Abstract

Metasurfaces can implement a wide variety of wave-manipulation functions with sub-wavelength layers. They are typically created from resonant elements, thus their refraction properties depend strongly on frequency. The resulting chromatic aberration is undesirable for most applications, motivating recent efforts in the development of achromatic metasurfaces. However, it remains unclear whether there are any physical limits on the achievable operating bandwidth of achromatic metasurfaces. Here we address this question, considering a common microwave metasurface geometry based on three metallic layers, separated by dielectric substrates. Since each of these metallic layers is modeled as an impedance, we apply Foster’s reactance theorem to determine the bandwidth over which they are physically realizable using passive, causal and lossless structures. We derive limits for the bandwidth and total size of the metasurface, showing that there is a trade-off between these two parameters. A higher angle of refraction, corresponding to a larger numerical aperture for a lens, further limits the realizable bandwidth. We consider both Huygens’ and Omega-bianisotropic metasurface types, and show that the limit is more severe for bianisotropic metasurfaces, making them less suitable for broadband achromatic designs.

© 2018 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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  1. N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: Generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
    [Crossref] [PubMed]
  2. C. L. Holloway, E. F. Kuester, J. A. Gordon, J. O’Hara, J. Booth, and D. R. Smith, “An overview of the theory and applications of metasurfaces: The two-dimensional equivalents of metamaterials,” IEEE Antennas Propag. Mag. 54, 10–35 (2012).
    [Crossref]
  3. A. E. Minovich, A. E. Miroshnichenko, A. Y. Bykov, T. V. Murzina, D. N. Neshev, and Y. S. Kivshar, “Functional and nonlinear optical metasurfaces,” Laser & Photonics Rev. 9, 195–213 (2015).
    [Crossref]
  4. A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science 339, 1232009 (2013).
    [Crossref] [PubMed]
  5. C. Pfeiffer and A. Grbic, “Metamaterial Huygens surfaces: Tailoring wave fronts with reflectionless sheets,” Phys. Rev. Lett. 110, 197401 (2013).
    [Crossref]
  6. 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] [PubMed]
  7. A. Epstein and G. V. Eleftheriades, “Huygens metasurfaces via the equivalence principle: Design and applications,” JOSA B 33, A31–A50 (2016).
    [Crossref]
  8. A. Epstein and G. V. Eleftheriades, “Arbitrary power-conserving field transformations with passive lossless omega-type bianisotropic metasurfaces,” IEEE Transactions on Antennas Propag. 64, 3880–3895 (2016).
    [Crossref]
  9. J. P. Wong, A. Epstein, and G. V. Eleftheriades, “Reflectionless wide-angle refracting metasurfaces,” IEEE Antennas Wirel. Propag. Lett. 15, 1293–1296 (2016).
    [Crossref]
  10. V. S. Asadchy, A. Díaz-Rubio, and S. A. Tretyakov, “Bianisotropic metasurfaces: physics and applications,” Nanophotonics 7, 1069–1094 (2018).
    [Crossref]
  11. S. Larouche and D. R. Smith, “Reconciliation of generalized refraction with diffraction theory,” Opt. Lett. 37, 2391–2393 (2012).
    [Crossref] [PubMed]
  12. J. Cheng, S. Inampudi, F. Fan, X. Wang, S. Chang, and H. Mosallaei, “Dielectric metasurfaces in transmission and reflection modes approaching and beyond bandwidth of conventional blazed grating,” Opt. express 26, 12547–12557 (2018).
    [Crossref] [PubMed]
  13. F. Aieta, M. A. Kats, P. Genevet, and F. Capasso, “Multiwavelength achromatic metasurfaces by dispersive phase compensation,” Science 347, 1342–1345 (2015).
    [Crossref] [PubMed]
  14. M. Khorasaninejad, F. Aieta, P. Kanhaiya, M. A. Kats, P. Genevet, D. Rousso, and F. Capasso, “Achromatic metasurface lens at telecommunication wavelengths,” Nano letters 15, 5358–5362 (2015).
    [Crossref] [PubMed]
  15. Y. Li, X. Li, M. Pu, Z. Zhao, X. Ma, Y. Wang, and X. Luo, “Achromatic flat optical components via compensation between structure and material dispersions,” Sci. reports 6, 19885 (2016).
    [Crossref]
  16. S. Wang, J. Lai, T. Wu, C. Chen, and J. Sun, “Wide-band achromatic flat focusing lens based on all-dielectric subwavelength metasurface,” Opt. express 25, 7121–7130 (2017).
    [Crossref] [PubMed]
  17. 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]
  18. 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 (2018).
    [Crossref] [PubMed]
  19. 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 (2018).
    [Crossref] [PubMed]
  20. S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. H. 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] [PubMed]
  21. M. Li, M. A. Al-Joumayly, and N. Behdad, “Broadband true-time-delay microwave lenses based on miniaturized element frequency selective surfaces,” IEEE Transactions on Antennas Propag. 61, 1166–1179 (2013).
    [Crossref]
  22. C. Pfeiffer and A. Grbic, “Millimeter-wave transmitarrays for wavefront and polarization control,” IEEE Transactions on Microw. Theory Tech. 61, 4407–4417 (2013).
    [Crossref]
  23. G. Lavigne, K. Achouri, V. Asadchy, S. Tretyakov, and C. Caloz, “Susceptibility derivation and experimental demonstration of refracting metasurfaces without spurious diffraction,” IEEE Trans on Antennas Propag. (2018).
    [Crossref]
  24. R. M. Foster, “A reactance theorem,” Bell Labs Tech. J. 3, 259–267 (1924).
    [Crossref]
  25. W. Geyi, P. Jarmuszewski, and Y. Qi, “The Foster reactance theorem for antennas and radiation-Q,” IEEE Transactions on Antennas Propag. 48, 401–408 (2000).
    [Crossref]
  26. P.-Y. Chen, C. Argyropoulos, and A. Alù, “Broadening the cloaking bandwidth with non-foster metasurfaces,” Phys. Rev. Lett. 111, 233001 (2013).
    [Crossref]
  27. J. Mou and Z. Shen, “Broadband and thin magnetic absorber with non-Foster metasurface for admittance matching,” Sci. Reports 7, 6922 (2017).
    [Crossref]

2018 (4)

V. S. Asadchy, A. Díaz-Rubio, and S. A. Tretyakov, “Bianisotropic metasurfaces: physics and applications,” Nanophotonics 7, 1069–1094 (2018).
[Crossref]

J. Cheng, S. Inampudi, F. Fan, X. Wang, S. Chang, and H. Mosallaei, “Dielectric metasurfaces in transmission and reflection modes approaching and beyond bandwidth of conventional blazed grating,” Opt. express 26, 12547–12557 (2018).
[Crossref] [PubMed]

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 (2018).
[Crossref] [PubMed]

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 (2018).
[Crossref] [PubMed]

2017 (4)

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. H. 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] [PubMed]

S. Wang, J. Lai, T. Wu, C. Chen, and J. Sun, “Wide-band achromatic flat focusing lens based on all-dielectric subwavelength metasurface,” Opt. express 25, 7121–7130 (2017).
[Crossref] [PubMed]

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]

J. Mou and Z. Shen, “Broadband and thin magnetic absorber with non-Foster metasurface for admittance matching,” Sci. Reports 7, 6922 (2017).
[Crossref]

2016 (4)

Y. Li, X. Li, M. Pu, Z. Zhao, X. Ma, Y. Wang, and X. Luo, “Achromatic flat optical components via compensation between structure and material dispersions,” Sci. reports 6, 19885 (2016).
[Crossref]

A. Epstein and G. V. Eleftheriades, “Huygens metasurfaces via the equivalence principle: Design and applications,” JOSA B 33, A31–A50 (2016).
[Crossref]

A. Epstein and G. V. Eleftheriades, “Arbitrary power-conserving field transformations with passive lossless omega-type bianisotropic metasurfaces,” IEEE Transactions on Antennas Propag. 64, 3880–3895 (2016).
[Crossref]

J. P. Wong, A. Epstein, and G. V. Eleftheriades, “Reflectionless wide-angle refracting metasurfaces,” IEEE Antennas Wirel. Propag. Lett. 15, 1293–1296 (2016).
[Crossref]

2015 (3)

A. E. Minovich, A. E. Miroshnichenko, A. Y. Bykov, T. V. Murzina, D. N. Neshev, and Y. S. Kivshar, “Functional and nonlinear optical metasurfaces,” Laser & Photonics Rev. 9, 195–213 (2015).
[Crossref]

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

M. Khorasaninejad, F. Aieta, P. Kanhaiya, M. A. Kats, P. Genevet, D. Rousso, and F. Capasso, “Achromatic metasurface lens at telecommunication wavelengths,” Nano letters 15, 5358–5362 (2015).
[Crossref] [PubMed]

2013 (6)

M. Li, M. A. Al-Joumayly, and N. Behdad, “Broadband true-time-delay microwave lenses based on miniaturized element frequency selective surfaces,” IEEE Transactions on Antennas Propag. 61, 1166–1179 (2013).
[Crossref]

C. Pfeiffer and A. Grbic, “Millimeter-wave transmitarrays for wavefront and polarization control,” IEEE Transactions on Microw. Theory Tech. 61, 4407–4417 (2013).
[Crossref]

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

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] [PubMed]

P.-Y. Chen, C. Argyropoulos, and A. Alù, “Broadening the cloaking bandwidth with non-foster metasurfaces,” Phys. Rev. Lett. 111, 233001 (2013).
[Crossref]

2012 (2)

C. L. Holloway, E. F. Kuester, J. A. Gordon, J. O’Hara, J. Booth, and D. R. Smith, “An overview of the theory and applications of metasurfaces: The two-dimensional equivalents of metamaterials,” IEEE Antennas Propag. Mag. 54, 10–35 (2012).
[Crossref]

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

2011 (1)

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: Generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref] [PubMed]

2000 (1)

W. Geyi, P. Jarmuszewski, and Y. Qi, “The Foster reactance theorem for antennas and radiation-Q,” IEEE Transactions on Antennas Propag. 48, 401–408 (2000).
[Crossref]

1924 (1)

R. M. Foster, “A reactance theorem,” Bell Labs Tech. J. 3, 259–267 (1924).
[Crossref]

Achouri, K.

G. Lavigne, K. Achouri, V. Asadchy, S. Tretyakov, and C. Caloz, “Susceptibility derivation and experimental demonstration of refracting metasurfaces without spurious diffraction,” IEEE Trans on Antennas Propag. (2018).
[Crossref]

Aieta, F.

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

M. Khorasaninejad, F. Aieta, P. Kanhaiya, M. A. Kats, P. Genevet, D. Rousso, and F. Capasso, “Achromatic metasurface lens at telecommunication wavelengths,” Nano letters 15, 5358–5362 (2015).
[Crossref] [PubMed]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: Generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref] [PubMed]

Al-Joumayly, M. A.

M. Li, M. A. Al-Joumayly, and N. Behdad, “Broadband true-time-delay microwave lenses based on miniaturized element frequency selective surfaces,” IEEE Transactions on Antennas Propag. 61, 1166–1179 (2013).
[Crossref]

Alù, A.

P.-Y. Chen, C. Argyropoulos, and A. Alù, “Broadening the cloaking bandwidth with non-foster metasurfaces,” Phys. Rev. Lett. 111, 233001 (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] [PubMed]

Arbabi, A.

Arbabi, E.

Argyropoulos, C.

P.-Y. Chen, C. Argyropoulos, and A. Alù, “Broadening the cloaking bandwidth with non-foster metasurfaces,” Phys. Rev. Lett. 111, 233001 (2013).
[Crossref]

Asadchy, V.

G. Lavigne, K. Achouri, V. Asadchy, S. Tretyakov, and C. Caloz, “Susceptibility derivation and experimental demonstration of refracting metasurfaces without spurious diffraction,” IEEE Trans on Antennas Propag. (2018).
[Crossref]

Asadchy, V. S.

V. S. Asadchy, A. Díaz-Rubio, and S. A. Tretyakov, “Bianisotropic metasurfaces: physics and applications,” Nanophotonics 7, 1069–1094 (2018).
[Crossref]

Behdad, N.

M. Li, M. A. Al-Joumayly, and N. Behdad, “Broadband true-time-delay microwave lenses based on miniaturized element frequency selective surfaces,” IEEE Transactions on Antennas Propag. 61, 1166–1179 (2013).
[Crossref]

Boltasseva, A.

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

Booth, J.

C. L. Holloway, E. F. Kuester, J. A. Gordon, J. O’Hara, J. Booth, and D. R. Smith, “An overview of the theory and applications of metasurfaces: The two-dimensional equivalents of metamaterials,” IEEE Antennas Propag. Mag. 54, 10–35 (2012).
[Crossref]

Bykov, A. Y.

A. E. Minovich, A. E. Miroshnichenko, A. Y. Bykov, T. V. Murzina, D. N. Neshev, and Y. S. Kivshar, “Functional and nonlinear optical metasurfaces,” Laser & Photonics Rev. 9, 195–213 (2015).
[Crossref]

Caloz, C.

G. Lavigne, K. Achouri, V. Asadchy, S. Tretyakov, and C. Caloz, “Susceptibility derivation and experimental demonstration of refracting metasurfaces without spurious diffraction,” IEEE Trans on Antennas Propag. (2018).
[Crossref]

Capasso, F.

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 (2018).
[Crossref] [PubMed]

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

M. Khorasaninejad, F. Aieta, P. Kanhaiya, M. A. Kats, P. Genevet, D. Rousso, and F. Capasso, “Achromatic metasurface lens at telecommunication wavelengths,” Nano letters 15, 5358–5362 (2015).
[Crossref] [PubMed]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: Generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref] [PubMed]

Chang, S.

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 (2018).
[Crossref] [PubMed]

Chen, C.

Chen, J.

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. H. 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] [PubMed]

Chen, J.-W.

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. H. 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] [PubMed]

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 (2018).
[Crossref] [PubMed]

Chen, P.-Y.

P.-Y. Chen, C. Argyropoulos, and A. Alù, “Broadening the cloaking bandwidth with non-foster metasurfaces,” Phys. Rev. Lett. 111, 233001 (2013).
[Crossref]

Chen, W. T.

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 (2018).
[Crossref] [PubMed]

Chen, Y. 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 (2018).
[Crossref] [PubMed]

Cheng, J.

Chu, C. H.

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. H. 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] [PubMed]

Díaz-Rubio, A.

V. S. Asadchy, A. Díaz-Rubio, and S. A. Tretyakov, “Bianisotropic metasurfaces: physics and applications,” Nanophotonics 7, 1069–1094 (2018).
[Crossref]

Eleftheriades, G. V.

J. P. Wong, A. Epstein, and G. V. Eleftheriades, “Reflectionless wide-angle refracting metasurfaces,” IEEE Antennas Wirel. Propag. Lett. 15, 1293–1296 (2016).
[Crossref]

A. Epstein and G. V. Eleftheriades, “Huygens metasurfaces via the equivalence principle: Design and applications,” JOSA B 33, A31–A50 (2016).
[Crossref]

A. Epstein and G. V. Eleftheriades, “Arbitrary power-conserving field transformations with passive lossless omega-type bianisotropic metasurfaces,” IEEE Transactions on Antennas Propag. 64, 3880–3895 (2016).
[Crossref]

Epstein, A.

J. P. Wong, A. Epstein, and G. V. Eleftheriades, “Reflectionless wide-angle refracting metasurfaces,” IEEE Antennas Wirel. Propag. Lett. 15, 1293–1296 (2016).
[Crossref]

A. Epstein and G. V. Eleftheriades, “Arbitrary power-conserving field transformations with passive lossless omega-type bianisotropic metasurfaces,” IEEE Transactions on Antennas Propag. 64, 3880–3895 (2016).
[Crossref]

A. Epstein and G. V. Eleftheriades, “Huygens metasurfaces via the equivalence principle: Design and applications,” JOSA B 33, A31–A50 (2016).
[Crossref]

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] [PubMed]

Fan, F.

Faraon, A.

Foster, R. M.

R. M. Foster, “A reactance theorem,” Bell Labs Tech. J. 3, 259–267 (1924).
[Crossref]

Gaburro, Z.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: Generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref] [PubMed]

Genevet, P.

M. Khorasaninejad, F. Aieta, P. Kanhaiya, M. A. Kats, P. Genevet, D. Rousso, and F. Capasso, “Achromatic metasurface lens at telecommunication wavelengths,” Nano letters 15, 5358–5362 (2015).
[Crossref] [PubMed]

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

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: Generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref] [PubMed]

Geyi, W.

W. Geyi, P. Jarmuszewski, and Y. Qi, “The Foster reactance theorem for antennas and radiation-Q,” IEEE Transactions on Antennas Propag. 48, 401–408 (2000).
[Crossref]

Gordon, J. A.

C. L. Holloway, E. F. Kuester, J. A. Gordon, J. O’Hara, J. Booth, and D. R. Smith, “An overview of the theory and applications of metasurfaces: The two-dimensional equivalents of metamaterials,” IEEE Antennas Propag. Mag. 54, 10–35 (2012).
[Crossref]

Grbic, A.

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

C. Pfeiffer and A. Grbic, “Millimeter-wave transmitarrays for wavefront and polarization control,” IEEE Transactions on Microw. Theory Tech. 61, 4407–4417 (2013).
[Crossref]

Holloway, C. L.

C. L. Holloway, E. F. Kuester, J. A. Gordon, J. O’Hara, J. Booth, and D. R. Smith, “An overview of the theory and applications of metasurfaces: The two-dimensional equivalents of metamaterials,” IEEE Antennas Propag. Mag. 54, 10–35 (2012).
[Crossref]

Horie, Y.

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 (2018).
[Crossref] [PubMed]

Inampudi, S.

Jarmuszewski, P.

W. Geyi, P. Jarmuszewski, and Y. Qi, “The Foster reactance theorem for antennas and radiation-Q,” IEEE Transactions on Antennas Propag. 48, 401–408 (2000).
[Crossref]

Kamali, S. M.

Kanhaiya, P.

M. Khorasaninejad, F. Aieta, P. Kanhaiya, M. A. Kats, P. Genevet, D. Rousso, and F. Capasso, “Achromatic metasurface lens at telecommunication wavelengths,” Nano letters 15, 5358–5362 (2015).
[Crossref] [PubMed]

Kats, M. A.

M. Khorasaninejad, F. Aieta, P. Kanhaiya, M. A. Kats, P. Genevet, D. Rousso, and F. Capasso, “Achromatic metasurface lens at telecommunication wavelengths,” Nano letters 15, 5358–5362 (2015).
[Crossref] [PubMed]

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

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: Generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref] [PubMed]

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 (2018).
[Crossref] [PubMed]

M. Khorasaninejad, F. Aieta, P. Kanhaiya, M. A. Kats, P. Genevet, D. Rousso, and F. Capasso, “Achromatic metasurface lens at telecommunication wavelengths,” Nano letters 15, 5358–5362 (2015).
[Crossref] [PubMed]

Kildishev, A. V.

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

Kivshar, Y. S.

A. E. Minovich, A. E. Miroshnichenko, A. Y. Bykov, T. V. Murzina, D. N. Neshev, and Y. S. Kivshar, “Functional and nonlinear optical metasurfaces,” Laser & Photonics Rev. 9, 195–213 (2015).
[Crossref]

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 (2018).
[Crossref] [PubMed]

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. H. 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] [PubMed]

Kuester, E. F.

C. L. Holloway, E. F. Kuester, J. A. Gordon, J. O’Hara, J. Booth, and D. R. Smith, “An overview of the theory and applications of metasurfaces: The two-dimensional equivalents of metamaterials,” IEEE Antennas Propag. Mag. 54, 10–35 (2012).
[Crossref]

Kuo, H. Y.

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 (2018).
[Crossref] [PubMed]

Lai, J.

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 (2018).
[Crossref] [PubMed]

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. H. 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] [PubMed]

Larouche, S.

Lavigne, G.

G. Lavigne, K. Achouri, V. Asadchy, S. Tretyakov, and C. Caloz, “Susceptibility derivation and experimental demonstration of refracting metasurfaces without spurious diffraction,” IEEE Trans on Antennas Propag. (2018).
[Crossref]

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 (2018).
[Crossref] [PubMed]

Li, M.

M. Li, M. A. Al-Joumayly, and N. Behdad, “Broadband true-time-delay microwave lenses based on miniaturized element frequency selective surfaces,” IEEE Transactions on Antennas Propag. 61, 1166–1179 (2013).
[Crossref]

Li, 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 (2018).
[Crossref] [PubMed]

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. H. 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] [PubMed]

Li, X.

Y. Li, X. Li, M. Pu, Z. Zhao, X. Ma, Y. Wang, and X. Luo, “Achromatic flat optical components via compensation between structure and material dispersions,” Sci. reports 6, 19885 (2016).
[Crossref]

Li, Y.

Y. Li, X. Li, M. Pu, Z. Zhao, X. Ma, Y. Wang, and X. Luo, “Achromatic flat optical components via compensation between structure and material dispersions,” Sci. reports 6, 19885 (2016).
[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 (2018).
[Crossref] [PubMed]

Lu, S.-H.

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. H. 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] [PubMed]

Luo, X.

Y. Li, X. Li, M. Pu, Z. Zhao, X. Ma, Y. Wang, and X. Luo, “Achromatic flat optical components via compensation between structure and material dispersions,” Sci. reports 6, 19885 (2016).
[Crossref]

Ma, X.

Y. Li, X. Li, M. Pu, Z. Zhao, X. Ma, Y. Wang, and X. Luo, “Achromatic flat optical components via compensation between structure and material dispersions,” Sci. reports 6, 19885 (2016).
[Crossref]

Minovich, A. E.

A. E. Minovich, A. E. Miroshnichenko, A. Y. Bykov, T. V. Murzina, D. N. Neshev, and Y. S. Kivshar, “Functional and nonlinear optical metasurfaces,” Laser & Photonics Rev. 9, 195–213 (2015).
[Crossref]

Miroshnichenko, A. E.

A. E. Minovich, A. E. Miroshnichenko, A. Y. Bykov, T. V. Murzina, D. N. Neshev, and Y. S. Kivshar, “Functional and nonlinear optical metasurfaces,” Laser & Photonics Rev. 9, 195–213 (2015).
[Crossref]

Monticone, F.

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] [PubMed]

Mosallaei, H.

Mou, J.

J. Mou and Z. Shen, “Broadband and thin magnetic absorber with non-Foster metasurface for admittance matching,” Sci. Reports 7, 6922 (2017).
[Crossref]

Murzina, T. V.

A. E. Minovich, A. E. Miroshnichenko, A. Y. Bykov, T. V. Murzina, D. N. Neshev, and Y. S. Kivshar, “Functional and nonlinear optical metasurfaces,” Laser & Photonics Rev. 9, 195–213 (2015).
[Crossref]

Neshev, D. N.

A. E. Minovich, A. E. Miroshnichenko, A. Y. Bykov, T. V. Murzina, D. N. Neshev, and Y. S. Kivshar, “Functional and nonlinear optical metasurfaces,” Laser & Photonics Rev. 9, 195–213 (2015).
[Crossref]

O’Hara, J.

C. L. Holloway, E. F. Kuester, J. A. Gordon, J. O’Hara, J. Booth, and D. R. Smith, “An overview of the theory and applications of metasurfaces: The two-dimensional equivalents of metamaterials,” IEEE Antennas Propag. Mag. 54, 10–35 (2012).
[Crossref]

Pfeiffer, C.

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

C. Pfeiffer and A. Grbic, “Millimeter-wave transmitarrays for wavefront and polarization control,” IEEE Transactions on Microw. Theory Tech. 61, 4407–4417 (2013).
[Crossref]

Pu, M.

Y. Li, X. Li, M. Pu, Z. Zhao, X. Ma, Y. Wang, and X. Luo, “Achromatic flat optical components via compensation between structure and material dispersions,” Sci. reports 6, 19885 (2016).
[Crossref]

Qi, Y.

W. Geyi, P. Jarmuszewski, and Y. Qi, “The Foster reactance theorem for antennas and radiation-Q,” IEEE Transactions on Antennas Propag. 48, 401–408 (2000).
[Crossref]

Rousso, D.

M. Khorasaninejad, F. Aieta, P. Kanhaiya, M. A. Kats, P. Genevet, D. Rousso, and F. Capasso, “Achromatic metasurface lens at telecommunication wavelengths,” Nano letters 15, 5358–5362 (2015).
[Crossref] [PubMed]

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 (2018).
[Crossref] [PubMed]

Shalaev, V. M.

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

Shen, Z.

J. Mou and Z. Shen, “Broadband and thin magnetic absorber with non-Foster metasurface for admittance matching,” Sci. Reports 7, 6922 (2017).
[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 (2018).
[Crossref] [PubMed]

Smith, D. R.

C. L. Holloway, E. F. Kuester, J. A. Gordon, J. O’Hara, J. Booth, and D. R. Smith, “An overview of the theory and applications of metasurfaces: The two-dimensional equivalents of metamaterials,” IEEE Antennas Propag. Mag. 54, 10–35 (2012).
[Crossref]

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

Su, V.-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 (2018).
[Crossref] [PubMed]

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. H. 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] [PubMed]

Sun, J.

Tetienne, J.-P.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: Generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref] [PubMed]

Tretyakov, S.

G. Lavigne, K. Achouri, V. Asadchy, S. Tretyakov, and C. Caloz, “Susceptibility derivation and experimental demonstration of refracting metasurfaces without spurious diffraction,” IEEE Trans on Antennas Propag. (2018).
[Crossref]

Tretyakov, S. A.

V. S. Asadchy, A. Díaz-Rubio, and S. A. Tretyakov, “Bianisotropic metasurfaces: physics and applications,” Nanophotonics 7, 1069–1094 (2018).
[Crossref]

Tsai, D. P.

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 (2018).
[Crossref] [PubMed]

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. H. 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] [PubMed]

Wang, J.-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 (2018).
[Crossref] [PubMed]

Wang, S.

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 (2018).
[Crossref] [PubMed]

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. H. 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] [PubMed]

S. Wang, J. Lai, T. Wu, C. Chen, and J. Sun, “Wide-band achromatic flat focusing lens based on all-dielectric subwavelength metasurface,” Opt. express 25, 7121–7130 (2017).
[Crossref] [PubMed]

Wang, X.

Wang, Y.

Y. Li, X. Li, M. Pu, Z. Zhao, X. Ma, Y. Wang, and X. Luo, “Achromatic flat optical components via compensation between structure and material dispersions,” Sci. reports 6, 19885 (2016).
[Crossref]

Wang, Z.

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 (2018).
[Crossref] [PubMed]

Wong, J. P.

J. P. Wong, A. Epstein, and G. V. Eleftheriades, “Reflectionless wide-angle refracting metasurfaces,” IEEE Antennas Wirel. Propag. Lett. 15, 1293–1296 (2016).
[Crossref]

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 (2018).
[Crossref] [PubMed]

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. H. 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] [PubMed]

Wu, T.

Xu, B.

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. H. 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] [PubMed]

Yu, N.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: Generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref] [PubMed]

Zhao, Z.

Y. Li, X. Li, M. Pu, Z. Zhao, X. Ma, Y. Wang, and X. Luo, “Achromatic flat optical components via compensation between structure and material dispersions,” Sci. reports 6, 19885 (2016).
[Crossref]

Zhu, A. Y.

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 (2018).
[Crossref] [PubMed]

Zhu, S.

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 (2018).
[Crossref] [PubMed]

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. H. 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] [PubMed]

Bell Labs Tech. J. (1)

R. M. Foster, “A reactance theorem,” Bell Labs Tech. J. 3, 259–267 (1924).
[Crossref]

IEEE Antennas Propag. Mag. (1)

C. L. Holloway, E. F. Kuester, J. A. Gordon, J. O’Hara, J. Booth, and D. R. Smith, “An overview of the theory and applications of metasurfaces: The two-dimensional equivalents of metamaterials,” IEEE Antennas Propag. Mag. 54, 10–35 (2012).
[Crossref]

IEEE Antennas Wirel. Propag. Lett. (1)

J. P. Wong, A. Epstein, and G. V. Eleftheriades, “Reflectionless wide-angle refracting metasurfaces,” IEEE Antennas Wirel. Propag. Lett. 15, 1293–1296 (2016).
[Crossref]

IEEE Transactions on Antennas Propag. (3)

W. Geyi, P. Jarmuszewski, and Y. Qi, “The Foster reactance theorem for antennas and radiation-Q,” IEEE Transactions on Antennas Propag. 48, 401–408 (2000).
[Crossref]

A. Epstein and G. V. Eleftheriades, “Arbitrary power-conserving field transformations with passive lossless omega-type bianisotropic metasurfaces,” IEEE Transactions on Antennas Propag. 64, 3880–3895 (2016).
[Crossref]

M. Li, M. A. Al-Joumayly, and N. Behdad, “Broadband true-time-delay microwave lenses based on miniaturized element frequency selective surfaces,” IEEE Transactions on Antennas Propag. 61, 1166–1179 (2013).
[Crossref]

IEEE Transactions on Microw. Theory Tech. (1)

C. Pfeiffer and A. Grbic, “Millimeter-wave transmitarrays for wavefront and polarization control,” IEEE Transactions on Microw. Theory Tech. 61, 4407–4417 (2013).
[Crossref]

JOSA B (1)

A. Epstein and G. V. Eleftheriades, “Huygens metasurfaces via the equivalence principle: Design and applications,” JOSA B 33, A31–A50 (2016).
[Crossref]

Laser & Photonics Rev. (1)

A. E. Minovich, A. E. Miroshnichenko, A. Y. Bykov, T. V. Murzina, D. N. Neshev, and Y. S. Kivshar, “Functional and nonlinear optical metasurfaces,” Laser & Photonics Rev. 9, 195–213 (2015).
[Crossref]

Nano letters (1)

M. Khorasaninejad, F. Aieta, P. Kanhaiya, M. A. Kats, P. Genevet, D. Rousso, and F. Capasso, “Achromatic metasurface lens at telecommunication wavelengths,” Nano letters 15, 5358–5362 (2015).
[Crossref] [PubMed]

Nanophotonics (1)

V. S. Asadchy, A. Díaz-Rubio, and S. A. Tretyakov, “Bianisotropic metasurfaces: physics and applications,” Nanophotonics 7, 1069–1094 (2018).
[Crossref]

Nat. Commun. (1)

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. H. 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] [PubMed]

Nat. Nanotechnol. (2)

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 (2018).
[Crossref] [PubMed]

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 (2018).
[Crossref] [PubMed]

Opt. express (2)

Opt. Lett. (1)

Optica (1)

Phys. Rev. Lett. (3)

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] [PubMed]

P.-Y. Chen, C. Argyropoulos, and A. Alù, “Broadening the cloaking bandwidth with non-foster metasurfaces,” Phys. Rev. Lett. 111, 233001 (2013).
[Crossref]

Sci. Reports (1)

J. Mou and Z. Shen, “Broadband and thin magnetic absorber with non-Foster metasurface for admittance matching,” Sci. Reports 7, 6922 (2017).
[Crossref]

Y. Li, X. Li, M. Pu, Z. Zhao, X. Ma, Y. Wang, and X. Luo, “Achromatic flat optical components via compensation between structure and material dispersions,” Sci. reports 6, 19885 (2016).
[Crossref]

Science (3)

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

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

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: Generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref] [PubMed]

Other (1)

G. Lavigne, K. Achouri, V. Asadchy, S. Tretyakov, and C. Caloz, “Susceptibility derivation and experimental demonstration of refracting metasurfaces without spurious diffraction,” IEEE Trans on Antennas Propag. (2018).
[Crossref]

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Figures (5)

Fig. 1
Fig. 1 (a) Metasurface with several different frequencies of incoming plane wave in refracting operation. (b) The Required phase response as a function of position, is shown for three different frequencies, where λ0 is the wavelength of the center frequency. (c) Equivalent circuit model of the three-layered structure.
Fig. 2
Fig. 2 The imaginary component of impedance (reactance) for each layer (blue curve) as a function of Φt (which is proportional to frequency ω) for (a) Huygens and (b) bianisotropic metasurfaces. According to Foster’s theorem, the frequency derivative of the reactance (red curve) must be positive to enable a passive realization. The shading indicates the regions of non-Foster reactance and the crosses mark the transition between Foster and non-Foster regions calculated from Eqs. (5) and (6).
Fig. 3
Fig. 3 Relationship between maximum metasurface size and fractional operating bandwidth for a purely passive realization in (a) Huygens and (b) bianisotropic refracting metasurfaces.
Fig. 4
Fig. 4 (a) Metasurface with several different frequencies of incoming plane wave in focusing operation. (b) The Required phase response as a function of position, is shown for three different frequencies, where λ0 is the wavelength of the center frequency.
Fig. 5
Fig. 5 Relationship between the radius and fractional bandwidth for a metasurface lens with (a) Huygens and (b) bianisotropic realizations. Results are shown for different values of normalized focal length.

Equations (17)

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Φ t ( x , ω ) = ω x n bg ( sin θ out sin θ in ) + Φ 0 ( ω ) ,
Z ( x , ω ) = [ j Z in cot ( Φ t + Φ 0 ) j Z in Z out sin ( Φ t + Φ 0 ) j Z in Z out sin ( Φ t + Φ 0 ) j Z out cot ( Φ t + Φ 0 ) ]
Z 2 ( x , ω ) = Z s 2 Z 12 ( cos ( 2 β s t ) 1 ) 2 det [ Z ] j 2 Z 0 Z 12 sin ( 2 β s t ) Z 1 , 3 ( x , ω ) = Z s det [ Z ] sin ( β s t ) j det [ Z ] cos ( β s t ) + Z s Z sin ( β s t ) , where Z = { Z 11 + Z 12 for Z 1 Z 22 + Z 12 for Z 3
d X n d Φ t > 0 ( n = 1 , 2 , 3 ) .
Φ t , a ( in ) = 2 π m + π 2 Φ 0 , Φ t , b ( in ) = 2 π m + 3 π 2 Φ 0 ,
Φ t , a , b ( out ) = 2 π m + π ± arccos ( Z ¯ ) Φ 0 ( only if 1 < Z ¯ < 1 ) .
Z ¯ = { Z in Z in Z out for Z 1 Z out Z in Z out for Z 3
Δ Φ t = Φ t , b ( in ) Φ t , a ( in ) = π .
Δ f Δ x 1 2 n bg | sin θ out sin θ in | ( Huygens )
Δ Φ t = Φ t , b ( out ) Φ t , b ( in ) = π 2 arccos ( Z ¯ ) .
Δ f Δ x π 2 arccos ( Z ¯ min ) 4 π n bg | sin θ out sin θ in | . ( bianisotropic )
Z ¯ min = min ( cos θ in cos θ out , cos θ out cos θ in ) .
Φ t ( x , ω ) = ω n bg Δ l ( x ) + Φ 0 ( ω ) ,
Δ l ( x ) = ( x 2 + F 2 F )
Δ l ( norm ) ( x ) = Δ l ( x ) x = 1 cos [ θ ( x ) ] sin [ θ ( x ) ] .
Δ f R 1 2 n bg Δ l max ( norm ) ( Huygens )
Δ f R π 2 arccos ( Z ¯ min ) 4 π n bg Δ l max ( norm ) . ( bianisotropic )

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