Abstract

We consider the problem of light transmission from a high refractive index medium into a low-index environment. While total internal reflection severely limits such transmission in systems with smooth interfaces, diffractive metasurfaces may help out-couple light that enters an interface at blazing angles. We demonstrate that the profile of the structured interface can be numerically optimized to target a specific emission pattern. Our study suggests that while metasurfaces can help to out-couple light from a range of incident directions, there exists a universal limit for total transmission efficiency that depends only on the dielectric properties of the two materials and is independent of the profile and the composition of the metasurface coupler.

© 2017 Optical Society of America

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References

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  1. H. K. Raut, V. A. Ganesh, A. S. Nair, and S. Tamakrishna, “Anti-reflective coatings: a critical in-depth review,” Energy Environ. Sci. 4, 3779–3804 (2011).
    [Crossref]
  2. S. J. Wilson and M. C. Hutley, “The optical properties of ‘moth eye’ antireflection surfaces,” J. Modern Opt. 29, 993–1009 (1982).
  3. J. J. Kim, J. Lee, S.-P. Yang, H. G. Kim, H.-S. Kweon, S. Yoo, and K.-H. Jeong, “Biology inspired organic light-emitting diodes,” Nano Lett. 16, 2994–3000 (2016).
    [Crossref]
  4. L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media, 2nd ed. (1982), Vol. 8.
  5. A. Niv, G. Biener, V. Kleiner, and E. Hasman, “Propagation-invariant vectorial Bessel beams obtained by use of quantized Pancharatnam–Berry phase optical elements,” Opt. Lett. 29, 238–240 (2004).
    [Crossref]
  6. 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]
  7. S. Sun, Q. He, S. Xiao, Q. Xu, X. Li, and L. Zhou, “Gradient-index meta-surfaces as a bridge linking propagating waves and surface waves,” Nat. Mater. 11, 426–431 (2012).
    [Crossref]
  8. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science 339, 1232009 (2013).
    [Crossref]
  9. 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]
  10. V. Galdi, V. Pierro, G. Castaldi, and N. Engheta, “Genetically optimized metasurface pairs for wideband out-of-phase mutual response,” IEEE Antennas Wireless Propag. Lett. 7, 788–791 (2008).
    [Crossref]
  11. M. I. Shalaev, J. Sun, A. Tsukernik, A. Pandey, K. Nikolskiy, and N. Litchinitser, “High-efficiency all-dielectric metasurfaces for ultracompact beam manipulation in transmission mode,” Nano Lett. 15, 6261–6266 (2015).
    [Crossref]
  12. E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1998), Vol. 3.
  13. C. Patrignani, et al. (Particle Data Group), “The review of particle physics,” Chin. Phys. C 40, 100001 (2016).
    [Crossref]
  14. K. X. Wang, Z. Yu, S. Sandhu, V. Liu, and S. Fan, “Condition for perfect antireflection by optical resonance at material interface,” Optica 1, 388–395 (2014).
    [Crossref]
  15. B. Zhang, J. Hendrickson, N. Nader, H.-T. Chen, and J. Guo, “Metasurface optical antireflection coating,” Appl. Phys. Lett. 105, 241113 (2014).
    [Crossref]
  16. M. G. Moharam and T. K. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 71, 811–818 (1981).
    [Crossref]
  17. https://viktor-podolskiy-research.wiki.uml.edu/RCWA , retrieved Jan. 2017.
  18. R. Eberhart and J. Kennedy, “A new optimizer using particle swarm theory,” in Proceedings of the Sixth International Symposium on Micro Machine and Human Science (1995), Vol. 1, pp. 39–43.
  19. J. Kennedy, “Particle swarm optimization,” in Encyclopedia of Machine Learning (2001), pp. 760–766.
  20. C. M. Roberts, S. Inampudi, and V. A. Podolskiy, “Diffractive interface theory: nonlocal susceptibility approach to the optics of metasurfaces,” Opt. Express 23, 2764–2776 (2015).
    [Crossref]
  21. E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).
    [Crossref]
  22. L. Novotny and B. Hecht, Principles of Nano-Optics, 2nd ed. (Cambridge University, 2012).

2016 (2)

J. J. Kim, J. Lee, S.-P. Yang, H. G. Kim, H.-S. Kweon, S. Yoo, and K.-H. Jeong, “Biology inspired organic light-emitting diodes,” Nano Lett. 16, 2994–3000 (2016).
[Crossref]

C. Patrignani, et al. (Particle Data Group), “The review of particle physics,” Chin. Phys. C 40, 100001 (2016).
[Crossref]

2015 (2)

C. M. Roberts, S. Inampudi, and V. A. Podolskiy, “Diffractive interface theory: nonlocal susceptibility approach to the optics of metasurfaces,” Opt. Express 23, 2764–2776 (2015).
[Crossref]

M. I. Shalaev, J. Sun, A. Tsukernik, A. Pandey, K. Nikolskiy, and N. Litchinitser, “High-efficiency all-dielectric metasurfaces for ultracompact beam manipulation in transmission mode,” Nano Lett. 15, 6261–6266 (2015).
[Crossref]

2014 (2)

K. X. Wang, Z. Yu, S. Sandhu, V. Liu, and S. Fan, “Condition for perfect antireflection by optical resonance at material interface,” Optica 1, 388–395 (2014).
[Crossref]

B. Zhang, J. Hendrickson, N. Nader, H.-T. Chen, and J. Guo, “Metasurface optical antireflection coating,” Appl. Phys. Lett. 105, 241113 (2014).
[Crossref]

2013 (2)

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

2012 (1)

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

2011 (2)

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]

H. K. Raut, V. A. Ganesh, A. S. Nair, and S. Tamakrishna, “Anti-reflective coatings: a critical in-depth review,” Energy Environ. Sci. 4, 3779–3804 (2011).
[Crossref]

2008 (1)

V. Galdi, V. Pierro, G. Castaldi, and N. Engheta, “Genetically optimized metasurface pairs for wideband out-of-phase mutual response,” IEEE Antennas Wireless Propag. Lett. 7, 788–791 (2008).
[Crossref]

2004 (1)

1982 (1)

S. J. Wilson and M. C. Hutley, “The optical properties of ‘moth eye’ antireflection surfaces,” J. Modern Opt. 29, 993–1009 (1982).

1981 (1)

1946 (1)

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).
[Crossref]

Aieta, F.

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]

Alù, A.

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]

Biener, G.

Boltasseva, A.

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

Capasso, F.

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]

Castaldi, G.

V. Galdi, V. Pierro, G. Castaldi, and N. Engheta, “Genetically optimized metasurface pairs for wideband out-of-phase mutual response,” IEEE Antennas Wireless Propag. Lett. 7, 788–791 (2008).
[Crossref]

Chen, H.-T.

B. Zhang, J. Hendrickson, N. Nader, H.-T. Chen, and J. Guo, “Metasurface optical antireflection coating,” Appl. Phys. Lett. 105, 241113 (2014).
[Crossref]

Eberhart, R.

R. Eberhart and J. Kennedy, “A new optimizer using particle swarm theory,” in Proceedings of the Sixth International Symposium on Micro Machine and Human Science (1995), Vol. 1, pp. 39–43.

Engheta, N.

V. Galdi, V. Pierro, G. Castaldi, and N. Engheta, “Genetically optimized metasurface pairs for wideband out-of-phase mutual response,” IEEE Antennas Wireless Propag. Lett. 7, 788–791 (2008).
[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]

Fan, S.

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]

Galdi, V.

V. Galdi, V. Pierro, G. Castaldi, and N. Engheta, “Genetically optimized metasurface pairs for wideband out-of-phase mutual response,” IEEE Antennas Wireless Propag. Lett. 7, 788–791 (2008).
[Crossref]

Ganesh, V. A.

H. K. Raut, V. A. Ganesh, A. S. Nair, and S. Tamakrishna, “Anti-reflective coatings: a critical in-depth review,” Energy Environ. Sci. 4, 3779–3804 (2011).
[Crossref]

Gaylord, T. K.

Genevet, 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]

Guo, J.

B. Zhang, J. Hendrickson, N. Nader, H.-T. Chen, and J. Guo, “Metasurface optical antireflection coating,” Appl. Phys. Lett. 105, 241113 (2014).
[Crossref]

Hasman, E.

He, Q.

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

Hecht, B.

L. Novotny and B. Hecht, Principles of Nano-Optics, 2nd ed. (Cambridge University, 2012).

Hendrickson, J.

B. Zhang, J. Hendrickson, N. Nader, H.-T. Chen, and J. Guo, “Metasurface optical antireflection coating,” Appl. Phys. Lett. 105, 241113 (2014).
[Crossref]

Hutley, M. C.

S. J. Wilson and M. C. Hutley, “The optical properties of ‘moth eye’ antireflection surfaces,” J. Modern Opt. 29, 993–1009 (1982).

Inampudi, S.

Jeong, K.-H.

J. J. Kim, J. Lee, S.-P. Yang, H. G. Kim, H.-S. Kweon, S. Yoo, and K.-H. Jeong, “Biology inspired organic light-emitting diodes,” Nano Lett. 16, 2994–3000 (2016).
[Crossref]

Kats, M. A.

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]

Kennedy, J.

R. Eberhart and J. Kennedy, “A new optimizer using particle swarm theory,” in Proceedings of the Sixth International Symposium on Micro Machine and Human Science (1995), Vol. 1, pp. 39–43.

J. Kennedy, “Particle swarm optimization,” in Encyclopedia of Machine Learning (2001), pp. 760–766.

Kildishev, V.

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

Kim, H. G.

J. J. Kim, J. Lee, S.-P. Yang, H. G. Kim, H.-S. Kweon, S. Yoo, and K.-H. Jeong, “Biology inspired organic light-emitting diodes,” Nano Lett. 16, 2994–3000 (2016).
[Crossref]

Kim, J. J.

J. J. Kim, J. Lee, S.-P. Yang, H. G. Kim, H.-S. Kweon, S. Yoo, and K.-H. Jeong, “Biology inspired organic light-emitting diodes,” Nano Lett. 16, 2994–3000 (2016).
[Crossref]

Kleiner, V.

Kweon, H.-S.

J. J. Kim, J. Lee, S.-P. Yang, H. G. Kim, H.-S. Kweon, S. Yoo, and K.-H. Jeong, “Biology inspired organic light-emitting diodes,” Nano Lett. 16, 2994–3000 (2016).
[Crossref]

Landau, L. D.

L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media, 2nd ed. (1982), Vol. 8.

Lee, J.

J. J. Kim, J. Lee, S.-P. Yang, H. G. Kim, H.-S. Kweon, S. Yoo, and K.-H. Jeong, “Biology inspired organic light-emitting diodes,” Nano Lett. 16, 2994–3000 (2016).
[Crossref]

Li, X.

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

Lifshitz, E. M.

L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media, 2nd ed. (1982), Vol. 8.

Litchinitser, N.

M. I. Shalaev, J. Sun, A. Tsukernik, A. Pandey, K. Nikolskiy, and N. Litchinitser, “High-efficiency all-dielectric metasurfaces for ultracompact beam manipulation in transmission mode,” Nano Lett. 15, 6261–6266 (2015).
[Crossref]

Liu, V.

Moharam, M. G.

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]

Nader, N.

B. Zhang, J. Hendrickson, N. Nader, H.-T. Chen, and J. Guo, “Metasurface optical antireflection coating,” Appl. Phys. Lett. 105, 241113 (2014).
[Crossref]

Nair, A. S.

H. K. Raut, V. A. Ganesh, A. S. Nair, and S. Tamakrishna, “Anti-reflective coatings: a critical in-depth review,” Energy Environ. Sci. 4, 3779–3804 (2011).
[Crossref]

Nikolskiy, K.

M. I. Shalaev, J. Sun, A. Tsukernik, A. Pandey, K. Nikolskiy, and N. Litchinitser, “High-efficiency all-dielectric metasurfaces for ultracompact beam manipulation in transmission mode,” Nano Lett. 15, 6261–6266 (2015).
[Crossref]

Niv, A.

Novotny, L.

L. Novotny and B. Hecht, Principles of Nano-Optics, 2nd ed. (Cambridge University, 2012).

Palik, E. D.

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

Pandey, A.

M. I. Shalaev, J. Sun, A. Tsukernik, A. Pandey, K. Nikolskiy, and N. Litchinitser, “High-efficiency all-dielectric metasurfaces for ultracompact beam manipulation in transmission mode,” Nano Lett. 15, 6261–6266 (2015).
[Crossref]

Patrignani, C.

C. Patrignani, et al. (Particle Data Group), “The review of particle physics,” Chin. Phys. C 40, 100001 (2016).
[Crossref]

Pierro, V.

V. Galdi, V. Pierro, G. Castaldi, and N. Engheta, “Genetically optimized metasurface pairs for wideband out-of-phase mutual response,” IEEE Antennas Wireless Propag. Lett. 7, 788–791 (2008).
[Crossref]

Pitaevskii, L. P.

L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media, 2nd ed. (1982), Vol. 8.

Podolskiy, V. A.

Purcell, E. M.

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).
[Crossref]

Raut, H. K.

H. K. Raut, V. A. Ganesh, A. S. Nair, and S. Tamakrishna, “Anti-reflective coatings: a critical in-depth review,” Energy Environ. Sci. 4, 3779–3804 (2011).
[Crossref]

Roberts, C. M.

Sandhu, S.

Shalaev, M. I.

M. I. Shalaev, J. Sun, A. Tsukernik, A. Pandey, K. Nikolskiy, and N. Litchinitser, “High-efficiency all-dielectric metasurfaces for ultracompact beam manipulation in transmission mode,” Nano Lett. 15, 6261–6266 (2015).
[Crossref]

Shalaev, V. M.

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

Sun, J.

M. I. Shalaev, J. Sun, A. Tsukernik, A. Pandey, K. Nikolskiy, and N. Litchinitser, “High-efficiency all-dielectric metasurfaces for ultracompact beam manipulation in transmission mode,” Nano Lett. 15, 6261–6266 (2015).
[Crossref]

Sun, S.

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

Tamakrishna, S.

H. K. Raut, V. A. Ganesh, A. S. Nair, and S. Tamakrishna, “Anti-reflective coatings: a critical in-depth review,” Energy Environ. Sci. 4, 3779–3804 (2011).
[Crossref]

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]

Tsukernik, A.

M. I. Shalaev, J. Sun, A. Tsukernik, A. Pandey, K. Nikolskiy, and N. Litchinitser, “High-efficiency all-dielectric metasurfaces for ultracompact beam manipulation in transmission mode,” Nano Lett. 15, 6261–6266 (2015).
[Crossref]

Wang, K. X.

Wilson, S. J.

S. J. Wilson and M. C. Hutley, “The optical properties of ‘moth eye’ antireflection surfaces,” J. Modern Opt. 29, 993–1009 (1982).

Xiao, S.

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

Xu, Q.

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

Yang, S.-P.

J. J. Kim, J. Lee, S.-P. Yang, H. G. Kim, H.-S. Kweon, S. Yoo, and K.-H. Jeong, “Biology inspired organic light-emitting diodes,” Nano Lett. 16, 2994–3000 (2016).
[Crossref]

Yoo, S.

J. J. Kim, J. Lee, S.-P. Yang, H. G. Kim, H.-S. Kweon, S. Yoo, and K.-H. Jeong, “Biology inspired organic light-emitting diodes,” Nano Lett. 16, 2994–3000 (2016).
[Crossref]

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]

Yu, Z.

Zhang, B.

B. Zhang, J. Hendrickson, N. Nader, H.-T. Chen, and J. Guo, “Metasurface optical antireflection coating,” Appl. Phys. Lett. 105, 241113 (2014).
[Crossref]

Zhou, L.

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

Appl. Phys. Lett. (1)

B. Zhang, J. Hendrickson, N. Nader, H.-T. Chen, and J. Guo, “Metasurface optical antireflection coating,” Appl. Phys. Lett. 105, 241113 (2014).
[Crossref]

Chin. Phys. C (1)

C. Patrignani, et al. (Particle Data Group), “The review of particle physics,” Chin. Phys. C 40, 100001 (2016).
[Crossref]

Energy Environ. Sci. (1)

H. K. Raut, V. A. Ganesh, A. S. Nair, and S. Tamakrishna, “Anti-reflective coatings: a critical in-depth review,” Energy Environ. Sci. 4, 3779–3804 (2011).
[Crossref]

IEEE Antennas Wireless Propag. Lett. (1)

V. Galdi, V. Pierro, G. Castaldi, and N. Engheta, “Genetically optimized metasurface pairs for wideband out-of-phase mutual response,” IEEE Antennas Wireless Propag. Lett. 7, 788–791 (2008).
[Crossref]

J. Modern Opt. (1)

S. J. Wilson and M. C. Hutley, “The optical properties of ‘moth eye’ antireflection surfaces,” J. Modern Opt. 29, 993–1009 (1982).

J. Opt. Soc. Am. (1)

Nano Lett. (2)

M. I. Shalaev, J. Sun, A. Tsukernik, A. Pandey, K. Nikolskiy, and N. Litchinitser, “High-efficiency all-dielectric metasurfaces for ultracompact beam manipulation in transmission mode,” Nano Lett. 15, 6261–6266 (2015).
[Crossref]

J. J. Kim, J. Lee, S.-P. Yang, H. G. Kim, H.-S. Kweon, S. Yoo, and K.-H. Jeong, “Biology inspired organic light-emitting diodes,” Nano Lett. 16, 2994–3000 (2016).
[Crossref]

Nat. Mater. (1)

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

Opt. Express (1)

Opt. Lett. (1)

Optica (1)

Phys. Rev. (1)

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).
[Crossref]

Phys. Rev. Lett. (1)

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]

Science (2)

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]

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

Other (6)

L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media, 2nd ed. (1982), Vol. 8.

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

https://viktor-podolskiy-research.wiki.uml.edu/RCWA , retrieved Jan. 2017.

R. Eberhart and J. Kennedy, “A new optimizer using particle swarm theory,” in Proceedings of the Sixth International Symposium on Micro Machine and Human Science (1995), Vol. 1, pp. 39–43.

J. Kennedy, “Particle swarm optimization,” in Encyclopedia of Machine Learning (2001), pp. 760–766.

L. Novotny and B. Hecht, Principles of Nano-Optics, 2nd ed. (Cambridge University, 2012).

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Figures (6)

Fig. 1.
Fig. 1.

Total transmitted power between a dielectric ( n = 3.3 ) and air ( n = 1 ) . TM- and TE-polarized light are represented by red and blue lines, respectively; panel (a) represents transmission from air into a dielectric, and panel (b) illustrates transmission from a dielectric into air.

Fig. 2.
Fig. 2.

Optimal extraction of light from high-index dielectric for the grating optimized with a particle swarm technique ( Λ = λ 0 / 4 , f = 0.65 , and h = 0.13 λ 0 ). Yellow, green, and blue lines represent specular TM transmission, respectively, as well as diffraction into m = + 1 and m = 1 orders. Total transmission is shown as a dotted black line. Panels (a) and (b) represent the same process as seen from the dielectric (a) and from air (b). Panel (c) illustrates the geometry of a single unit cell for the optimization study.

Fig. 3.
Fig. 3.

(a) and (b) Optimized transmission from the high-index media into low-index environment, as seen from dielectric (a) and air (b), obtained with genetic algorithm for Λ = 0.99 λ 0 , h = 0.44 λ 0 , and N = 101 . Lines of different colors represent contributions from individual diffraction orders (yellow, green, and blue lines correspond to specular, m = + 1 , and m = 1 channels); dashed black line represents total transmission. Panel (c) illustrates profile of the optimal metasurface, with white and black regions corresponding to air and high-index dielectric, respectively.

Fig. 4.
Fig. 4.

Illustration of the thermodynamic limit on total transmission by a diffractive interface. The metasurface that has no upper limit on transmission into a given output angle enables the heat transfer between the three blackbodies, initially in thermal equilibrium. Only one diffraction order is shown for clarity.

Fig. 5.
Fig. 5.

Maximum total transmission through the interface [see Eq. (1)] for different substrate/superstrate index ratios/polarizations. Line and symbols represent Eq. (2) and the results of optimization studies, respectively.

Fig. 6.
Fig. 6.

Nearly angle-independent transmission from high-index into low-index media with diffractive metasurface. (a) and (b) Total transmission for TM-polarized light as seen from dielectric (a) and air (b) side. Black line represents total transmission; red line represents optimization target; Λ = 9.93 λ 0 , h = 0.31 λ 0 , N = 201 ; minimum feature size 0.049 λ 0 . Panel (c) shows the profile of optimal metasurface; black and white regions represent dielectric and air, respectively.

Equations (2)

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FOM = c 2 ω n 1 m = ω n 1 c ω n 1 c T m ( k x ) d k x ,
FOM max = n 2 n 1 .

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