Abstract

We present a formalism for understanding the electromagnetism of metasurfaces, optically thin composite films with engineered diffraction. The technique, diffractive interface theory (DIT), takes explicit advantage of the small optical thickness of a metasurface, eliminating the need for solving for light propagation inside the film and providing a direct link between the spatial profile of a metasurface and its diffractive properties. Predictions of DIT are compared with full-wave numerical solutions of Maxwell’s equations, demonstrating DIT’s validity and computational advantages for optically thin structures. Applications of the DIT range from understanding of fundamentals of light-matter interaction in metasurfaces to efficient analysis of generalized refraction to metasurface optimization.

© 2015 Optical Society of America

Full Article  |  PDF Article

Corrections

Christopher M. Roberts, Sandeep Inampudi, and Viktor A. Podolskiy, "Diffractive Interface Theory: nonlocal polarizability approach to the optics of metasurfaces: erratum," Opt. Express 25, 13834-13835 (2017)
https://www.osapublishing.org/oe/abstract.cfm?uri=oe-25-12-13834

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References

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2014 (3)

J. Wong, M. Selvanayagam, and G. V. Eleftheriades, “Design of unit cells and demonstration of methods for synthesizing huygens metasurfaces,” Photon. Nanostruct. 12, 360–375 (2014).
[Crossref]

B. M. Wells, A. V. Zayats, and V. A. Podolskiy, “Nonlocal optics of plasmonic nanowire metamaterials,” Phys. Rev. B 89, 035111 (2014).
[Crossref]

S. Law, C. Roberts, T. Kilpatrick, L. Yu, T. Ribaudo, E. Shaner, V. Podolskiy, and D. Wasserman, “All-semiconductor negative-index plasmonic absorbers,” Phys. Rev. Letters 112, 017401 (2014).
[Crossref]

2013 (4)

N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. Dalvit, and H.-T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340, 1304–1307 (2013).
[Crossref] [PubMed]

S. Xiao, Q. He, C. Qu, X. Li, S. Sun, and L. Zhou, “Mode-expansion theory for inhomogeneous meta-surfaces,” Opt. Express 21, 27219–27237 (2013).
[Crossref] [PubMed]

M. Farmahini-Farahani, J. Cheng, and H. Mosallaei, “Metasurfaces nanoantennas for light processing,” J. Opt. Soc. Am. B 30, 2365–2370 (2013).
[Crossref]

Y. Liu and X. Zhang, “Metasurfaces for manipulating surface plasmons,” Appl. Phys. Lett. 103, 141101 (2013).
[Crossref]

2012 (3)

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

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science 335, 427 (2012).
[Crossref]

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. Materials 11, 426–431 (2012).
[Crossref]

2011 (3)

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]

Y. Zhao and A. Alù, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B 84, 205428 (2011).
[Crossref]

Y. Zhao, N. Engheta, and A. Alù, “Homogenization of plasmonic metasurfaces modeled as transmission-line loads,” Metamaterials 5, 90–96 (2011).
[Crossref]

2010 (1)

X.X. Liu and A. Alù, “Subwavelength leaky-wave optical nanoantennas: Directive radiation from linear arrays of plasmonic nanoparticles,” Phys. Rev. B 82, 144305 (2010)
[Crossref]

2009 (1)

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

2007 (1)

F. J. García de Abajo, “Colloquium: Light scattering by particle and hole arrays,” Rev. Mod. Phys. 79, 1267–1290 (2007).
[Crossref]

2006 (1)

A. Alù and N. Engheta, “Theory of linear chains of metamaterial/plasmonic particles as subdiffraction optical nanotransmission lines,” Phys. Rev”. B 74205436 (2006).

2005 (1)

N. Dahan, A. Niv, G. Biener, V. Kleiner, and E. Hasman, “Space-variant polarization manipulation of a thermal emission by a SiO2 subwavelength grating supporting surface phonon-polaritons,” Appl. Phys. Lett. 86, 191102 (2005).
[Crossref]

2004 (1)

2001 (1)

S. Steshenko, F. Capalino, P. Alitalo, and S. Tretyakov, Effective model and investigation of the near-field enhancement and subwavelength imaging properties of multilayer arrays of plasmonic nanospheres, Phys. Rev. E 84, 016607 (2001)
[Crossref]

1998 (1)

N. Stefanou, V. Yannopapas, and A. Modinos, “Heterostructures of photonic crystals: frequency bands and transmission coefficients,” Comput. Phys. Commun. 113, 49–77 (1998).
[Crossref]

1990 (1)

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990).
[Crossref] [PubMed]

1988 (1)

M. Idemen, “Straightforward derivation of boundary conditions on sheet simulating an anisotropic thin layer,” Electron. Lett. 24, 663–665 (1988).
[Crossref]

1981 (1)

1977 (1)

1972 (1)

P. Johnson and R. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370 (1972).
[Crossref]

1956 (1)

S. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466 (1956).

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] [PubMed]

Alitalo, P.

S. Steshenko, F. Capalino, P. Alitalo, and S. Tretyakov, Effective model and investigation of the near-field enhancement and subwavelength imaging properties of multilayer arrays of plasmonic nanospheres, Phys. Rev. E 84, 016607 (2001)
[Crossref]

Alù, A.

Y. Zhao and A. Alù, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B 84, 205428 (2011).
[Crossref]

Y. Zhao, N. Engheta, and A. Alù, “Homogenization of plasmonic metasurfaces modeled as transmission-line loads,” Metamaterials 5, 90–96 (2011).
[Crossref]

X.X. Liu and A. Alù, “Subwavelength leaky-wave optical nanoantennas: Directive radiation from linear arrays of plasmonic nanoparticles,” Phys. Rev. B 82, 144305 (2010)
[Crossref]

A. Alù and N. Engheta, “Theory of linear chains of metamaterial/plasmonic particles as subdiffraction optical nanotransmission lines,” Phys. Rev”. B 74205436 (2006).

Azad, A. K.

N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. Dalvit, and H.-T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340, 1304–1307 (2013).
[Crossref] [PubMed]

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

Biener, G.

N. Dahan, A. Niv, G. Biener, V. Kleiner, and E. Hasman, “Space-variant polarization manipulation of a thermal emission by a SiO2 subwavelength grating supporting surface phonon-polaritons,” Appl. Phys. Lett. 86, 191102 (2005).
[Crossref]

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] [PubMed]

Boltasseva, A.

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science 335, 427 (2012).
[Crossref]

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

Bomzon, Z.

Z. Bomzon and E. Hasman, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett.77 (2000).

Capalino, F.

S. Steshenko, F. Capalino, P. Alitalo, and S. Tretyakov, Effective model and investigation of the near-field enhancement and subwavelength imaging properties of multilayer arrays of plasmonic nanospheres, Phys. Rev. E 84, 016607 (2001)
[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] [PubMed]

Chan, C. T.

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990).
[Crossref] [PubMed]

Chen, H.-T.

N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. Dalvit, and H.-T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340, 1304–1307 (2013).
[Crossref] [PubMed]

Cheng, J.

Chowdhury, D. R.

N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. Dalvit, and H.-T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340, 1304–1307 (2013).
[Crossref] [PubMed]

Christy, R.

P. Johnson and R. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370 (1972).
[Crossref]

Dahan, N.

N. Dahan, A. Niv, G. Biener, V. Kleiner, and E. Hasman, “Space-variant polarization manipulation of a thermal emission by a SiO2 subwavelength grating supporting surface phonon-polaritons,” Appl. Phys. Lett. 86, 191102 (2005).
[Crossref]

Dalvit, D. A.

N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. Dalvit, and H.-T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340, 1304–1307 (2013).
[Crossref] [PubMed]

Dienstfrey, A.

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

Eleftheriades, G. V.

J. Wong, M. Selvanayagam, and G. V. Eleftheriades, “Design of unit cells and demonstration of methods for synthesizing huygens metasurfaces,” Photon. Nanostruct. 12, 360–375 (2014).
[Crossref]

Emani, N. K.

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science 335, 427 (2012).
[Crossref]

Engheta, N.

Y. Zhao, N. Engheta, and A. Alù, “Homogenization of plasmonic metasurfaces modeled as transmission-line loads,” Metamaterials 5, 90–96 (2011).
[Crossref]

A. Alù and N. Engheta, “Theory of linear chains of metamaterial/plasmonic particles as subdiffraction optical nanotransmission lines,” Phys. Rev”. B 74205436 (2006).

Farmahini-Farahani, M.

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]

García de Abajo, F. J.

F. J. García de Abajo, “Colloquium: Light scattering by particle and hole arrays,” Rev. Mod. Phys. 79, 1267–1290 (2007).
[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] [PubMed]

Goldberg, D.E.

D.E. Goldberg, Genetic Algorithms in Search, Optimization, & Machine Learning (Addison-Wesley1989)

Grady, N. K.

N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. Dalvit, and H.-T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340, 1304–1307 (2013).
[Crossref] [PubMed]

Hagness, S.

A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-difference Time-domain Method, Artech House antennas and propagation library (Artech House, 2005).

Hasman, E.

N. Dahan, A. Niv, G. Biener, V. Kleiner, and E. Hasman, “Space-variant polarization manipulation of a thermal emission by a SiO2 subwavelength grating supporting surface phonon-polaritons,” Appl. Phys. Lett. 86, 191102 (2005).
[Crossref]

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] [PubMed]

Z. Bomzon and E. Hasman, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett.77 (2000).

He, Q.

S. Xiao, Q. He, C. Qu, X. Li, S. Sun, and L. Zhou, “Mode-expansion theory for inhomogeneous meta-surfaces,” Opt. Express 21, 27219–27237 (2013).
[Crossref] [PubMed]

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. Materials 11, 426–431 (2012).
[Crossref]

Heyes, J. E.

N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. Dalvit, and H.-T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340, 1304–1307 (2013).
[Crossref] [PubMed]

Ho, K. M.

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990).
[Crossref] [PubMed]

Holloway, C. L.

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

Hong, C. S.

Idemen, M.

M. Idemen, “Straightforward derivation of boundary conditions on sheet simulating an anisotropic thin layer,” Electron. Lett. 24, 663–665 (1988).
[Crossref]

Jackson, J.

J. Jackson, Classical Electrodynamics (Wiley, 1998).

Jin, J.

J. Jin, Finite Element-Boundary Element Methods for Electromagnetic Scattering (University of Michigan, 1989).

Johnson, P.

P. Johnson and R. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370 (1972).
[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] [PubMed]

Kildishev, A. V.

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science 335, 427 (2012).
[Crossref]

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

Kilpatrick, T.

S. Law, C. Roberts, T. Kilpatrick, L. Yu, T. Ribaudo, E. Shaner, V. Podolskiy, and D. Wasserman, “All-semiconductor negative-index plasmonic absorbers,” Phys. Rev. Letters 112, 017401 (2014).
[Crossref]

Kleiner, V.

N. Dahan, A. Niv, G. Biener, V. Kleiner, and E. Hasman, “Space-variant polarization manipulation of a thermal emission by a SiO2 subwavelength grating supporting surface phonon-polaritons,” Appl. Phys. Lett. 86, 191102 (2005).
[Crossref]

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] [PubMed]

Kuester, E. F.

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

Larouche, S.

Law, S.

S. Law, C. Roberts, T. Kilpatrick, L. Yu, T. Ribaudo, E. Shaner, V. Podolskiy, and D. Wasserman, “All-semiconductor negative-index plasmonic absorbers,” Phys. Rev. Letters 112, 017401 (2014).
[Crossref]

Li, X.

S. Xiao, Q. He, C. Qu, X. Li, S. Sun, and L. Zhou, “Mode-expansion theory for inhomogeneous meta-surfaces,” Opt. Express 21, 27219–27237 (2013).
[Crossref] [PubMed]

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. Materials 11, 426–431 (2012).
[Crossref]

Liu, X.X.

X.X. Liu and A. Alù, “Subwavelength leaky-wave optical nanoantennas: Directive radiation from linear arrays of plasmonic nanoparticles,” Phys. Rev. B 82, 144305 (2010)
[Crossref]

Liu, Y.

Y. Liu and X. Zhang, “Metasurfaces for manipulating surface plasmons,” Appl. Phys. Lett. 103, 141101 (2013).
[Crossref]

Milton, G.

G. Milton, The Theory of Composites, Cambridge Monographs on Applied and Computational Mathematics (Cambridge University, 2002).
[Crossref]

Modinos, A.

N. Stefanou, V. Yannopapas, and A. Modinos, “Heterostructures of photonic crystals: frequency bands and transmission coefficients,” Comput. Phys. Commun. 113, 49–77 (1998).
[Crossref]

Moharam, M. G.

Mosallaei, H.

Ni, X.

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science 335, 427 (2012).
[Crossref]

Niv, A.

N. Dahan, A. Niv, G. Biener, V. Kleiner, and E. Hasman, “Space-variant polarization manipulation of a thermal emission by a SiO2 subwavelength grating supporting surface phonon-polaritons,” Appl. Phys. Lett. 86, 191102 (2005).
[Crossref]

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] [PubMed]

Noginov, M.

M. Noginov and V. Podolskiy, Tutorials in Metamaterials, Series in Nano-Optics and Nanophotonics (Taylor & Francis, 2011).

O’Hara, J. F.

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

Pekar, S.

S. Pekar, Sov. Phys. JETP6, 785 (1958).

Podolskiy, V.

S. Law, C. Roberts, T. Kilpatrick, L. Yu, T. Ribaudo, E. Shaner, V. Podolskiy, and D. Wasserman, “All-semiconductor negative-index plasmonic absorbers,” Phys. Rev. Letters 112, 017401 (2014).
[Crossref]

M. Noginov and V. Podolskiy, Tutorials in Metamaterials, Series in Nano-Optics and Nanophotonics (Taylor & Francis, 2011).

Podolskiy, V. A.

B. M. Wells, A. V. Zayats, and V. A. Podolskiy, “Nonlocal optics of plasmonic nanowire metamaterials,” Phys. Rev. B 89, 035111 (2014).
[Crossref]

Qu, C.

Raether, H.

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings, Springer Tracts in Modern Physics (Springer Berlin Heidelberg, 2013).

Reiten, M. T.

N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. Dalvit, and H.-T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340, 1304–1307 (2013).
[Crossref] [PubMed]

Ribaudo, T.

S. Law, C. Roberts, T. Kilpatrick, L. Yu, T. Ribaudo, E. Shaner, V. Podolskiy, and D. Wasserman, “All-semiconductor negative-index plasmonic absorbers,” Phys. Rev. Letters 112, 017401 (2014).
[Crossref]

Roberts, C.

S. Law, C. Roberts, T. Kilpatrick, L. Yu, T. Ribaudo, E. Shaner, V. Podolskiy, and D. Wasserman, “All-semiconductor negative-index plasmonic absorbers,” Phys. Rev. Letters 112, 017401 (2014).
[Crossref]

Rytov, S.

S. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466 (1956).

Selvanayagam, M.

J. Wong, M. Selvanayagam, and G. V. Eleftheriades, “Design of unit cells and demonstration of methods for synthesizing huygens metasurfaces,” Photon. Nanostruct. 12, 360–375 (2014).
[Crossref]

Shalaev, V. M.

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science 335, 427 (2012).
[Crossref]

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

Shaner, E.

S. Law, C. Roberts, T. Kilpatrick, L. Yu, T. Ribaudo, E. Shaner, V. Podolskiy, and D. Wasserman, “All-semiconductor negative-index plasmonic absorbers,” Phys. Rev. Letters 112, 017401 (2014).
[Crossref]

Smith, D. R.

Soukoulis, C. M.

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990).
[Crossref] [PubMed]

Stefanou, N.

N. Stefanou, V. Yannopapas, and A. Modinos, “Heterostructures of photonic crystals: frequency bands and transmission coefficients,” Comput. Phys. Commun. 113, 49–77 (1998).
[Crossref]

Steshenko, S.

S. Steshenko, F. Capalino, P. Alitalo, and S. Tretyakov, Effective model and investigation of the near-field enhancement and subwavelength imaging properties of multilayer arrays of plasmonic nanospheres, Phys. Rev. E 84, 016607 (2001)
[Crossref]

Sun, S.

S. Xiao, Q. He, C. Qu, X. Li, S. Sun, and L. Zhou, “Mode-expansion theory for inhomogeneous meta-surfaces,” Opt. Express 21, 27219–27237 (2013).
[Crossref] [PubMed]

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. Materials 11, 426–431 (2012).
[Crossref]

Taflove, A.

A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-difference Time-domain Method, Artech House antennas and propagation library (Artech House, 2005).

Taylor, A. J.

N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. Dalvit, and H.-T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340, 1304–1307 (2013).
[Crossref] [PubMed]

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

Tretyakov, S.

S. Steshenko, F. Capalino, P. Alitalo, and S. Tretyakov, Effective model and investigation of the near-field enhancement and subwavelength imaging properties of multilayer arrays of plasmonic nanospheres, Phys. Rev. E 84, 016607 (2001)
[Crossref]

Wasserman, D.

S. Law, C. Roberts, T. Kilpatrick, L. Yu, T. Ribaudo, E. Shaner, V. Podolskiy, and D. Wasserman, “All-semiconductor negative-index plasmonic absorbers,” Phys. Rev. Letters 112, 017401 (2014).
[Crossref]

Wells, B. M.

B. M. Wells, A. V. Zayats, and V. A. Podolskiy, “Nonlocal optics of plasmonic nanowire metamaterials,” Phys. Rev. B 89, 035111 (2014).
[Crossref]

Wong, J.

J. Wong, M. Selvanayagam, and G. V. Eleftheriades, “Design of unit cells and demonstration of methods for synthesizing huygens metasurfaces,” Photon. Nanostruct. 12, 360–375 (2014).
[Crossref]

Xiao, S.

S. Xiao, Q. He, C. Qu, X. Li, S. Sun, and L. Zhou, “Mode-expansion theory for inhomogeneous meta-surfaces,” Opt. Express 21, 27219–27237 (2013).
[Crossref] [PubMed]

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. Materials 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. Materials 11, 426–431 (2012).
[Crossref]

Yannopapas, V.

N. Stefanou, V. Yannopapas, and A. Modinos, “Heterostructures of photonic crystals: frequency bands and transmission coefficients,” Comput. Phys. Commun. 113, 49–77 (1998).
[Crossref]

Yariv, A.

Yeh, P.

Yu, L.

S. Law, C. Roberts, T. Kilpatrick, L. Yu, T. Ribaudo, E. Shaner, V. Podolskiy, and D. Wasserman, “All-semiconductor negative-index plasmonic absorbers,” Phys. Rev. Letters 112, 017401 (2014).
[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] [PubMed]

Zayats, A. V.

B. M. Wells, A. V. Zayats, and V. A. Podolskiy, “Nonlocal optics of plasmonic nanowire metamaterials,” Phys. Rev. B 89, 035111 (2014).
[Crossref]

Zeng, Y.

N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. Dalvit, and H.-T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340, 1304–1307 (2013).
[Crossref] [PubMed]

Zhang, X.

Y. Liu and X. Zhang, “Metasurfaces for manipulating surface plasmons,” Appl. Phys. Lett. 103, 141101 (2013).
[Crossref]

Zhao, Y.

Y. Zhao, N. Engheta, and A. Alù, “Homogenization of plasmonic metasurfaces modeled as transmission-line loads,” Metamaterials 5, 90–96 (2011).
[Crossref]

Y. Zhao and A. Alù, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B 84, 205428 (2011).
[Crossref]

Zhou, L.

S. Xiao, Q. He, C. Qu, X. Li, S. Sun, and L. Zhou, “Mode-expansion theory for inhomogeneous meta-surfaces,” Opt. Express 21, 27219–27237 (2013).
[Crossref] [PubMed]

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. Materials 11, 426–431 (2012).
[Crossref]

Appl. Phys. Lett. (2)

N. Dahan, A. Niv, G. Biener, V. Kleiner, and E. Hasman, “Space-variant polarization manipulation of a thermal emission by a SiO2 subwavelength grating supporting surface phonon-polaritons,” Appl. Phys. Lett. 86, 191102 (2005).
[Crossref]

Y. Liu and X. Zhang, “Metasurfaces for manipulating surface plasmons,” Appl. Phys. Lett. 103, 141101 (2013).
[Crossref]

B (1)

A. Alù and N. Engheta, “Theory of linear chains of metamaterial/plasmonic particles as subdiffraction optical nanotransmission lines,” Phys. Rev”. B 74205436 (2006).

Comput. Phys. Commun. (1)

N. Stefanou, V. Yannopapas, and A. Modinos, “Heterostructures of photonic crystals: frequency bands and transmission coefficients,” Comput. Phys. Commun. 113, 49–77 (1998).
[Crossref]

Electron. Lett. (1)

M. Idemen, “Straightforward derivation of boundary conditions on sheet simulating an anisotropic thin layer,” Electron. Lett. 24, 663–665 (1988).
[Crossref]

J. Opt. Soc. Am. (2)

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

Metamaterials (2)

Y. Zhao, N. Engheta, and A. Alù, “Homogenization of plasmonic metasurfaces modeled as transmission-line loads,” Metamaterials 5, 90–96 (2011).
[Crossref]

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

Nat. Materials (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. Materials 11, 426–431 (2012).
[Crossref]

Opt. Express (1)

Opt. Lett. (2)

Photon. Nanostruct. (1)

J. Wong, M. Selvanayagam, and G. V. Eleftheriades, “Design of unit cells and demonstration of methods for synthesizing huygens metasurfaces,” Photon. Nanostruct. 12, 360–375 (2014).
[Crossref]

Phys. Rev. B (4)

B. M. Wells, A. V. Zayats, and V. A. Podolskiy, “Nonlocal optics of plasmonic nanowire metamaterials,” Phys. Rev. B 89, 035111 (2014).
[Crossref]

P. Johnson and R. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370 (1972).
[Crossref]

Y. Zhao and A. Alù, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B 84, 205428 (2011).
[Crossref]

X.X. Liu and A. Alù, “Subwavelength leaky-wave optical nanoantennas: Directive radiation from linear arrays of plasmonic nanoparticles,” Phys. Rev. B 82, 144305 (2010)
[Crossref]

Phys. Rev. E (1)

S. Steshenko, F. Capalino, P. Alitalo, and S. Tretyakov, Effective model and investigation of the near-field enhancement and subwavelength imaging properties of multilayer arrays of plasmonic nanospheres, Phys. Rev. E 84, 016607 (2001)
[Crossref]

Phys. Rev. Lett. (1)

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990).
[Crossref] [PubMed]

Phys. Rev. Letters (1)

S. Law, C. Roberts, T. Kilpatrick, L. Yu, T. Ribaudo, E. Shaner, V. Podolskiy, and D. Wasserman, “All-semiconductor negative-index plasmonic absorbers,” Phys. Rev. Letters 112, 017401 (2014).
[Crossref]

Rev. Mod. Phys. (1)

F. J. García de Abajo, “Colloquium: Light scattering by particle and hole arrays,” Rev. Mod. Phys. 79, 1267–1290 (2007).
[Crossref]

Science (3)

N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. Dalvit, and H.-T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340, 1304–1307 (2013).
[Crossref] [PubMed]

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science 335, 427 (2012).
[Crossref]

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

Sov. Phys. JETP (1)

S. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466 (1956).

Other (12)

J. Jackson, Classical Electrodynamics (Wiley, 1998).

S. Pekar, Sov. Phys. JETP6, 785 (1958).

D.E. Goldberg, Genetic Algorithms in Search, Optimization, & Machine Learning (Addison-Wesley1989)

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings, Springer Tracts in Modern Physics (Springer Berlin Heidelberg, 2013).

“Kepler compute architecture white paper,” Tech. rep., NVIDIA Corperation (2012).

“cuBLAS API v6.0,” Tech. rep., NVIDIA Corperation (2014).

Z. Bomzon and E. Hasman, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett.77 (2000).

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

J. Jin, Finite Element-Boundary Element Methods for Electromagnetic Scattering (University of Michigan, 1989).

A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-difference Time-domain Method, Artech House antennas and propagation library (Artech House, 2005).

G. Milton, The Theory of Composites, Cambridge Monographs on Applied and Computational Mathematics (Cambridge University, 2002).
[Crossref]

M. Noginov and V. Podolskiy, Tutorials in Metamaterials, Series in Nano-Optics and Nanophotonics (Taylor & Francis, 2011).

Supplementary Material (6)

» Media 1: AVI (609 KB)     
» Media 2: AVI (885 KB)     
» Media 3: AVI (874 KB)     
» Media 4: AVI (820 KB)     
» Media 5: AVI (814 KB)     
» Media 6: AVI (752 KB)     

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Figures (6)

Fig. 1
Fig. 1 Schematic geometry of metasurface structure; A metasurface with periods Λxy and dielectric susceptibility χ(g)(x,y) is sandwiched between bulk materials with dielectric permittivities ε(1) and ε(2). The system is irradiated by plane wave(s) with amplitude(s) C ( 1 ) +; scattered light is represented as a set of plane waves with amplitudes C ( 1 ) (reflected light) and C ( 2 ) + (refracted light). DIT approximation is valid in regime hλ0 (see text for details)
Fig. 2
Fig. 2 Dispersion of guided waves supported by a thin metallic film as a function of film thickness h; solid and dashed lines represent analytical results and DIT calculations respectively; ε(1) = ε(2) = 1,ε(g) = −10 + 1i
Fig. 3
Fig. 3 Diffraction by a metasurface formed by an array of plasmonic disks [ε(g) = −10+1i; (c)–(e) h = λ0/50; (f)–(h) h = λ0/20] deposited on dielectric substrate [ε(2) = 10.8]; (a) schematic of the metasurface configuration; (b) computational speed-up of DIT vs. RCWA; symbols of different color represent RCWA (DIT) runs on CPU or GPU as indicated by the legend; data for DIT CPU runs are multiplied by 10; (c),(f) 0th order reflection and transmission; (d),(e),(g),(h) higher-order reflection and transmission; solid lines and symbols represent RCWA and DIT calculations, respectively; angular dependence of h = λ0/50 system is shown in Media 1, Media 2, Media 3, Media 4, Media 5, and Media 6.
Fig. 4
Fig. 4 Amplitude and phase of the in-plane components of the electric field above the center of a highly metallic (ε(g) = −2683+1367i) nano-antenna array (see inset for geometry; h = λ0/100). DIT results are shown in panels (a),(b),(c), and (d); RCWA results are shown in panels (e),(f),(g), and (h)
Fig. 5
Fig. 5 Optical properties of nano-antenna-based polarization converter; (a) cross-section of the structure [see inset in Fig. 4(d) for geometry of the metasurface]; nano-antennae layer and gold ground layer are both 200nm thick (hg); periodicity Λx = Λy = 68μm, antenna wire length L = 82μm, antenna width w = 10μm, dielectic layer height hd = 33μm and angles θ = 45°, and α = 25°. (b–d) Co-polarized (blue) and Cross-polarized (green) 0th order reflection calculated with DIT (solid lines) and RCWA (dashed lines) with (b) highly lossy spacer layer [εd = 3(1 + 2i)], (c) medium loss spacer layer [εd = 3(1 + .5i)], and (d) low loss spacer layer [εd = 3(1 + .05i)].
Fig. 6
Fig. 6 Optimization of the metasurface for maximum diffraction of light into +1 diffraction order; fixed parameters: Λ = 15.92μm, grating thickness h = 10nm,λ0 = 8μm, and the resilution of the binary mask Λ/N. Panel (a) represents the evolution of the performance of the sample used in Genetic Algorithm-based optimization routine, showing fitness (R+1) for the best member of the population for a given generation (optimization step) [solid line] and mean fitness of the generation [dashed black line]. Black, green, blue, red, and magenta lines represent results for N = 128, N = 64, N = 32, N = 16, and N = 8 respectively; selected points of optimization procedure are validated with RCWA calculations (black dots). Panel (b) shows results of the optimization, the unit cell that maximizes R+1 for each of the chosen values N after 300 optimization steps.

Equations (16)

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

ε = 1 + 4 π χ .
χ ( x , y , z ) = χ ( b ) + χ ( g ) ( x , y ) δ ( z ) h .
× E = i ω c H
× H = i ω c ( E + 4 π P ) ,
4 π ( P ) 2 E = ω 2 c 2 ( E + 4 π P ) .
Δ H x = 4 π i ω h c χ ( g ) ( x , y ) E y avg Δ H y = 4 π i ω h c χ ( g ) ( x , y ) E x avg ,
Δ E x = 4 π P z x Δ E y = 4 π P z y
E α ( b ) ( r ) = j α , j ( b ) ( z ) e i k j , x x + i k j , y y H α ( b ) ( r ) = j α , j ( b ) ( z ) e i k j , x x + i k j , y y .
k j , x = k 0 x + 2 π j x Λ x ; k j , y = k 0 y + 2 π j y Λ y
( x ( b ) y ( b ) x ( b ) y ( b ) ) = F ( b ) ( C T E ( b ) + C T M ( b ) + C T E ( b ) C T M ( b ) )
χ ( g ) ( x , y ) = j χ ^ j ( g ) e i ( k j , x x + k j , y y )
( I O K x X z K y K x X z K x O I K y X z K y K y X z K x O X x y I O X x y O O I ) F ( 1 ) ( C T E ( 1 ) + C T M ( 1 ) + C T E ( 1 ) C T M ( 1 ) ) = ( I O K x X z K y K x X z K x O I K y X z K y K y X z K x O X x y I O X x y O O I ) F ( 2 ) ( C T E ( 2 ) + C T M ( 2 ) + C T E ( 2 ) C T M ( 2 ) )
j , z ( b ) = c ω ε ( b ) ( k j , x j , y ( b ) k j , y j , x ( b ) ) j , z ( b ) = c ω ( k j , x ε j , y ( b ) k j , y ε j , x ( b ) )
F ( b ) = ( K y ϕ ( b ) + K x K z ( b ) ε ( b ) ϕ ( b ) + K y ϕ ( b ) K x K z ( b ) ε ( b ) ϕ ( b ) K x ϕ ( b ) + K y K z ( b ) ε ( b ) ϕ ( b ) + K x ϕ ( b ) K y K z ( b ) ε ( b ) ϕ ( b ) K x K z ( b ) ϕ ( b ) + K y ϕ ( b ) + K x K z ( b ) ϕ ( b ) K y ϕ ( b ) K y K z ( b ) ϕ ( b ) + K x ϕ ( b ) + K y K z ( b ) ϕ ( b ) K x ϕ ( b ) )
m , n P m , n e i ( k m , x x + k n , y y ) = m , n p , q χ ^ m p , n q ε p , q e i ( k m , x x + k n , y y )
Δ ε α = 4 π i h K α χ ˜ ( b ) ( I + 4 π χ ˜ ( b ) ) 1 D z avg

Metrics