Abstract

Transmission phase control is experimentally demonstrated using stacked metal-dielectric hole arrays with a two-dimensional geometric design. The transmission phase varies drastically with small frequency shifts due to structural resonances. Laterally propagating surface plasmon polaritons excited by the periodic hole array roughly determine the resonance frequency, whereas localized resonances in each hole determine the dispersion. The transmission phase at various frequencies is directly evaluated using interferometric microscopy, and the formation of an inclined wavefront is demonstrated using a beam steering element in which the hole shapes gradually change in-plane from square to circular.

© 2012 OSA

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    [CrossRef]
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    [CrossRef] [PubMed]
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  4. D. Inoue, A. Miura, T. Nomura, H. Fujikawa, K. Sato, N. Ikeda, D. Tsuya, Y. Sugimoto, and Y. Koide, “Polarization independent visible color filter comprising an aluminum film with surface-plasmon enhanced transmission through a subwavelength array of holes,” Appl. Phys. Lett.98, 093113 (2011).
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    [CrossRef]
  7. F. J. García-Vidal, E. Moreno, J. A. Porto, and L. Martín-Morenno, “Transmission of light through a single rectangular hole,” Phys. Rev. Lett.95, 103901 (2005).
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  8. P. Lalanne, J. C. Rodier, and J. P. Hugonin, “Surface plasmons of metallic surfaces perforated by nanohole arrays,” J. Opt. A: Pure Appl. Opt.7, 422–426 (2005).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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  26. Y. Kurokawa and H. T. Miyazaki, “Metal-insulator-metal plasmon nanocavities: analysis of optical properties,” Phys. Rev. B75, 035411 (2007).
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    [CrossRef]
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    [CrossRef] [PubMed]
  29. M. Beruete, M. Sorolla, and I. Campillo, “Left-handed extraordinary optical transmission through a photonic crystal of subwavelength hole arrays,” Opt. Express14, 5445–5455 (2006).
    [CrossRef] [PubMed]
  30. R. Marqués, L. Jelinek, F. Mesa, and F. Medina, “Analytical theory of wave propagation through stacked fishnet metamaterials,” Opt. Express17, 11582–11593 (2009).
    [CrossRef] [PubMed]
  31. H. Yoshida, T. Matsui, A. Miura, N. Ikeda, M. Ochiai, Y. Sugimoto, H. Fujikawa, and M. Ozaki, “Uniform liquid crystal alignment on metallic nanohole arrays by vapor-phase deposition of silane coupling agent,” Opt. Mater. Express2, 893–899 (2012).
    [CrossRef]
  32. N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tatienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science334, 333–337 (2011).
    [CrossRef] [PubMed]
  33. X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science335, 427 (2012).
    [CrossRef]

2012

2011

M. Iwanaga, “In-plane plasmonic modes of negative group velocity in perforated waveguides,” Opt. Lett.36, 2504–2506 (2011).
[CrossRef] [PubMed]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tatienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science334, 333–337 (2011).
[CrossRef] [PubMed]

J. Yang, C. Sauvan, H. T. Liu, and P. Lalanne, “Theory of fishnet negative-index optical metamaterials,” Phys. Rev. Lett.107, 043903 (2011).
[CrossRef] [PubMed]

D. Inoue, A. Miura, T. Nomura, H. Fujikawa, K. Sato, N. Ikeda, D. Tsuya, Y. Sugimoto, and Y. Koide, “Polarization independent visible color filter comprising an aluminum film with surface-plasmon enhanced transmission through a subwavelength array of holes,” Appl. Phys. Lett.98, 093113 (2011).
[CrossRef]

2009

R. Ortuño, C. García-Meca, F. J. Rodríguez-Fortuño, J. Martí, and A. Martínez, “Role of surface plasmon polaritons on optical transmission through double layer metallic hole arrays,” Phys. Rev. B79, 075425 (2009).
[CrossRef]

R. Marqués, L. Jelinek, F. Mesa, and F. Medina, “Analytical theory of wave propagation through stacked fishnet metamaterials,” Opt. Express17, 11582–11593 (2009).
[CrossRef] [PubMed]

2008

A. Mary, S. G. Rodrigo, F. J. Garcia-Vidal, and L. Martin-Moreno, “Theory of negative-refractive-index response of double-fishnet structures,” Phys. Rev. Lett.101, 103902 (2008).
[CrossRef] [PubMed]

H. Liu and P. Lalanne, “Microscopic theory of the extraordinary optical transmission,” Nature (London)452, 728–731 (2008).
[CrossRef]

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature (London)455, 376–380 (2008).
[CrossRef]

2007

Y. Kurokawa and H. T. Miyazaki, “Metal-insulator-metal plasmon nanocavities: analysis of optical properties,” Phys. Rev. B75, 035411 (2007).
[CrossRef]

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature (London)445, 39–46 (2007).
[CrossRef]

G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, “Design-related losses of double-fishnet negative-index photonic metamaterials,” Opt. Express15, 11536–11541 (2007).
[CrossRef] [PubMed]

2006

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Low-loss negative-index metamaterial at telecommunication wavelengths,” Opt. Lett.31, 1800–1802 (2006).
[CrossRef] [PubMed]

M. Beruete, M. Sorolla, and I. Campillo, “Left-handed extraordinary optical transmission through a photonic crystal of subwavelength hole arrays,” Opt. Express14, 5445–5455 (2006).
[CrossRef] [PubMed]

Z. Ruan and M. Qiu, “Enhanced transmission through periodic arrays of subwavelength holes: the role of localized waveguide resonances,” Phys. Rev. Lett.96, 233901 (2006).
[CrossRef] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science312, 892–894 (2006).
[CrossRef] [PubMed]

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B73, 035407 (2006).
[CrossRef]

H. T. Miyazaki and Y. Kurokawa, “Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity,” Phys. Rev. Lett.96, 097401 (2006).
[CrossRef] [PubMed]

2005

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett.95, 137404 (2005).
[CrossRef] [PubMed]

D. R. Smith, D. C. Vier, Th. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E71, 036617 (2005).
[CrossRef]

F. J. García-Vidal, E. Moreno, J. A. Porto, and L. Martín-Morenno, “Transmission of light through a single rectangular hole,” Phys. Rev. Lett.95, 103901 (2005).
[CrossRef] [PubMed]

P. Lalanne, J. C. Rodier, and J. P. Hugonin, “Surface plasmons of metallic surfaces perforated by nanohole arrays,” J. Opt. A: Pure Appl. Opt.7, 422–426 (2005).
[CrossRef]

S. Zhang, W. Fan, K. J. Malloy, S. R. J. Brueck, N. C. Panoiu, and R. M. Osgood, “Near-infrared double negative metamaterials,” Opt. Express13, 4922–4929 (2005).
[CrossRef] [PubMed]

M. B. Sinclair, M. P. de Boer, and A. D. Corwin, “Long-working-distance incoherent-light interference microscope,” Appl. Opt.44, 7714–7721 (2005).
[CrossRef] [PubMed]

2004

K. J. Klein Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Strong influence of hole shape on extraordinary tTransmission through periodic arrays of subwavelength holes,” Phys. Rev. Lett.92, 183901 (2004).
[CrossRef]

X. Chen, T. M. Grzegorczyk, B-I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E70, 016608 (2004).
[CrossRef]

2001

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett.86, 1114–1117 (2001).
[CrossRef] [PubMed]

1998

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature (London)391, 667–669 (1998).
[CrossRef]

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B58, 6779–6782 (1998).
[CrossRef]

A. D. Rakić, A. B. Djurišić, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt.37, 5271–5283 (1998).
[CrossRef]

Aieta, F.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tatienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science334, 333–337 (2011).
[CrossRef] [PubMed]

Atwater, H. A.

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B73, 035407 (2006).
[CrossRef]

Bartal, G.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature (London)455, 376–380 (2008).
[CrossRef]

Beruete, M.

Boltasseva, A.

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science335, 427 (2012).
[CrossRef]

Brueck, S. R. J.

S. Zhang, W. Fan, K. J. Malloy, S. R. J. Brueck, N. C. Panoiu, and R. M. Osgood, “Near-infrared double negative metamaterials,” Opt. Express13, 4922–4929 (2005).
[CrossRef] [PubMed]

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett.95, 137404 (2005).
[CrossRef] [PubMed]

Campillo, I.

Capasso, F.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tatienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science334, 333–337 (2011).
[CrossRef] [PubMed]

Chen, X.

X. Chen, T. M. Grzegorczyk, B-I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E70, 016608 (2004).
[CrossRef]

Corwin, A. D.

de Boer, M. P.

Dionne, J. A.

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B73, 035407 (2006).
[CrossRef]

Djurišic, A. B.

Dolling, G.

Ebbesen, T. W.

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature (London)445, 39–46 (2007).
[CrossRef]

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett.86, 1114–1117 (2001).
[CrossRef] [PubMed]

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B58, 6779–6782 (1998).
[CrossRef]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature (London)391, 667–669 (1998).
[CrossRef]

Elazar, J. M.

Emani, N. K.

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science335, 427 (2012).
[CrossRef]

Enkrich, C.

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science312, 892–894 (2006).
[CrossRef] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Low-loss negative-index metamaterial at telecommunication wavelengths,” Opt. Lett.31, 1800–1802 (2006).
[CrossRef] [PubMed]

Enoch, S.

K. J. Klein Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Strong influence of hole shape on extraordinary tTransmission through periodic arrays of subwavelength holes,” Phys. Rev. Lett.92, 183901 (2004).
[CrossRef]

Fan, W.

S. Zhang, W. Fan, K. J. Malloy, S. R. J. Brueck, N. C. Panoiu, and R. M. Osgood, “Near-infrared double negative metamaterials,” Opt. Express13, 4922–4929 (2005).
[CrossRef] [PubMed]

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett.95, 137404 (2005).
[CrossRef] [PubMed]

Fujikawa, H.

H. Yoshida, T. Matsui, A. Miura, N. Ikeda, M. Ochiai, Y. Sugimoto, H. Fujikawa, and M. Ozaki, “Uniform liquid crystal alignment on metallic nanohole arrays by vapor-phase deposition of silane coupling agent,” Opt. Mater. Express2, 893–899 (2012).
[CrossRef]

D. Inoue, A. Miura, T. Nomura, H. Fujikawa, K. Sato, N. Ikeda, D. Tsuya, Y. Sugimoto, and Y. Koide, “Polarization independent visible color filter comprising an aluminum film with surface-plasmon enhanced transmission through a subwavelength array of holes,” Appl. Phys. Lett.98, 093113 (2011).
[CrossRef]

Gaburro, Z.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tatienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science334, 333–337 (2011).
[CrossRef] [PubMed]

García-Meca, C.

R. Ortuño, C. García-Meca, F. J. Rodríguez-Fortuño, J. Martí, and A. Martínez, “Role of surface plasmon polaritons on optical transmission through double layer metallic hole arrays,” Phys. Rev. B79, 075425 (2009).
[CrossRef]

Garcia-Vidal, F. J.

A. Mary, S. G. Rodrigo, F. J. Garcia-Vidal, and L. Martin-Moreno, “Theory of negative-refractive-index response of double-fishnet structures,” Phys. Rev. Lett.101, 103902 (2008).
[CrossRef] [PubMed]

García-Vidal, F. J.

F. J. García-Vidal, E. Moreno, J. A. Porto, and L. Martín-Morenno, “Transmission of light through a single rectangular hole,” Phys. Rev. Lett.95, 103901 (2005).
[CrossRef] [PubMed]

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett.86, 1114–1117 (2001).
[CrossRef] [PubMed]

Genet, C.

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature (London)445, 39–46 (2007).
[CrossRef]

Genevet, P.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tatienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science334, 333–337 (2011).
[CrossRef] [PubMed]

Genov, D. A.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature (London)455, 376–380 (2008).
[CrossRef]

Ghaemi, H. F.

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B58, 6779–6782 (1998).
[CrossRef]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature (London)391, 667–669 (1998).
[CrossRef]

Grupp, D. E.

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B58, 6779–6782 (1998).
[CrossRef]

Grzegorczyk, T. M.

X. Chen, T. M. Grzegorczyk, B-I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E70, 016608 (2004).
[CrossRef]

Hugonin, J. P.

P. Lalanne, J. C. Rodier, and J. P. Hugonin, “Surface plasmons of metallic surfaces perforated by nanohole arrays,” J. Opt. A: Pure Appl. Opt.7, 422–426 (2005).
[CrossRef]

Ikeda, N.

H. Yoshida, T. Matsui, A. Miura, N. Ikeda, M. Ochiai, Y. Sugimoto, H. Fujikawa, and M. Ozaki, “Uniform liquid crystal alignment on metallic nanohole arrays by vapor-phase deposition of silane coupling agent,” Opt. Mater. Express2, 893–899 (2012).
[CrossRef]

D. Inoue, A. Miura, T. Nomura, H. Fujikawa, K. Sato, N. Ikeda, D. Tsuya, Y. Sugimoto, and Y. Koide, “Polarization independent visible color filter comprising an aluminum film with surface-plasmon enhanced transmission through a subwavelength array of holes,” Appl. Phys. Lett.98, 093113 (2011).
[CrossRef]

Inoue, D.

D. Inoue, A. Miura, T. Nomura, H. Fujikawa, K. Sato, N. Ikeda, D. Tsuya, Y. Sugimoto, and Y. Koide, “Polarization independent visible color filter comprising an aluminum film with surface-plasmon enhanced transmission through a subwavelength array of holes,” Appl. Phys. Lett.98, 093113 (2011).
[CrossRef]

Iwanaga, M.

Jelinek, L.

Kats, M. A.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tatienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science334, 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,” Science335, 427 (2012).
[CrossRef]

Klein Koerkamp, K. J.

K. J. Klein Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Strong influence of hole shape on extraordinary tTransmission through periodic arrays of subwavelength holes,” Phys. Rev. Lett.92, 183901 (2004).
[CrossRef]

Koide, Y.

D. Inoue, A. Miura, T. Nomura, H. Fujikawa, K. Sato, N. Ikeda, D. Tsuya, Y. Sugimoto, and Y. Koide, “Polarization independent visible color filter comprising an aluminum film with surface-plasmon enhanced transmission through a subwavelength array of holes,” Appl. Phys. Lett.98, 093113 (2011).
[CrossRef]

Kong, J. A.

X. Chen, T. M. Grzegorczyk, B-I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E70, 016608 (2004).
[CrossRef]

Koschny, Th.

D. R. Smith, D. C. Vier, Th. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E71, 036617 (2005).
[CrossRef]

Kuipers, L.

K. J. Klein Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Strong influence of hole shape on extraordinary tTransmission through periodic arrays of subwavelength holes,” Phys. Rev. Lett.92, 183901 (2004).
[CrossRef]

Kurokawa, Y.

Y. Kurokawa and H. T. Miyazaki, “Metal-insulator-metal plasmon nanocavities: analysis of optical properties,” Phys. Rev. B75, 035411 (2007).
[CrossRef]

H. T. Miyazaki and Y. Kurokawa, “Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity,” Phys. Rev. Lett.96, 097401 (2006).
[CrossRef] [PubMed]

Lalanne, P.

J. Yang, C. Sauvan, H. T. Liu, and P. Lalanne, “Theory of fishnet negative-index optical metamaterials,” Phys. Rev. Lett.107, 043903 (2011).
[CrossRef] [PubMed]

H. Liu and P. Lalanne, “Microscopic theory of the extraordinary optical transmission,” Nature (London)452, 728–731 (2008).
[CrossRef]

P. Lalanne, J. C. Rodier, and J. P. Hugonin, “Surface plasmons of metallic surfaces perforated by nanohole arrays,” J. Opt. A: Pure Appl. Opt.7, 422–426 (2005).
[CrossRef]

Lezec, H. J.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett.86, 1114–1117 (2001).
[CrossRef] [PubMed]

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B58, 6779–6782 (1998).
[CrossRef]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature (London)391, 667–669 (1998).
[CrossRef]

Linden, S.

Liu, H.

H. Liu and P. Lalanne, “Microscopic theory of the extraordinary optical transmission,” Nature (London)452, 728–731 (2008).
[CrossRef]

Liu, H. T.

J. Yang, C. Sauvan, H. T. Liu, and P. Lalanne, “Theory of fishnet negative-index optical metamaterials,” Phys. Rev. Lett.107, 043903 (2011).
[CrossRef] [PubMed]

Maier, S. A.

S. A. Maier, Plasmonics: Fundamentals and Applications (Splinger-Verlag, 2007).

Majewski, M. L.

Malloy, K. J.

S. Zhang, W. Fan, K. J. Malloy, S. R. J. Brueck, N. C. Panoiu, and R. M. Osgood, “Near-infrared double negative metamaterials,” Opt. Express13, 4922–4929 (2005).
[CrossRef] [PubMed]

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett.95, 137404 (2005).
[CrossRef] [PubMed]

Marqués, R.

Martí, J.

R. Ortuño, C. García-Meca, F. J. Rodríguez-Fortuño, J. Martí, and A. Martínez, “Role of surface plasmon polaritons on optical transmission through double layer metallic hole arrays,” Phys. Rev. B79, 075425 (2009).
[CrossRef]

Martínez, A.

R. Ortuño, C. García-Meca, F. J. Rodríguez-Fortuño, J. Martí, and A. Martínez, “Role of surface plasmon polaritons on optical transmission through double layer metallic hole arrays,” Phys. Rev. B79, 075425 (2009).
[CrossRef]

Martín-Morenno, L.

F. J. García-Vidal, E. Moreno, J. A. Porto, and L. Martín-Morenno, “Transmission of light through a single rectangular hole,” Phys. Rev. Lett.95, 103901 (2005).
[CrossRef] [PubMed]

Martin-Moreno, L.

A. Mary, S. G. Rodrigo, F. J. Garcia-Vidal, and L. Martin-Moreno, “Theory of negative-refractive-index response of double-fishnet structures,” Phys. Rev. Lett.101, 103902 (2008).
[CrossRef] [PubMed]

Martín-Moreno, L.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett.86, 1114–1117 (2001).
[CrossRef] [PubMed]

Mary, A.

A. Mary, S. G. Rodrigo, F. J. Garcia-Vidal, and L. Martin-Moreno, “Theory of negative-refractive-index response of double-fishnet structures,” Phys. Rev. Lett.101, 103902 (2008).
[CrossRef] [PubMed]

Matsui, T.

Medina, F.

Mesa, F.

Miura, A.

H. Yoshida, T. Matsui, A. Miura, N. Ikeda, M. Ochiai, Y. Sugimoto, H. Fujikawa, and M. Ozaki, “Uniform liquid crystal alignment on metallic nanohole arrays by vapor-phase deposition of silane coupling agent,” Opt. Mater. Express2, 893–899 (2012).
[CrossRef]

D. Inoue, A. Miura, T. Nomura, H. Fujikawa, K. Sato, N. Ikeda, D. Tsuya, Y. Sugimoto, and Y. Koide, “Polarization independent visible color filter comprising an aluminum film with surface-plasmon enhanced transmission through a subwavelength array of holes,” Appl. Phys. Lett.98, 093113 (2011).
[CrossRef]

Miyazaki, H. T.

Y. Kurokawa and H. T. Miyazaki, “Metal-insulator-metal plasmon nanocavities: analysis of optical properties,” Phys. Rev. B75, 035411 (2007).
[CrossRef]

H. T. Miyazaki and Y. Kurokawa, “Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity,” Phys. Rev. Lett.96, 097401 (2006).
[CrossRef] [PubMed]

Moreno, E.

F. J. García-Vidal, E. Moreno, J. A. Porto, and L. Martín-Morenno, “Transmission of light through a single rectangular hole,” Phys. Rev. Lett.95, 103901 (2005).
[CrossRef] [PubMed]

Ni, X.

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science335, 427 (2012).
[CrossRef]

Nomura, T.

D. Inoue, A. Miura, T. Nomura, H. Fujikawa, K. Sato, N. Ikeda, D. Tsuya, Y. Sugimoto, and Y. Koide, “Polarization independent visible color filter comprising an aluminum film with surface-plasmon enhanced transmission through a subwavelength array of holes,” Appl. Phys. Lett.98, 093113 (2011).
[CrossRef]

Ochiai, M.

Ortuño, R.

R. Ortuño, C. García-Meca, F. J. Rodríguez-Fortuño, J. Martí, and A. Martínez, “Role of surface plasmon polaritons on optical transmission through double layer metallic hole arrays,” Phys. Rev. B79, 075425 (2009).
[CrossRef]

Osgood, R. M.

S. Zhang, W. Fan, K. J. Malloy, S. R. J. Brueck, N. C. Panoiu, and R. M. Osgood, “Near-infrared double negative metamaterials,” Opt. Express13, 4922–4929 (2005).
[CrossRef] [PubMed]

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett.95, 137404 (2005).
[CrossRef] [PubMed]

Ozaki, M.

Pacheco, J.

X. Chen, T. M. Grzegorczyk, B-I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E70, 016608 (2004).
[CrossRef]

Panoiu, N. C.

S. Zhang, W. Fan, K. J. Malloy, S. R. J. Brueck, N. C. Panoiu, and R. M. Osgood, “Near-infrared double negative metamaterials,” Opt. Express13, 4922–4929 (2005).
[CrossRef] [PubMed]

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett.95, 137404 (2005).
[CrossRef] [PubMed]

Pellerin, K. M.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett.86, 1114–1117 (2001).
[CrossRef] [PubMed]

Pendry, J. B.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett.86, 1114–1117 (2001).
[CrossRef] [PubMed]

Polman, A.

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B73, 035407 (2006).
[CrossRef]

Porto, J. A.

F. J. García-Vidal, E. Moreno, J. A. Porto, and L. Martín-Morenno, “Transmission of light through a single rectangular hole,” Phys. Rev. Lett.95, 103901 (2005).
[CrossRef] [PubMed]

Qiu, M.

Z. Ruan and M. Qiu, “Enhanced transmission through periodic arrays of subwavelength holes: the role of localized waveguide resonances,” Phys. Rev. Lett.96, 233901 (2006).
[CrossRef] [PubMed]

Rakic, A. D.

Rodier, J. C.

P. Lalanne, J. C. Rodier, and J. P. Hugonin, “Surface plasmons of metallic surfaces perforated by nanohole arrays,” J. Opt. A: Pure Appl. Opt.7, 422–426 (2005).
[CrossRef]

Rodrigo, S. G.

A. Mary, S. G. Rodrigo, F. J. Garcia-Vidal, and L. Martin-Moreno, “Theory of negative-refractive-index response of double-fishnet structures,” Phys. Rev. Lett.101, 103902 (2008).
[CrossRef] [PubMed]

Rodríguez-Fortuño, F. J.

R. Ortuño, C. García-Meca, F. J. Rodríguez-Fortuño, J. Martí, and A. Martínez, “Role of surface plasmon polaritons on optical transmission through double layer metallic hole arrays,” Phys. Rev. B79, 075425 (2009).
[CrossRef]

Ruan, Z.

Z. Ruan and M. Qiu, “Enhanced transmission through periodic arrays of subwavelength holes: the role of localized waveguide resonances,” Phys. Rev. Lett.96, 233901 (2006).
[CrossRef] [PubMed]

Sato, K.

D. Inoue, A. Miura, T. Nomura, H. Fujikawa, K. Sato, N. Ikeda, D. Tsuya, Y. Sugimoto, and Y. Koide, “Polarization independent visible color filter comprising an aluminum film with surface-plasmon enhanced transmission through a subwavelength array of holes,” Appl. Phys. Lett.98, 093113 (2011).
[CrossRef]

Sauvan, C.

J. Yang, C. Sauvan, H. T. Liu, and P. Lalanne, “Theory of fishnet negative-index optical metamaterials,” Phys. Rev. Lett.107, 043903 (2011).
[CrossRef] [PubMed]

Segerink, F. B.

K. J. Klein Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Strong influence of hole shape on extraordinary tTransmission through periodic arrays of subwavelength holes,” Phys. Rev. Lett.92, 183901 (2004).
[CrossRef]

Shalaev, V. M.

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science335, 427 (2012).
[CrossRef]

Sinclair, M. B.

Smith, D. R.

D. R. Smith, D. C. Vier, Th. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E71, 036617 (2005).
[CrossRef]

Sorolla, M.

Soukoulis, C. M.

G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, “Design-related losses of double-fishnet negative-index photonic metamaterials,” Opt. Express15, 11536–11541 (2007).
[CrossRef] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science312, 892–894 (2006).
[CrossRef] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Low-loss negative-index metamaterial at telecommunication wavelengths,” Opt. Lett.31, 1800–1802 (2006).
[CrossRef] [PubMed]

D. R. Smith, D. C. Vier, Th. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E71, 036617 (2005).
[CrossRef]

Sugimoto, Y.

H. Yoshida, T. Matsui, A. Miura, N. Ikeda, M. Ochiai, Y. Sugimoto, H. Fujikawa, and M. Ozaki, “Uniform liquid crystal alignment on metallic nanohole arrays by vapor-phase deposition of silane coupling agent,” Opt. Mater. Express2, 893–899 (2012).
[CrossRef]

D. Inoue, A. Miura, T. Nomura, H. Fujikawa, K. Sato, N. Ikeda, D. Tsuya, Y. Sugimoto, and Y. Koide, “Polarization independent visible color filter comprising an aluminum film with surface-plasmon enhanced transmission through a subwavelength array of holes,” Appl. Phys. Lett.98, 093113 (2011).
[CrossRef]

Sweatlock, L. A.

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B73, 035407 (2006).
[CrossRef]

Tatienne, J.-P.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tatienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science334, 333–337 (2011).
[CrossRef] [PubMed]

Thio, T.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett.86, 1114–1117 (2001).
[CrossRef] [PubMed]

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B58, 6779–6782 (1998).
[CrossRef]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature (London)391, 667–669 (1998).
[CrossRef]

Tsuya, D.

D. Inoue, A. Miura, T. Nomura, H. Fujikawa, K. Sato, N. Ikeda, D. Tsuya, Y. Sugimoto, and Y. Koide, “Polarization independent visible color filter comprising an aluminum film with surface-plasmon enhanced transmission through a subwavelength array of holes,” Appl. Phys. Lett.98, 093113 (2011).
[CrossRef]

Ulin-Avila, E.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature (London)455, 376–380 (2008).
[CrossRef]

Valentine, J.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature (London)455, 376–380 (2008).
[CrossRef]

van Hulst, N. F.

K. J. Klein Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Strong influence of hole shape on extraordinary tTransmission through periodic arrays of subwavelength holes,” Phys. Rev. Lett.92, 183901 (2004).
[CrossRef]

Vier, D. C.

D. R. Smith, D. C. Vier, Th. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E71, 036617 (2005).
[CrossRef]

Wegener, M.

Wolff, P. A.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature (London)391, 667–669 (1998).
[CrossRef]

Wu, B-I.

X. Chen, T. M. Grzegorczyk, B-I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E70, 016608 (2004).
[CrossRef]

Yang, J.

J. Yang, C. Sauvan, H. T. Liu, and P. Lalanne, “Theory of fishnet negative-index optical metamaterials,” Phys. Rev. Lett.107, 043903 (2011).
[CrossRef] [PubMed]

Yoshida, H.

Yu, N.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tatienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science334, 333–337 (2011).
[CrossRef] [PubMed]

Zentgraf, T.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature (London)455, 376–380 (2008).
[CrossRef]

Zhang, S.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature (London)455, 376–380 (2008).
[CrossRef]

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett.95, 137404 (2005).
[CrossRef] [PubMed]

S. Zhang, W. Fan, K. J. Malloy, S. R. J. Brueck, N. C. Panoiu, and R. M. Osgood, “Near-infrared double negative metamaterials,” Opt. Express13, 4922–4929 (2005).
[CrossRef] [PubMed]

Zhang, X.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature (London)455, 376–380 (2008).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

D. Inoue, A. Miura, T. Nomura, H. Fujikawa, K. Sato, N. Ikeda, D. Tsuya, Y. Sugimoto, and Y. Koide, “Polarization independent visible color filter comprising an aluminum film with surface-plasmon enhanced transmission through a subwavelength array of holes,” Appl. Phys. Lett.98, 093113 (2011).
[CrossRef]

J. Opt. A: Pure Appl. Opt.

P. Lalanne, J. C. Rodier, and J. P. Hugonin, “Surface plasmons of metallic surfaces perforated by nanohole arrays,” J. Opt. A: Pure Appl. Opt.7, 422–426 (2005).
[CrossRef]

Nature (London)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature (London)391, 667–669 (1998).
[CrossRef]

H. Liu and P. Lalanne, “Microscopic theory of the extraordinary optical transmission,” Nature (London)452, 728–731 (2008).
[CrossRef]

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature (London)455, 376–380 (2008).
[CrossRef]

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature (London)445, 39–46 (2007).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Mater. Express

Phys. Rev. B

R. Ortuño, C. García-Meca, F. J. Rodríguez-Fortuño, J. Martí, and A. Martínez, “Role of surface plasmon polaritons on optical transmission through double layer metallic hole arrays,” Phys. Rev. B79, 075425 (2009).
[CrossRef]

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B73, 035407 (2006).
[CrossRef]

Y. Kurokawa and H. T. Miyazaki, “Metal-insulator-metal plasmon nanocavities: analysis of optical properties,” Phys. Rev. B75, 035411 (2007).
[CrossRef]

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B58, 6779–6782 (1998).
[CrossRef]

Phys. Rev. E

X. Chen, T. M. Grzegorczyk, B-I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E70, 016608 (2004).
[CrossRef]

D. R. Smith, D. C. Vier, Th. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E71, 036617 (2005).
[CrossRef]

Phys. Rev. Lett.

A. Mary, S. G. Rodrigo, F. J. Garcia-Vidal, and L. Martin-Moreno, “Theory of negative-refractive-index response of double-fishnet structures,” Phys. Rev. Lett.101, 103902 (2008).
[CrossRef] [PubMed]

H. T. Miyazaki and Y. Kurokawa, “Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity,” Phys. Rev. Lett.96, 097401 (2006).
[CrossRef] [PubMed]

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett.95, 137404 (2005).
[CrossRef] [PubMed]

F. J. García-Vidal, E. Moreno, J. A. Porto, and L. Martín-Morenno, “Transmission of light through a single rectangular hole,” Phys. Rev. Lett.95, 103901 (2005).
[CrossRef] [PubMed]

Z. Ruan and M. Qiu, “Enhanced transmission through periodic arrays of subwavelength holes: the role of localized waveguide resonances,” Phys. Rev. Lett.96, 233901 (2006).
[CrossRef] [PubMed]

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett.86, 1114–1117 (2001).
[CrossRef] [PubMed]

J. Yang, C. Sauvan, H. T. Liu, and P. Lalanne, “Theory of fishnet negative-index optical metamaterials,” Phys. Rev. Lett.107, 043903 (2011).
[CrossRef] [PubMed]

K. J. Klein Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Strong influence of hole shape on extraordinary tTransmission through periodic arrays of subwavelength holes,” Phys. Rev. Lett.92, 183901 (2004).
[CrossRef]

Science

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tatienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science334, 333–337 (2011).
[CrossRef] [PubMed]

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science335, 427 (2012).
[CrossRef]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science312, 892–894 (2006).
[CrossRef] [PubMed]

Other

S. A. Maier, Plasmonics: Fundamentals and Applications (Splinger-Verlag, 2007).

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Figures (7)

Fig. 1
Fig. 1

(a) Dispersion relation for a single interface SPP and a gap SPP. The green line represents the reciprocal lattice vector Gx. (b) Numerically calculated transmittance through the SHA. The geometry of the SHA is depicted in the inset. The model in the inset is for the case of the square-hole SHA. The sidewall slope of the holes is assumed to be 90 degrees to the substrate plane in the calculation. (c) Numerically calculated transmission phase relative to that for a vacuum layer with the same thickness as the SHA. Gray horizontal solid lines in (a) to (c) represent the intersections between laterally propagating SPPs and the grating momentum, ωsingle and ωgap. The rightmost axis shows the normalized frequency a/λ for a = 1000 nm. The arrow in (b) denotes the transmission peak around ωgap for the square-hole SHA.

Fig. 2
Fig. 2

Scanning electron micrographs of fabricated SHAs with a = 1000 nm. (a) Top view of the square-hole SHA, (b) top view of the circular-hole hole SHA, and (c) cross-sectional view of the square-hole SHA. The layer on top of the SHA in (c) is a residue from the dry etching process, which is removed before the optical measurements. All scale bars are 1 μm.

Fig. 3
Fig. 3

Experimental setup based on a near-infrared microscope (Olympus BX-51IR). LD, external-cavity wavelength-tunable diode laser (New Focus Velocity TLB-6326, λ = 1470–1545 nm); W, achromatic half-wave plate; ND, neutral density filter; BS, pellicle beam splitter; S, sample; OL, objective lens (Olympus LMPlanIR, 20X, NA=0.40, NA: numerical aperture); L, achromatic doublet lens (f = 40.0 mm, f: focal length); IL, imaging lens (f = 180.0 mm); C, near-infrared camera (Hamamatsu Photonics, C10633-13, λ = 900 – 1700 nm); X, halogen lamp; PL, polarizer; AL, analyzer; F, visible cut filter; OF, optical fiber (NA = 0.2, diameter: 400 μm); SM, spectrometer (Lambda Vision, TFCAM-7000F/NIR, λ = 900 – 1700 nm).

Fig. 4
Fig. 4

Calculated (calc.) and measured (meas.) transmission spectra for square- and circular-hole SHAs. Symbols and solid lines represent calculated and measured results, respectively. Blue represents the results for square-hole SHAs, and orange for circular-hole SHAs. ωsingle and ωgap are shown by gray horizontal lines. The arrow denotes the transmission peak around ωgap for the square-hole SHA.

Fig. 5
Fig. 5

Additional fabrication process and result of interferometric observation. (a) – (c) FIB milling process. (a) Left side, stacked Al/SiO2 layers; Right side, SHA. (b) FIB milling of overlap region. (c) Left side, stacked Al/SiO2 layers; Center, standard region (S1) and overetched region (S2); Right side, SHA region (S3). (d) SEM image of fabricated structure. Scale bar is 5 μm. (e) Transmission interferometric image of square-hole SHA with a = 1000 nm at λ = 1530 nm. Scale bar is 150 μm. Another etched area with the same depth as the S1 region is also seen to the right of the SHA region (S3).

Fig. 6
Fig. 6

(a) Calculated (calc.) and measured (meas.) transmission phase for square- and circular-hole SHAs relative to a vacuum layer with the same thickness as the SHAs. All notations, symbols and lines are the same as in Fig. 4. (b)–(e) Transmission interferometric images of SHA. Corresponding data points are indicated in (a). Display ranges of the interferometric images are the same as in Fig. 5(e). (b) circular-hole SHA with a = 1000 nm at λ = 1475 nm. (c) square-hole SHA with a = 1000 nm at λ = 1540 nm. (d) circular-hole SHA with a = 1000 nm at λ = 1540 nm. (e) circular-hole SHA with a = 900 nm at λ = 1530 nm. Gray horizontal solid lines represent ωsingle and ωgap. Gray dashed lines show the transmission phase through media with various apparent refractive indices n (a = 1000 nm and d = 580 nm).

Fig. 7
Fig. 7

Experimental demonstration of beam steering element. (a) SEM image of the beam steering element. Scale bar is 10 μm. Insets are magnified images of circular and square holes. The double-headed arrow indicates the polarization direction of the incident light. (b) Interferometric image of the beam steering element. Scale bar is 150 μm. (c) Phase distribution plots based on analysis of interferometric images for various frequencies. The horizontal axis shows the position from the center of the transition region.

Equations (2)

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k sp = k inc / / + i G x + j G y ,
Δ ϕ j i = 2 π Δ m j i + 2 π q j i ,

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