V.-C. Su, S. Wang, M. K. Chen, T. L. Chung, Y. H. Chen, H. Y. Kuo, J.-W. Chen, J. Chen, Y.-T. Huang, J.-H. Wang, C. H. Chu, P. Chieh Wu, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “Achromatic metalens array for full-colour light-field imaging,” Nat. Nanotechnol. 14, 227–231 (2019).
[Crossref]

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, M.-K. Chen, H. Y. Kuo, B. H. Chen, Y. H. Chen, T.-T. Huang, J.-H. Wang, R.-M. Lin, C.-H. Kuan, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13, 227–232 (2018).
[Crossref]

Kurt, H.

Lai, Y.-C.

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, M.-K. Chen, H. Y. Kuo, B. H. Chen, Y. H. Chen, T.-T. Huang, J.-H. Wang, R.-M. Lin, C.-H. Kuan, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13, 227–232 (2018).
[Crossref]

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. Hung Chu, J.-W. Chen, S.-H. Lu, J. Chen, B. Xu, C.-H. Kuan, T. Li, S. Zhu, and D. P. Tsai, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8, 187 (2017).
[Crossref]

Lalanne, P.

P. Lalanne and P. Chavel, “Metalenses at visible wavelengths: past, present, perspectives,” Laser Photon. Rev. 11, 1600295 (2017).
[Crossref]

Lami, S. K.

F. Balli, M. A. Sultan, S. K. Lami, and J. T. Hastings, “A hybrid achromatic metalens,” arXiv:1909.07941 (2019).

Lee, E.

W. T. Chen, A. Y. Zhu, V. Sanjeev, M. Khorasaninejad, Z. Shi, E. Lee, and F. Capasso, “A broadband achromatic metalens for focusing and imaging in the visible,” Nat. Nanotechnol. 13, 220–226 (2018).
[Crossref]

Li, J.

Li, T.

R. J. Lin, V.-C. Su, S. Wang, M. K. Chen, T. L. Chung, Y. H. Chen, H. Y. Kuo, J.-W. Chen, J. Chen, Y.-T. Huang, J.-H. Wang, C. H. Chu, P. Chieh Wu, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “Achromatic metalens array for full-colour light-field imaging,” Nat. Nanotechnol. 14, 227–231 (2019).
[Crossref]

Q. Cheng, M. Ma, D. Yu, Z. Shen, J. Xie, J. Wang, N. Xu, H. Guo, W. Hu, S. Wang, T. Li, and S. Zhuang, “Broadband achromatic metalens in terahertz regime,” Sci. Bull. 64, 1525–1531 (2019).
[Crossref]

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, M.-K. Chen, H. Y. Kuo, B. H. Chen, Y. H. Chen, T.-T. Huang, J.-H. Wang, R.-M. Lin, C.-H. Kuan, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13, 227–232 (2018).
[Crossref]

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. Hung Chu, J.-W. Chen, S.-H. Lu, J. Chen, B. Xu, C.-H. Kuan, T. Li, S. Zhu, and D. P. Tsai, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8, 187 (2017).
[Crossref]

Liang, H.

Lin, R. J.

R. J. Lin, V.-C. Su, S. Wang, M. K. Chen, T. L. Chung, Y. H. Chen, H. Y. Kuo, J.-W. Chen, J. Chen, Y.-T. Huang, J.-H. Wang, C. H. Chu, P. Chieh Wu, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “Achromatic metalens array for full-colour light-field imaging,” Nat. Nanotechnol. 14, 227–231 (2019).
[Crossref]

Lin, R.-M.

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, M.-K. Chen, H. Y. Kuo, B. H. Chen, Y. H. Chen, T.-T. Huang, J.-H. Wang, R.-M. Lin, C.-H. Kuan, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13, 227–232 (2018).
[Crossref]

Lin, Z.

Liu, A.-Q.

M. L. Tseng, H.-H. Hsiao, C. H. Chu, M. K. Chen, G. Sun, A.-Q. Liu, and D. P. Tsai, “Metalenses: Advances and applications,” Adv. Opt. Mater. 6, 1800554 (2018).
[Crossref]

Lu, M.

S. Shrestha, A. C. Overvig, M. Lu, A. Stein, and N. Yu, “Broadband achromatic dielectric metalenses,” Light: Sci. Appl. 7, 85 (2018).
[Crossref]

Lu, S.-H.

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. Hung Chu, J.-W. Chen, S.-H. Lu, J. Chen, B. Xu, C.-H. Kuan, T. Li, S. Zhu, and D. P. Tsai, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8, 187 (2017).
[Crossref]

Ma, M.

Q. Cheng, M. Ma, D. Yu, Z. Shen, J. Xie, J. Wang, N. Xu, H. Guo, W. Hu, S. Wang, T. Li, and S. Zhuang, “Broadband achromatic metalens in terahertz regime,” Sci. Bull. 64, 1525–1531 (2019).
[Crossref]

Majumdar, A.

S. Colburn, A. Zhan, and A. Majumdar, “Metasurface optics for full-color computational imaging,” Sci. Adv. 4, eaar2114 (2018).
[Crossref]

L. Huang, J. Whitehead, S. Colburn, and A. Majumdar, “Design and analysis of extended depth of focus metalenses for achromatic computational imaging,” arXiv:2003.09599 (2020).

Majumder, A.

S. Banerji, M. Meem, A. Majumder, F. G. Vasquez, B. Sensale-Rodriguez, and R. Menon, “Imaging with flat optics: metalenses or diffractive lenses?” Optica 6, 805–810 (2019).
[Crossref]

J. M. Meem, S. Banerji, A. Majumder, J. C. Garcia, P. W. C. Hon, B. Sensale-Rodriquez, and R. Menon, “Imaging from the visible to the longwave infrared wavelengths via an inverse-designed flat lens,” https://arxiv.org/abs/2001.03684 (2020).

Mann, S. A.

Martins, A.

Martins, E. R.

Meem, J. M.

J. M. Meem, S. Banerji, A. Majumder, J. C. Garcia, P. W. C. Hon, B. Sensale-Rodriquez, and R. Menon, “Imaging from the visible to the longwave infrared wavelengths via an inverse-designed flat lens,” https://arxiv.org/abs/2001.03684 (2020).

Meem, M.

Menon, R.

S. Banerji, M. Meem, A. Majumder, F. G. Vasquez, B. Sensale-Rodriguez, and R. Menon, “Imaging with flat optics: metalenses or diffractive lenses?” Optica 6, 805–810 (2019).
[Crossref]

N. Mohammad, M. Meem, P. Wang, and R. Menon, “Broadband imaging with one planar diffractive lens,” Sci. Rep. 8, 2799 (2018).
[Crossref]

J. M. Meem, S. Banerji, A. Majumder, J. C. Garcia, P. W. C. Hon, B. Sensale-Rodriquez, and R. Menon, “Imaging from the visible to the longwave infrared wavelengths via an inverse-designed flat lens,” https://arxiv.org/abs/2001.03684 (2020).

Miller, D. A. B.

D. A. B. Miller, “Fundamental limit to linear one-dimensional slow light structures,” Phys. Rev. Lett. 99, 203903 (2007).
[Crossref]

Miller, O. D.

Mohammad, N.

N. Mohammad, M. Meem, P. Wang, and R. Menon, “Broadband imaging with one planar diffractive lens,” Sci. Rep. 8, 2799 (2018).
[Crossref]

Monticone, F.

F. Monticone and A. Alù, “Invisibility exposed: physical bounds on passive cloaking,” Optica 3, 718–724 (2016).
[Crossref]

A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, “Performing mathematical operations with metamaterials,” Science 343, 160–163 (2014).
[Crossref]

F. Monticone, N. M. Estakhri, and A. Alù, “Full control of nanoscale optical transmission with a composite metascreen,” Phys. Rev. Lett. 110, 203903 (2013).
[Crossref]

Nielsen, M. G.

A. Pors, M. G. Nielsen, and S. I. Bozhevolnyi, “Analog computing using reflective plasmonic metasurfaces,” Nano Lett. 15, 791–797 (2015).
[Crossref]

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. USA 113, 10473–10478 (2016).
[Crossref]

Ohlídal, I.

T. Siefke, S. Kroker, K. Pfeiffer, O. Puffky, K. Dietrich, D. Franta, I. Ohlídal, A. Szeghalmi, E.-B. Kley, and A. Tünnermann, “Materials pushing the application limits of wire grid polarizers further into the deep ultraviolet spectral range,” Adv. Opt. Mater. 4, 1780–1786 (2016).
[Crossref]

Olk, A. E.

A. A. Fathnan, A. E. Olk, and D. A. Powell, “Broadband anomalous reflection with dispersion controlled metasurfaces,” arXiv:1912.03936 (2019).

Overvig, A. C.

S. Shrestha, A. C. Overvig, M. Lu, A. Stein, and N. Yu, “Broadband achromatic dielectric metalenses,” Light: Sci. Appl. 7, 85 (2018).
[Crossref]

Ozer, A.

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1998), Vol. 3.

Patrini, M.

R. Ferrini, M. Patrini, and S. Franchi, “Optical functions from 0.02 to 6  eV of AlxGa1-xSb/GaSb epitaxial layers,” J. Appl. Phys. 84, 4517–4524 (1998).
[Crossref]

Pertsch, T.

Pfeiffer, C.

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

Pfeiffer, K.

T. Siefke, S. Kroker, K. Pfeiffer, O. Puffky, K. Dietrich, D. Franta, I. Ohlídal, A. Szeghalmi, E.-B. Kley, and A. Tünnermann, “Materials pushing the application limits of wire grid polarizers further into the deep ultraviolet spectral range,” Adv. Opt. Mater. 4, 1780–1786 (2016).
[Crossref]

Pors, A.

A. Pors, M. G. Nielsen, and S. I. Bozhevolnyi, “Analog computing using reflective plasmonic metasurfaces,” Nano Lett. 15, 791–797 (2015).
[Crossref]

Powell, D. A.

A. A. Fathnan and D. A. Powell, “Bandwidth and size limits of achromatic printed-circuit metasurfaces,” Opt. Express 26, 29440–29450 (2018).
[Crossref]

A. A. Fathnan, A. E. Olk, and D. A. Powell, “Broadband anomalous reflection with dispersion controlled metasurfaces,” arXiv:1912.03936 (2019).

Pozar, D. M.

D. M. Pozar, “Flat lens antenna concept using aperture coupled microstrip patches,” Electron. Lett. 32, 2109–2111 (1996).
[Crossref]

Puffky, O.

T. Siefke, S. Kroker, K. Pfeiffer, O. Puffky, K. Dietrich, D. Franta, I. Ohlídal, A. Szeghalmi, E.-B. Kley, and A. Tünnermann, “Materials pushing the application limits of wire grid polarizers further into the deep ultraviolet spectral range,” Adv. Opt. Mater. 4, 1780–1786 (2016).
[Crossref]

Rafol, S.

S. Zhang, A. Soibel, S. Keo, D. Wilson, S. Rafol, D. Z. Ting, A. She, S. D. Gunapala, and F. Capasso, “Solid-immersion metalenses for infrared focal plane arrays,” Appl. Phys. Lett. 113, 111104 (2018).
[Crossref]

Ray, V.

M. Ye, V. Ray, and Y. S. Yi, “Achromatic flat subwavelength grating lens over whole visible bandwidths,” IEEE Photon. Technol. Lett. 30, 955–958 (2018).
[Crossref]

Sanjeev, V.

W. T. Chen, A. Y. Zhu, V. Sanjeev, M. Khorasaninejad, Z. Shi, E. Lee, and F. Capasso, “A broadband achromatic metalens for focusing and imaging in the visible,” Nat. Nanotechnol. 13, 220–226 (2018).
[Crossref]

M. Khorasaninejad, Z. Shi, A. Y. Zhu, W. T. Chen, V. Sanjeev, A. Zaidi, and F. Capasso, “Achromatic metalens over 60  nm bandwidth in the visible and metalens with reverse chromatic dispersion,” Nano Lett. 17, 1819–1824 (2017).
[Crossref]

Sensale-Rodriguez, B.

Sensale-Rodriquez, B.

J. M. Meem, S. Banerji, A. Majumder, J. C. Garcia, P. W. C. Hon, B. Sensale-Rodriquez, and R. Menon, “Imaging from the visible to the longwave infrared wavelengths via an inverse-designed flat lens,” https://arxiv.org/abs/2001.03684 (2020).

She, A.

S. Zhang, A. Soibel, S. Keo, D. Wilson, S. Rafol, D. Z. Ting, A. She, S. D. Gunapala, and F. Capasso, “Solid-immersion metalenses for infrared focal plane arrays,” Appl. Phys. Lett. 113, 111104 (2018).
[Crossref]

Shen, Z.

Q. Cheng, M. Ma, D. Yu, Z. Shen, J. Xie, J. Wang, N. Xu, H. Guo, W. Hu, S. Wang, T. Li, and S. Zhuang, “Broadband achromatic metalens in terahertz regime,” Sci. Bull. 64, 1525–1531 (2019).
[Crossref]

Shi, Z.

W. T. Chen, A. Y. Zhu, V. Sanjeev, M. Khorasaninejad, Z. Shi, E. Lee, and F. Capasso, “A broadband achromatic metalens for focusing and imaging in the visible,” Nat. Nanotechnol. 13, 220–226 (2018).
[Crossref]

M. Khorasaninejad, Z. Shi, A. Y. Zhu, W. T. Chen, V. Sanjeev, A. Zaidi, and F. Capasso, “Achromatic metalens over 60  nm bandwidth in the visible and metalens with reverse chromatic dispersion,” Nano Lett. 17, 1819–1824 (2017).
[Crossref]

Shrestha, S.

S. Shrestha, A. C. Overvig, M. Lu, A. Stein, and N. Yu, “Broadband achromatic dielectric metalenses,” Light: Sci. Appl. 7, 85 (2018).
[Crossref]

Siefke, T.

T. Siefke, S. Kroker, K. Pfeiffer, O. Puffky, K. Dietrich, D. Franta, I. Ohlídal, A. Szeghalmi, E.-B. Kley, and A. Tünnermann, “Materials pushing the application limits of wire grid polarizers further into the deep ultraviolet spectral range,” Adv. Opt. Mater. 4, 1780–1786 (2016).
[Crossref]

Silva, A.

A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, “Performing mathematical operations with metamaterials,” Science 343, 160–163 (2014).
[Crossref]

Sisler, J.

W. T. Chen, A. Y. Zhu, J. Sisler, Z. Bharwani, and F. Capasso, “A broadband achromatic polarization-insensitive metalens consisting of anisotropic nanostructures,” Nat. Commun. 10, 1–7 (2019).
[Crossref]

Soibel, A.

S. Zhang, A. Soibel, S. Keo, D. Wilson, S. Rafol, D. Z. Ting, A. She, S. D. Gunapala, and F. Capasso, “Solid-immersion metalenses for infrared focal plane arrays,” Appl. Phys. Lett. 113, 111104 (2018).
[Crossref]

Sounas, D. L.

Staude, I.

Stein, A.

S. Shrestha, A. C. Overvig, M. Lu, A. Stein, and N. Yu, “Broadband achromatic dielectric metalenses,” Light: Sci. Appl. 7, 85 (2018).
[Crossref]

Su, V.-C.

R. J. Lin, V.-C. Su, S. Wang, M. K. Chen, T. L. Chung, Y. H. Chen, H. Y. Kuo, J.-W. Chen, J. Chen, Y.-T. Huang, J.-H. Wang, C. H. Chu, P. Chieh Wu, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “Achromatic metalens array for full-colour light-field imaging,” Nat. Nanotechnol. 14, 227–231 (2019).
[Crossref]

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, M.-K. Chen, H. Y. Kuo, B. H. Chen, Y. H. Chen, T.-T. Huang, J.-H. Wang, R.-M. Lin, C.-H. Kuan, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13, 227–232 (2018).
[Crossref]

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. Hung Chu, J.-W. Chen, S.-H. Lu, J. Chen, B. Xu, C.-H. Kuan, T. Li, S. Zhu, and D. P. Tsai, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8, 187 (2017).
[Crossref]

Sultan, M. A.

F. Balli, M. A. Sultan, S. K. Lami, and J. T. Hastings, “A hybrid achromatic metalens,” arXiv:1909.07941 (2019).

Sun, G.

M. L. Tseng, H.-H. Hsiao, C. H. Chu, M. K. Chen, G. Sun, A.-Q. Liu, and D. P. Tsai, “Metalenses: Advances and applications,” Adv. Opt. Mater. 6, 1800554 (2018).
[Crossref]

Szeghalmi, A.

T. Siefke, S. Kroker, K. Pfeiffer, O. Puffky, K. Dietrich, D. Franta, I. Ohlídal, A. Szeghalmi, E.-B. Kley, and A. Tünnermann, “Materials pushing the application limits of wire grid polarizers further into the deep ultraviolet spectral range,” Adv. Opt. Mater. 4, 1780–1786 (2016).
[Crossref]

Taghinejad, H.

S. Abdollahramezani, O. Hemmatyar, H. Taghinejad, A. Krasnok, Y. Kiarashinejad, M. Zandehshahvar, A. Alu, and A. Adibi, “Tunable nanophotonics enabled by chalcogenide phase-change materials,” arXiv:2001.06335 (2020).

Ting, D. Z.

S. Zhang, A. Soibel, S. Keo, D. Wilson, S. Rafol, D. Z. Ting, A. She, S. D. Gunapala, and F. Capasso, “Solid-immersion metalenses for infrared focal plane arrays,” Appl. Phys. Lett. 113, 111104 (2018).
[Crossref]

Tretyakov, S. A.

S. A. Tretyakov, Analytical Modeling in Applied Electromagnetics (Artech House, 2003).

Tsai, D. P.

R. J. Lin, V.-C. Su, S. Wang, M. K. Chen, T. L. Chung, Y. H. Chen, H. Y. Kuo, J.-W. Chen, J. Chen, Y.-T. Huang, J.-H. Wang, C. H. Chu, P. Chieh Wu, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “Achromatic metalens array for full-colour light-field imaging,” Nat. Nanotechnol. 14, 227–231 (2019).
[Crossref]

M. L. Tseng, H.-H. Hsiao, C. H. Chu, M. K. Chen, G. Sun, A.-Q. Liu, and D. P. Tsai, “Metalenses: Advances and applications,” Adv. Opt. Mater. 6, 1800554 (2018).
[Crossref]

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, M.-K. Chen, H. Y. Kuo, B. H. Chen, Y. H. Chen, T.-T. Huang, J.-H. Wang, R.-M. Lin, C.-H. Kuan, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13, 227–232 (2018).
[Crossref]

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. Hung Chu, J.-W. Chen, S.-H. Lu, J. Chen, B. Xu, C.-H. Kuan, T. Li, S. Zhu, and D. P. Tsai, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8, 187 (2017).
[Crossref]

Tseng, M. L.

M. L. Tseng, H.-H. Hsiao, C. H. Chu, M. K. Chen, G. Sun, A.-Q. Liu, and D. P. Tsai, “Metalenses: Advances and applications,” Adv. Opt. Mater. 6, 1800554 (2018).
[Crossref]

Tucker, R. S.

Tünnermann, A.

T. Siefke, S. Kroker, K. Pfeiffer, O. Puffky, K. Dietrich, D. Franta, I. Ohlídal, A. Szeghalmi, E.-B. Kley, and A. Tünnermann, “Materials pushing the application limits of wire grid polarizers further into the deep ultraviolet spectral range,” Adv. Opt. Mater. 4, 1780–1786 (2016).
[Crossref]

Vasquez, F. G.

Wang, J.

Q. Cheng, M. Ma, D. Yu, Z. Shen, J. Xie, J. Wang, N. Xu, H. Guo, W. Hu, S. Wang, T. Li, and S. Zhuang, “Broadband achromatic metalens in terahertz regime,” Sci. Bull. 64, 1525–1531 (2019).
[Crossref]

Wang, J.-H.

R. J. Lin, V.-C. Su, S. Wang, M. K. Chen, T. L. Chung, Y. H. Chen, H. Y. Kuo, J.-W. Chen, J. Chen, Y.-T. Huang, J.-H. Wang, C. H. Chu, P. Chieh Wu, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “Achromatic metalens array for full-colour light-field imaging,” Nat. Nanotechnol. 14, 227–231 (2019).
[Crossref]

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, M.-K. Chen, H. Y. Kuo, B. H. Chen, Y. H. Chen, T.-T. Huang, J.-H. Wang, R.-M. Lin, C.-H. Kuan, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13, 227–232 (2018).
[Crossref]

Wang, P.

N. Mohammad, M. Meem, P. Wang, and R. Menon, “Broadband imaging with one planar diffractive lens,” Sci. Rep. 8, 2799 (2018).
[Crossref]

Wang, S.

R. J. Lin, V.-C. Su, S. Wang, M. K. Chen, T. L. Chung, Y. H. Chen, H. Y. Kuo, J.-W. Chen, J. Chen, Y.-T. Huang, J.-H. Wang, C. H. Chu, P. Chieh Wu, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “Achromatic metalens array for full-colour light-field imaging,” Nat. Nanotechnol. 14, 227–231 (2019).
[Crossref]

Q. Cheng, M. Ma, D. Yu, Z. Shen, J. Xie, J. Wang, N. Xu, H. Guo, W. Hu, S. Wang, T. Li, and S. Zhuang, “Broadband achromatic metalens in terahertz regime,” Sci. Bull. 64, 1525–1531 (2019).
[Crossref]

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, M.-K. Chen, H. Y. Kuo, B. H. Chen, Y. H. Chen, T.-T. Huang, J.-H. Wang, R.-M. Lin, C.-H. Kuan, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13, 227–232 (2018).
[Crossref]

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. Hung Chu, J.-W. Chen, S.-H. Lu, J. Chen, B. Xu, C.-H. Kuan, T. Li, S. Zhu, and D. P. Tsai, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8, 187 (2017).
[Crossref]

Wang, Z.

R. J. Lin, V.-C. Su, S. Wang, M. K. Chen, T. L. Chung, Y. H. Chen, H. Y. Kuo, J.-W. Chen, J. Chen, Y.-T. Huang, J.-H. Wang, C. H. Chu, P. Chieh Wu, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “Achromatic metalens array for full-colour light-field imaging,” Nat. Nanotechnol. 14, 227–231 (2019).
[Crossref]

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, M.-K. Chen, H. Y. Kuo, B. H. Chen, Y. H. Chen, T.-T. Huang, J.-H. Wang, R.-M. Lin, C.-H. Kuan, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13, 227–232 (2018).
[Crossref]

Wen, J.

B. Yu, J. Wen, X. Chen, and D. Zhang, “An achromatic metalens in the near-infrared region with an array based on a single nano-rod unit,” Appl. Phys. Express 12, 092003 (2019).
[Crossref]

Werdehausen, D.

Whitehead, J.

L. Huang, J. Whitehead, S. Colburn, and A. Majumdar, “Design and analysis of extended depth of focus metalenses for achromatic computational imaging,” arXiv:2003.09599 (2020).

Wilson, D.

S. Zhang, A. Soibel, S. Keo, D. Wilson, S. Rafol, D. Z. Ting, A. She, S. D. Gunapala, and F. Capasso, “Solid-immersion metalenses for infrared focal plane arrays,” Appl. Phys. Lett. 113, 111104 (2018).
[Crossref]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1980).

Wu, P. C.

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, M.-K. Chen, H. Y. Kuo, B. H. Chen, Y. H. Chen, T.-T. Huang, J.-H. Wang, R.-M. Lin, C.-H. Kuan, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13, 227–232 (2018).
[Crossref]

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. Hung Chu, J.-W. Chen, S.-H. Lu, J. Chen, B. Xu, C.-H. Kuan, T. Li, S. Zhu, and D. P. Tsai, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8, 187 (2017).
[Crossref]

Wyant, J. C.

J. C. Wyant and K. Creath, “Basic wavefront aberration theory for optical metrology,” in Applied Optics and Optical Engineering, Volume XI, R. R. Shannon and J. C. Wyant, eds. (Academic, 1992), Vol. 11.

Xie, J.

Q. Cheng, M. Ma, D. Yu, Z. Shen, J. Xie, J. Wang, N. Xu, H. Guo, W. Hu, S. Wang, T. Li, and S. Zhuang, “Broadband achromatic metalens in terahertz regime,” Sci. Bull. 64, 1525–1531 (2019).
[Crossref]

Xu, B.

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. Hung Chu, J.-W. Chen, S.-H. Lu, J. Chen, B. Xu, C.-H. Kuan, T. Li, S. Zhu, and D. P. Tsai, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8, 187 (2017).
[Crossref]

Xu, N.

Q. Cheng, M. Ma, D. Yu, Z. Shen, J. Xie, J. Wang, N. Xu, H. Guo, W. Hu, S. Wang, T. Li, and S. Zhuang, “Broadband achromatic metalens in terahertz regime,” Sci. Bull. 64, 1525–1531 (2019).
[Crossref]

Ye, M.

M. Ye, V. Ray, and Y. S. Yi, “Achromatic flat subwavelength grating lens over whole visible bandwidths,” IEEE Photon. Technol. Lett. 30, 955–958 (2018).
[Crossref]

Yi, Y. S.

M. Ye, V. Ray, and Y. S. Yi, “Achromatic flat subwavelength grating lens over whole visible bandwidths,” IEEE Photon. Technol. Lett. 30, 955–958 (2018).
[Crossref]

Yilmaz, N.

Yu, B.

B. Yu, J. Wen, X. Chen, and D. Zhang, “An achromatic metalens in the near-infrared region with an array based on a single nano-rod unit,” Appl. Phys. Express 12, 092003 (2019).
[Crossref]

Yu, D.

Q. Cheng, M. Ma, D. Yu, Z. Shen, J. Xie, J. Wang, N. Xu, H. Guo, W. Hu, S. Wang, T. Li, and S. Zhuang, “Broadband achromatic metalens in terahertz regime,” Sci. Bull. 64, 1525–1531 (2019).
[Crossref]

Yu, N.

S. Shrestha, A. C. Overvig, M. Lu, A. Stein, and N. Yu, “Broadband achromatic dielectric metalenses,” Light: Sci. Appl. 7, 85 (2018).
[Crossref]

Zaidi, A.

M. Khorasaninejad, Z. Shi, A. Y. Zhu, W. T. Chen, V. Sanjeev, A. Zaidi, and F. Capasso, “Achromatic metalens over 60  nm bandwidth in the visible and metalens with reverse chromatic dispersion,” Nano Lett. 17, 1819–1824 (2017).
[Crossref]

Zandehshahvar, M.

S. Abdollahramezani, O. Hemmatyar, H. Taghinejad, A. Krasnok, Y. Kiarashinejad, M. Zandehshahvar, A. Alu, and A. Adibi, “Tunable nanophotonics enabled by chalcogenide phase-change materials,” arXiv:2001.06335 (2020).

Zhan, A.

S. Colburn, A. Zhan, and A. Majumdar, “Metasurface optics for full-color computational imaging,” Sci. Adv. 4, eaar2114 (2018).
[Crossref]

Zhang, D.

B. Yu, J. Wen, X. Chen, and D. Zhang, “An achromatic metalens in the near-infrared region with an array based on a single nano-rod unit,” Appl. Phys. Express 12, 092003 (2019).
[Crossref]

Zhang, S.

S. Zhang, A. Soibel, S. Keo, D. Wilson, S. Rafol, D. Z. Ting, A. She, S. D. Gunapala, and F. Capasso, “Solid-immersion metalenses for infrared focal plane arrays,” Appl. Phys. Lett. 113, 111104 (2018).
[Crossref]

Zhou, J.

Zhu, A. Y.

W. T. Chen, A. Y. Zhu, J. Sisler, Z. Bharwani, and F. Capasso, “A broadband achromatic polarization-insensitive metalens consisting of anisotropic nanostructures,” Nat. Commun. 10, 1–7 (2019).
[Crossref]

W. T. Chen, A. Y. Zhu, V. Sanjeev, M. Khorasaninejad, Z. Shi, E. Lee, and F. Capasso, “A broadband achromatic metalens for focusing and imaging in the visible,” Nat. Nanotechnol. 13, 220–226 (2018).
[Crossref]

M. Khorasaninejad, Z. Shi, A. Y. Zhu, W. T. Chen, V. Sanjeev, A. Zaidi, and F. Capasso, “Achromatic metalens over 60  nm bandwidth in the visible and metalens with reverse chromatic dispersion,” Nano Lett. 17, 1819–1824 (2017).
[Crossref]

Zhu, S.

R. J. Lin, V.-C. Su, S. Wang, M. K. Chen, T. L. Chung, Y. H. Chen, H. Y. Kuo, J.-W. Chen, J. Chen, Y.-T. Huang, J.-H. Wang, C. H. Chu, P. Chieh Wu, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “Achromatic metalens array for full-colour light-field imaging,” Nat. Nanotechnol. 14, 227–231 (2019).
[Crossref]

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, M.-K. Chen, H. Y. Kuo, B. H. Chen, Y. H. Chen, T.-T. Huang, J.-H. Wang, R.-M. Lin, C.-H. Kuan, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13, 227–232 (2018).
[Crossref]

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. Hung Chu, J.-W. Chen, S.-H. Lu, J. Chen, B. Xu, C.-H. Kuan, T. Li, S. Zhu, and D. P. Tsai, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8, 187 (2017).
[Crossref]

Zhuang, S.

Q. Cheng, M. Ma, D. Yu, Z. Shen, J. Xie, J. Wang, N. Xu, H. Guo, W. Hu, S. Wang, T. Li, and S. Zhuang, “Broadband achromatic metalens in terahertz regime,” Sci. Bull. 64, 1525–1531 (2019).
[Crossref]

Adv. Opt. Mater. (2)

M. L. Tseng, H.-H. Hsiao, C. H. Chu, M. K. Chen, G. Sun, A.-Q. Liu, and D. P. Tsai, “Metalenses: Advances and applications,” Adv. Opt. Mater. 6, 1800554 (2018).
[Crossref]

T. Siefke, S. Kroker, K. Pfeiffer, O. Puffky, K. Dietrich, D. Franta, I. Ohlídal, A. Szeghalmi, E.-B. Kley, and A. Tünnermann, “Materials pushing the application limits of wire grid polarizers further into the deep ultraviolet spectral range,” Adv. Opt. Mater. 4, 1780–1786 (2016).
[Crossref]

Appl. Phys. Express (1)

B. Yu, J. Wen, X. Chen, and D. Zhang, “An achromatic metalens in the near-infrared region with an array based on a single nano-rod unit,” Appl. Phys. Express 12, 092003 (2019).
[Crossref]

Appl. Phys. Lett. (1)

S. Zhang, A. Soibel, S. Keo, D. Wilson, S. Rafol, D. Z. Ting, A. She, S. D. Gunapala, and F. Capasso, “Solid-immersion metalenses for infrared focal plane arrays,” Appl. Phys. Lett. 113, 111104 (2018).
[Crossref]

Electron. Lett. (1)

D. M. Pozar, “Flat lens antenna concept using aperture coupled microstrip patches,” Electron. Lett. 32, 2109–2111 (1996).
[Crossref]

IEEE Photon. Technol. Lett. (1)

M. Ye, V. Ray, and Y. S. Yi, “Achromatic flat subwavelength grating lens over whole visible bandwidths,” IEEE Photon. Technol. Lett. 30, 955–958 (2018).
[Crossref]

J. Appl. Phys. (1)

R. Ferrini, M. Patrini, and S. Franchi, “Optical functions from 0.02 to 6  eV of AlxGa1-xSb/GaSb epitaxial layers,” J. Appl. Phys. 84, 4517–4524 (1998).
[Crossref]

J. Franklin Inst. (1)

R. Fano, “Theoretical limitations on the broadband matching of arbitrary impedances,” J. Franklin Inst. 249, 57–83 (1950).
[Crossref]

J. Lightwave Technol. (1)

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

Laser Photon. Rev. (1)

P. Lalanne and P. Chavel, “Metalenses at visible wavelengths: past, present, perspectives,” Laser Photon. Rev. 11, 1600295 (2017).
[Crossref]

Light: Sci. Appl. (1)

S. Shrestha, A. C. Overvig, M. Lu, A. Stein, and N. Yu, “Broadband achromatic dielectric metalenses,” Light: Sci. Appl. 7, 85 (2018).
[Crossref]

Nano Lett. (2)

A. Pors, M. G. Nielsen, and S. I. Bozhevolnyi, “Analog computing using reflective plasmonic metasurfaces,” Nano Lett. 15, 791–797 (2015).
[Crossref]

M. Khorasaninejad, Z. Shi, A. Y. Zhu, W. T. Chen, V. Sanjeev, A. Zaidi, and F. Capasso, “Achromatic metalens over 60  nm bandwidth in the visible and metalens with reverse chromatic dispersion,” Nano Lett. 17, 1819–1824 (2017).
[Crossref]

Nat. Commun. (2)

W. T. Chen, A. Y. Zhu, J. Sisler, Z. Bharwani, and F. Capasso, “A broadband achromatic polarization-insensitive metalens consisting of anisotropic nanostructures,” Nat. Commun. 10, 1–7 (2019).
[Crossref]

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. Hung Chu, J.-W. Chen, S.-H. Lu, J. Chen, B. Xu, C.-H. Kuan, T. Li, S. Zhu, and D. P. Tsai, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8, 187 (2017).
[Crossref]

Nat. Nanotechnol. (3)

R. J. Lin, V.-C. Su, S. Wang, M. K. Chen, T. L. Chung, Y. H. Chen, H. Y. Kuo, J.-W. Chen, J. Chen, Y.-T. Huang, J.-H. Wang, C. H. Chu, P. Chieh Wu, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “Achromatic metalens array for full-colour light-field imaging,” Nat. Nanotechnol. 14, 227–231 (2019).
[Crossref]

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, M.-K. Chen, H. Y. Kuo, B. H. Chen, Y. H. Chen, T.-T. Huang, J.-H. Wang, R.-M. Lin, C.-H. Kuan, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13, 227–232 (2018).
[Crossref]

W. T. Chen, A. Y. Zhu, V. Sanjeev, M. Khorasaninejad, Z. Shi, E. Lee, and F. Capasso, “A broadband achromatic metalens for focusing and imaging in the visible,” Nat. Nanotechnol. 13, 220–226 (2018).
[Crossref]

Opt. Express (5)

Opt. Lett. (1)

Optica (5)

Phys. Rev. Lett. (3)

D. A. B. Miller, “Fundamental limit to linear one-dimensional slow light structures,” Phys. Rev. Lett. 99, 203903 (2007).
[Crossref]

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

F. Monticone, N. M. Estakhri, and A. Alù, “Full control of nanoscale optical transmission with a composite metascreen,” Phys. Rev. Lett. 110, 203903 (2013).
[Crossref]

Proc. Natl. Acad. Sci. USA (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. USA 113, 10473–10478 (2016).
[Crossref]

Sci. Adv. (1)

S. Colburn, A. Zhan, and A. Majumdar, “Metasurface optics for full-color computational imaging,” Sci. Adv. 4, eaar2114 (2018).
[Crossref]

Sci. Bull. (1)

Q. Cheng, M. Ma, D. Yu, Z. Shen, J. Xie, J. Wang, N. Xu, H. Guo, W. Hu, S. Wang, T. Li, and S. Zhuang, “Broadband achromatic metalens in terahertz regime,” Sci. Bull. 64, 1525–1531 (2019).
[Crossref]

Sci. Rep. (1)

N. Mohammad, M. Meem, P. Wang, and R. Menon, “Broadband imaging with one planar diffractive lens,” Sci. Rep. 8, 2799 (2018).
[Crossref]

Science (2)

M. Khorasaninejad and F. Capasso, “Metalenses: versatile multifunctional photonic components,” Science 358, eaam8100 (2017).
[Crossref]

A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, “Performing mathematical operations with metamaterials,” Science 343, 160–163 (2014).
[Crossref]

Other (12)

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1980).

F. Balli, M. A. Sultan, S. K. Lami, and J. T. Hastings, “A hybrid achromatic metalens,” arXiv:1909.07941 (2019).

A. A. Fathnan, A. E. Olk, and D. A. Powell, “Broadband anomalous reflection with dispersion controlled metasurfaces,” arXiv:1912.03936 (2019).

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999).

L. Huang, J. Whitehead, S. Colburn, and A. Majumdar, “Design and analysis of extended depth of focus metalenses for achromatic computational imaging,” arXiv:2003.09599 (2020).

E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1998), Vol. 3.

J. Khurgin, “Bandwidth limitation in slow light schemes,” in Slow Light: Science and Applications, J. Khurgin and R. S. Tucker, eds. (Taylor & Francis Group, 2008), chap. 15, pp. 293–320.

J. C. Wyant and K. Creath, “Basic wavefront aberration theory for optical metrology,” in Applied Optics and Optical Engineering, Volume XI, R. R. Shannon and J. C. Wyant, eds. (Academic, 1992), Vol. 11.

J. W. Hardy, “Adaptive optics for astronomical telescopes,” in Adaptive Optics for Astronomical Telescopes (Oxford University, 1998), chap. 4, p. 104–134.

S. Abdollahramezani, O. Hemmatyar, H. Taghinejad, A. Krasnok, Y. Kiarashinejad, M. Zandehshahvar, A. Alu, and A. Adibi, “Tunable nanophotonics enabled by chalcogenide phase-change materials,” arXiv:2001.06335 (2020).

S. A. Tretyakov, Analytical Modeling in Applied Electromagnetics (Artech House, 2003).

J. M. Meem, S. Banerji, A. Majumder, J. C. Garcia, P. W. C. Hon, B. Sensale-Rodriquez, and R. Menon, “Imaging from the visible to the longwave infrared wavelengths via an inverse-designed flat lens,” https://arxiv.org/abs/2001.03684 (2020).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1.
Fig. 1. Delay-line model of a thin broadband metalens. Radially arranged delay lines provide a broadband signal the necessary group delay $\Delta T(r) $ to compensate for the difference in arrival times at the focus, while the phase pattern $\varphi (r) $ creates a spherical wavefront according to Eqs. (1) and (2).
Fig. 2.
Fig. 2. Comparisons of published achromatic metalens designs against the derived bandwidth limits. (a) Limit based on the single-resonator TBP bound, given by Eq. (12). Not surprisingly, most data points exceed this bound except for some thin devices. (b) Limit based on Tucker’s TBP bound, given by Eq. (13). Each data point in the plots represent a single design, with each label corresponding to a specific row in Table 1. The performance of each metalens is represented in terms of numerical aperture and bandwidth. In order to compare vastly different designs against the bandwidth bounds, the bandwidths are normalized by $c$, $F$, and the corresponding $\kappa$ [see Eq. (8)]. In both panels, the lowest blue curve represents the function $\Theta ({\rm NA}/{n_b}) = c/F\Delta T_{\text{max}}$, where $\Delta T_{\text{max}}$ is the required time delay for ideal operation, given by Eq. (6). Fig. 2(b) includes both the upper bound for ideal metalenses with no aberrations, $\Delta {T_{{\rm err}}} = 0$ ($\Theta$, lower solid blue curve), and the bound for highly aberrated metalenses with an error $\Delta {T_{{\rm err}}} = 0.8\Delta T_{\text{max}}$ ($\Theta /0.2$, dashed blue curve) and $\Delta {T_{{\rm err}}} = 0.9\Delta T_{\text{max}}$ ($\Theta /0.1$, upper solid blue curve), which correspond to low values of the Strehl ratio according to Eq. (17). All design parameters and bandwidth values are given in Table 1.
Fig. 3.
Fig. 3. Different bandwidth limits compared to the performance of a specific metalens design, from Ref. [9] (central wavelength ${\lambda _c} = 518$ nm): single-resonator limit [Eq. (9), dotted-dashed green curve]; Tucker’s limit [Eq. (10), dashed black], and Miller’s limit [Eq. (11), solid red] using the refractive-index/permittivity contrast considered in Ref. [9]; design-independent Tucker’s limit (dashed purple) with the highest refractive index for lossless dielectrics naturally available at optical frequency, $n \approx 4$. The inset includes the same curves and an additional curve (solid orange) for a design-independent version of Miller’s limit with the highest permittivity contrast (in magnitude) available at optical frequency $\eta \approx 100$ [26] (which may include the case of metallic materials as well as materials with loss and gain).
Fig. 4.
Fig. 4. Comparison of the bandwidth limit for achromatic performance (blue), based on Miller’s TBP, Eq. (14), and the Bode–Fano bandwidth limit on reflection reduction, Eq. (18) (orange), as a function of the product of permittivity contrast and normalized thickness: $\eta L/{\lambda _c}$. The limits are compared for various values of NA and in-band reflection coefficient $|\Gamma |$. As an example, we considered a dielectric metalens with $F = 100{\lambda _c}$ and ${\varepsilon _b} = 1$. In order to apply the Bode–Fano limit to the considered problem and compare it with Miller’s limit, we treat the metasurface as a homogeneous slab with averaged refractive index, and a permittivity contrast $\eta = \varepsilon - {\varepsilon _b} = {\eta _{{\rm max}}}$ (further details in the text). For a given value of NA and $|\Gamma |$, there is an optimal value of $\eta L/{\lambda _c}$, where the two limits intersect, that maximizes $\Delta \omega$.

Tables (1)

Tables Icon

Table 1. Summary of Design Parameters and Performance Values of Broadband Achromatic Metalenses in the Literaturea

Equations (18)

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

φ ( r , ω ) = ω c ( F 2 + r 2 F ) ,
φ ( r , ω ) = φ ( r , ω c ) + ( ω ω c ) φ ( r , ω ) ω | ω = ω c + 1 2 ( ω ω c ) 2 2 φ ( r , ω ) ω 2 | ω = ω c + ,
Δ T Δ ω κ ,
Δ T ( r ) = φ ω ( r ) φ ω ( R )
= 1 c ( F 2 + R 2 F 2 + r 2 ) .
Δ T m a x = F c ( 1 + ( R / F ) 2 1 ) .
N A = n b sin θ = n b sin [ a r c t a n ( R F ) ] ,
Δ ω κ c F ( 1 + ( R / F ) 2 1 ) = κ c 1 ( N A / n b ) 2 F ( 1 1 ( N A / n b ) 2 ) .
κ = 2.
κ = 2 π L λ c ( n m a x n m i n ) ,
κ = π 3 L λ c η max ,
Δ ω 2 c F Θ ( N A n b ) ,
Δ ω ω c L Δ n F Θ ( N A n b ) ,
Δ ω ω c 2 3 L η m a x F Θ ( N A n b ) ,
Θ ( N A n b ) = 1 ( N A / n b ) 2 1 1 ( N A / n b ) 2 .
S e ( k 0 σ ) 2 ,
S exp ( ( α 1 ( ω ω c ) Δ T e r r ) 2 ) .
Δ ω ω c 1 L / λ c ( ε ε b ) [ log 1 | Γ | ] 1 ,

Metrics