Abstract

We theoretically develop a hybrid architecture consisting of photonic integrated circuit and plasmonic nanoantennas to fully control optical far-field radiation with unprecedented flexibility. By exploiting asymmetric and lateral excitation from silicon waveguides, single gold nanorod and cascaded nanorod pair can function as component radiation pixels, featured by full 2π phase coverage and nanoscale footprint. These radiation pixels allow us to design scalable on-chip devices in a wavefront engineering fashion. We numerically demonstrate beam collimation with 30° out of the incident plane and nearly diffraction limited divergence angle. We also present high-numerical-aperture (NA) beam focusing with NA ≈0.65 and vector beam generation (the radially-polarized mode) with the mode similarity greater than 44%. This concept and approach constitutes a designable optical platform, which might be a future bridge between integrated photonics and metasurface functionalities.

© 2017 Optical Society of America

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2016 (3)

D. Conteduca, F. Dell’Olio, C. Ciminelli, T. F. Krauss, and M. N. Armenise, “Design of a high-performance optical tweezer for nanoparticle trapping,” Appl. Phys., A Mater. Sci. Process. 122(4), 1–6 (2016).
[Crossref]

F. Peyskens, A. Dhakal, P. Van Dorpe, N. Le Thomas, and R. Baets, “Surface Enhanced Raman Spectroscopy Using a Single Mode Nanophotonic-Plasmonic Platform,” ACS Photonics 3(1), 102–108 (2016).
[Crossref]

Y.-Z. Sun, R. Bachelot, S. Blaize, Z.-Y. Li, and W. Ding, “Vector beam generation via micrometer-scale photonic integrated circuits and plasmonic nano-antennae,” J. Opt. Soc. Am. B 33(3), 360 (2016).
[Crossref]

2015 (1)

Y. Luo, M. Chamanzar, A. Apuzzo, R. Salas-Montiel, K. N. Nguyen, S. Blaize, and A. Adibi, “On-chip hybrid photonic-plasmonic light concentrator for nanofocusing in an integrated silicon photonics platform,” Nano Lett. 15(2), 849–856 (2015).
[Crossref] [PubMed]

2014 (6)

Y. Yang, W. Wang, P. Moitra, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Dielectric meta-reflectarray for broadband linear polarization conversion and optical vortex generation,” Nano Lett. 14(3), 1394–1399 (2014).
[Crossref] [PubMed]

T. Sugita, K. Yanazawa, S. Maeda, H. F. Hofmann, and Y. Kadoya, “Radiation pattern of plasmonic nano-antennas in a homogeneous medium,” Opt. Express 22(11), 13263–13268 (2014).
[Crossref] [PubMed]

H. Aouani, M. Rahmani, M. Navarro-Cía, and S. A. Maier, “Third-harmonic-upconversion enhancement from a single semiconductor nanoparticle coupled to a plasmonic antenna,” Nat. Nanotechnol. 9(4), 290–294 (2014).
[Crossref] [PubMed]

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
[Crossref] [PubMed]

I. M. Hancu, A. G. Curto, M. Castro-López, M. Kuttge, and N. F. van Hulst, “Multipolar interference for directed light emission,” Nano Lett. 14(1), 166–171 (2014).
[Crossref] [PubMed]

W. Ding, Y.-H. Chen, and Z.-Y. Li, “Unidirectional emissions from dielectric photonic circuits decorated with plasmonic phased antenna arrays,” Chin. Phys. B 23(3), 037301 (2014).
[Crossref]

2013 (6)

D. Vercruysse, Y. Sonnefraud, N. Verellen, F. B. Fuchs, G. Di Martino, L. Lagae, V. V. Moshchalkov, S. A. Maier, and P. Van Dorpe, “Unidirectional side scattering of light by a single-element nanoantenna,” Nano Lett. 13(8), 3843–3849 (2013).
[Crossref] [PubMed]

C. Pfeiffer and A. Grbic, “Metamaterial Huygens’ surfaces: tailoring wave fronts with reflectionless sheets,” Phys. Rev. Lett. 110(19), 197401 (2013).
[Crossref] [PubMed]

N. Liu, F. Wen, Y. Zhao, Y. Wang, P. Nordlander, N. J. Halas, and A. Alù, “Individual nanoantennas loaded with three-dimensional optical nanocircuits,” Nano Lett. 13(1), 142–147 (2013).
[Crossref] [PubMed]

I. Massiot, C. Colin, C. Sauvan, P. Lalanne, P. R. Cabarrocas, J. L. Pelouard, and S. Collin, “Multi-resonant absorption in ultra-thin silicon solar cells with metallic nanowires,” Opt. Express 21(S3Suppl 3), A372–A381 (2013).
[Crossref] [PubMed]

M. Chamanzar, Z. Xia, S. Yegnanarayanan, and A. Adibi, “Hybrid integrated plasmonic-photonic waveguides for on-chip localized surface plasmon resonance (LSPR) sensing and spectroscopy,” Opt. Express 21(26), 32086–32098 (2013).
[Crossref] [PubMed]

J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493(7431), 195–199 (2013).
[Crossref] [PubMed]

2012 (6)

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[Crossref] [PubMed]

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12(12), 6328–6333 (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(6067), 427 (2012).
[Crossref] [PubMed]

F. Aieta, P. Genevet, N. Yu, M. A. Kats, Z. Gaburro, and F. Capasso, “Out-of-plane reflection and refraction of light by anisotropic optical antenna metasurfaces with phase discontinuities,” Nano Lett. 12(3), 1702–1706 (2012).
[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. Mater. 11(5), 426–431 (2012).
[Crossref] [PubMed]

F. Bernal Arango, A. Kwadrin, and A. F. Koenderink, “Plasmonic Antennas Hybridized with Dielectric Waveguides,” ACS Nano 6(11), 10156–10167 (2012).
[Crossref] [PubMed]

2011 (5)

V. Giannini, A. I. Fernández-Domínguez, S. C. Heck, and S. A. Maier, “Plasmonic nanoantennas: fundamentals and their use in controlling the radiative properties of nanoemitters,” Chem. Rev. 111(6), 3888–3912 (2011).
[Crossref] [PubMed]

N. Liu, M. L. Tang, M. Hentschel, H. Giessen, and A. P. Alivisatos, “Nanoantenna-enhanced gas sensing in a single tailored nanofocus,” Nat. Mater. 10(8), 631–636 (2011).
[Crossref] [PubMed]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

L. Novotny and N. van Hulst, “Antennas for light,” Nat. Photonics 5(2), 83–90 (2011).
[Crossref]

A. Lupu, N. Dubrovina, R. Ghasemi, A. Degiron, and A. de Lustrac, “Metal-dielectric metamaterials for guided wave silicon photonics,” Opt. Express 19(24), 24746–24761 (2011).
[Crossref] [PubMed]

2010 (4)

K. Van Acoleyen, H. Rogier, and R. Baets, “Two-dimensional optical phased array antenna on silicon-on-insulator,” Opt. Express 18(13), 13655–13660 (2010).
[Crossref] [PubMed]

A. B. Evlyukhin, S. I. Bozhevolnyi, A. Pors, M. G. Nielsen, I. P. Radko, M. Willatzen, and O. Albrektsen, “Detuned electrical dipoles for plasmonic sensing,” Nano Lett. 10(11), 4571–4577 (2010).
[Crossref] [PubMed]

T. Kosako, Y. Kadoya, and H. F. Hofmann, “Directional control of light by a nano-optical Yagi–Uda antenna,” Nat. Photonics 4(5), 312–315 (2010).
[Crossref]

A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, “Unidirectional emission of a quantum dot coupled to a nanoantenna,” Science 329(5994), 930–933 (2010).
[Crossref] [PubMed]

2009 (6)

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460(7259), 1110–1112 (2009).
[Crossref] [PubMed]

P. Bharadwaj, B. Deutsch, and L. Novotny, “Optical Antennas,” Adv. Opt. Photonics 1(3), 438 (2009).
[Crossref]

N. Verellen, Y. Sonnefraud, H. Sobhani, F. Hao, V. V. Moshchalkov, P. Van Dorpe, P. Nordlander, and S. A. Maier, “Fano resonances in individual coherent plasmonic nanocavities,” Nano Lett. 9(4), 1663–1667 (2009).
[Crossref] [PubMed]

M. Righini, P. Ghenuche, S. Cherukulappurath, V. Myroshnychenko, F. J. García de Abajo, and R. Quidant, “Nano-optical trapping of Rayleigh particles and Escherichia coli bacteria with resonant optical antennas,” Nano Lett. 9(10), 3387–3391 (2009).
[Crossref] [PubMed]

G. Lerosey, D. F. P. Pile, P. Matheu, G. Bartal, and X. Zhang, “Controlling the phase and amplitude of plasmon sources at a subwavelength scale,” Nano Lett. 9(1), 327–331 (2009).
[Crossref] [PubMed]

W. Ding, R. Bachelot, R. Espiau de Lamaestre, D. Macias, A. L. Baudrion, and P. Royer, “Understanding near/far-field engineering of optical dimer antennas through geometry modification,” Opt. Express 17(23), 21228–21239 (2009).
[Crossref] [PubMed]

2008 (3)

K. R. Catchpole and A. Polman, “Plasmonic solar cells,” Opt. Express 16(26), 21793–21800 (2008).
[Crossref] [PubMed]

S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 453(7196), 757–760 (2008).
[Crossref] [PubMed]

L. Tang, S. E. Kocabas, S. Latif, A. K. Okyay, D.-S. Ly-Gagnon, K. C. Saraswat, and D. A. B. Miller, “Nanometre-scale germanium photodetector enhanced by a near-infrared dipole antenna,” Nat. Photonics 2(4), 226–229 (2008).
[Crossref]

2007 (3)

C. Hubert, L. Billot, P. M. Adam, R. Bachelot, P. Royer, J. Grand, D. Gindre, K. D. Dorkenoo, and A. Fort, “Role of surface plasmon in second harmonic generation from gold nanorods,” Appl. Phys. Lett. 90(18), 181105 (2007).
[Crossref]

W. Ding, S. R. Andrews, and S. A. Maier, “Internal excitation and superfocusing of surface plasmon polaritons on a silver-coated optical fiber tip,” Phys. Rev. A 75(6), 063822 (2007).
[Crossref]

L. Novotny, “Effective wavelength scaling for optical antennas,” Phys. Rev. Lett. 98(26), 266802 (2007).
[Crossref] [PubMed]

2005 (4)

C. Hubert, A. Rumyantseva, G. Lerondel, J. Grand, S. Kostcheev, L. Billot, A. Vial, R. Bachelot, P. Royer, S.-H. Chang, S. K. Gray, G. P. Wiederrecht, and G. C. Schatz, “Near-field photochemical imaging of noble metal nanostructures,” Nano Lett. 5(4), 615–619 (2005).
[Crossref] [PubMed]

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308(5728), 1607–1609 (2005).
[Crossref] [PubMed]

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett. 95(25), 257403 (2005).
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M. Lipson, “Guiding, modulating, and emitting light on siliconchallenges and opportunities,” J. Lightwave Technol. 23(12), 4222–4238 (2005).
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2004 (1)

H. G. Frey, S. Witt, K. Felderer, and R. Guckenberger, “High-resolution imaging of single fluorescent molecules with the optical near-field of a metal tip,” Phys. Rev. Lett. 93(20), 200801 (2004).
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2003 (1)

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302(5644), 419–422 (2003).
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2002 (1)

D. Parker and D. C. Zimmermann, “Phased arrays - part 1: Theory and architectures,” IEEE Trans. Microw. Theory Tech. 50(3), 678–687 (2002).
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1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
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Adam, P. M.

C. Hubert, L. Billot, P. M. Adam, R. Bachelot, P. Royer, J. Grand, D. Gindre, K. D. Dorkenoo, and A. Fort, “Role of surface plasmon in second harmonic generation from gold nanorods,” Appl. Phys. Lett. 90(18), 181105 (2007).
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Adibi, A.

Y. Luo, M. Chamanzar, A. Apuzzo, R. Salas-Montiel, K. N. Nguyen, S. Blaize, and A. Adibi, “On-chip hybrid photonic-plasmonic light concentrator for nanofocusing in an integrated silicon photonics platform,” Nano Lett. 15(2), 849–856 (2015).
[Crossref] [PubMed]

M. Chamanzar, Z. Xia, S. Yegnanarayanan, and A. Adibi, “Hybrid integrated plasmonic-photonic waveguides for on-chip localized surface plasmon resonance (LSPR) sensing and spectroscopy,” Opt. Express 21(26), 32086–32098 (2013).
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Aieta, F.

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[Crossref] [PubMed]

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12(12), 6328–6333 (2012).
[Crossref] [PubMed]

F. Aieta, P. Genevet, N. Yu, M. A. Kats, Z. Gaburro, and F. Capasso, “Out-of-plane reflection and refraction of light by anisotropic optical antenna metasurfaces with phase discontinuities,” Nano Lett. 12(3), 1702–1706 (2012).
[Crossref] [PubMed]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
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Albrektsen, O.

A. B. Evlyukhin, S. I. Bozhevolnyi, A. Pors, M. G. Nielsen, I. P. Radko, M. Willatzen, and O. Albrektsen, “Detuned electrical dipoles for plasmonic sensing,” Nano Lett. 10(11), 4571–4577 (2010).
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Alivisatos, A. P.

N. Liu, M. L. Tang, M. Hentschel, H. Giessen, and A. P. Alivisatos, “Nanoantenna-enhanced gas sensing in a single tailored nanofocus,” Nat. Mater. 10(8), 631–636 (2011).
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N. Liu, F. Wen, Y. Zhao, Y. Wang, P. Nordlander, N. J. Halas, and A. Alù, “Individual nanoantennas loaded with three-dimensional optical nanocircuits,” Nano Lett. 13(1), 142–147 (2013).
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Andrews, S. R.

W. Ding, S. R. Andrews, and S. A. Maier, “Internal excitation and superfocusing of surface plasmon polaritons on a silver-coated optical fiber tip,” Phys. Rev. A 75(6), 063822 (2007).
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H. Aouani, M. Rahmani, M. Navarro-Cía, and S. A. Maier, “Third-harmonic-upconversion enhancement from a single semiconductor nanoparticle coupled to a plasmonic antenna,” Nat. Nanotechnol. 9(4), 290–294 (2014).
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Apuzzo, A.

Y. Luo, M. Chamanzar, A. Apuzzo, R. Salas-Montiel, K. N. Nguyen, S. Blaize, and A. Adibi, “On-chip hybrid photonic-plasmonic light concentrator for nanofocusing in an integrated silicon photonics platform,” Nano Lett. 15(2), 849–856 (2015).
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Armenise, M. N.

D. Conteduca, F. Dell’Olio, C. Ciminelli, T. F. Krauss, and M. N. Armenise, “Design of a high-performance optical tweezer for nanoparticle trapping,” Appl. Phys., A Mater. Sci. Process. 122(4), 1–6 (2016).
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Aussenegg, F. R.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett. 95(25), 257403 (2005).
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Bachelot, R.

Y.-Z. Sun, R. Bachelot, S. Blaize, Z.-Y. Li, and W. Ding, “Vector beam generation via micrometer-scale photonic integrated circuits and plasmonic nano-antennae,” J. Opt. Soc. Am. B 33(3), 360 (2016).
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W. Ding, R. Bachelot, R. Espiau de Lamaestre, D. Macias, A. L. Baudrion, and P. Royer, “Understanding near/far-field engineering of optical dimer antennas through geometry modification,” Opt. Express 17(23), 21228–21239 (2009).
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C. Hubert, L. Billot, P. M. Adam, R. Bachelot, P. Royer, J. Grand, D. Gindre, K. D. Dorkenoo, and A. Fort, “Role of surface plasmon in second harmonic generation from gold nanorods,” Appl. Phys. Lett. 90(18), 181105 (2007).
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C. Hubert, A. Rumyantseva, G. Lerondel, J. Grand, S. Kostcheev, L. Billot, A. Vial, R. Bachelot, P. Royer, S.-H. Chang, S. K. Gray, G. P. Wiederrecht, and G. C. Schatz, “Near-field photochemical imaging of noble metal nanostructures,” Nano Lett. 5(4), 615–619 (2005).
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Baets, R.

F. Peyskens, A. Dhakal, P. Van Dorpe, N. Le Thomas, and R. Baets, “Surface Enhanced Raman Spectroscopy Using a Single Mode Nanophotonic-Plasmonic Platform,” ACS Photonics 3(1), 102–108 (2016).
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K. Van Acoleyen, H. Rogier, and R. Baets, “Two-dimensional optical phased array antenna on silicon-on-insulator,” Opt. Express 18(13), 13655–13660 (2010).
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Bakker, R.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460(7259), 1110–1112 (2009).
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G. Lerosey, D. F. P. Pile, P. Matheu, G. Bartal, and X. Zhang, “Controlling the phase and amplitude of plasmon sources at a subwavelength scale,” Nano Lett. 9(1), 327–331 (2009).
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Baudrion, A. L.

Belgrave, A. M.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460(7259), 1110–1112 (2009).
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Bernal Arango, F.

F. Bernal Arango, A. Kwadrin, and A. F. Koenderink, “Plasmonic Antennas Hybridized with Dielectric Waveguides,” ACS Nano 6(11), 10156–10167 (2012).
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Bharadwaj, P.

P. Bharadwaj, B. Deutsch, and L. Novotny, “Optical Antennas,” Adv. Opt. Photonics 1(3), 438 (2009).
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Billot, L.

C. Hubert, L. Billot, P. M. Adam, R. Bachelot, P. Royer, J. Grand, D. Gindre, K. D. Dorkenoo, and A. Fort, “Role of surface plasmon in second harmonic generation from gold nanorods,” Appl. Phys. Lett. 90(18), 181105 (2007).
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C. Hubert, A. Rumyantseva, G. Lerondel, J. Grand, S. Kostcheev, L. Billot, A. Vial, R. Bachelot, P. Royer, S.-H. Chang, S. K. Gray, G. P. Wiederrecht, and G. C. Schatz, “Near-field photochemical imaging of noble metal nanostructures,” Nano Lett. 5(4), 615–619 (2005).
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Blaize, S.

Y.-Z. Sun, R. Bachelot, S. Blaize, Z.-Y. Li, and W. Ding, “Vector beam generation via micrometer-scale photonic integrated circuits and plasmonic nano-antennae,” J. Opt. Soc. Am. B 33(3), 360 (2016).
[Crossref]

Y. Luo, M. Chamanzar, A. Apuzzo, R. Salas-Montiel, K. N. Nguyen, S. Blaize, and A. Adibi, “On-chip hybrid photonic-plasmonic light concentrator for nanofocusing in an integrated silicon photonics platform,” Nano Lett. 15(2), 849–856 (2015).
[Crossref] [PubMed]

Blanchard, R.

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[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(6067), 427 (2012).
[Crossref] [PubMed]

Bozhevolnyi, S. I.

A. B. Evlyukhin, S. I. Bozhevolnyi, A. Pors, M. G. Nielsen, I. P. Radko, M. Willatzen, and O. Albrektsen, “Detuned electrical dipoles for plasmonic sensing,” Nano Lett. 10(11), 4571–4577 (2010).
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Briggs, D. P.

Y. Yang, W. Wang, P. Moitra, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Dielectric meta-reflectarray for broadband linear polarization conversion and optical vortex generation,” Nano Lett. 14(3), 1394–1399 (2014).
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Cabarrocas, P. R.

Capasso, F.

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
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N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12(12), 6328–6333 (2012).
[Crossref] [PubMed]

F. Aieta, P. Genevet, N. Yu, M. A. Kats, Z. Gaburro, and F. Capasso, “Out-of-plane reflection and refraction of light by anisotropic optical antenna metasurfaces with phase discontinuities,” Nano Lett. 12(3), 1702–1706 (2012).
[Crossref] [PubMed]

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[Crossref] [PubMed]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
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Castro-López, M.

I. M. Hancu, A. G. Curto, M. Castro-López, M. Kuttge, and N. F. van Hulst, “Multipolar interference for directed light emission,” Nano Lett. 14(1), 166–171 (2014).
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Catchpole, K. R.

Chamanzar, M.

Y. Luo, M. Chamanzar, A. Apuzzo, R. Salas-Montiel, K. N. Nguyen, S. Blaize, and A. Adibi, “On-chip hybrid photonic-plasmonic light concentrator for nanofocusing in an integrated silicon photonics platform,” Nano Lett. 15(2), 849–856 (2015).
[Crossref] [PubMed]

M. Chamanzar, Z. Xia, S. Yegnanarayanan, and A. Adibi, “Hybrid integrated plasmonic-photonic waveguides for on-chip localized surface plasmon resonance (LSPR) sensing and spectroscopy,” Opt. Express 21(26), 32086–32098 (2013).
[Crossref] [PubMed]

Chang, S.-H.

C. Hubert, A. Rumyantseva, G. Lerondel, J. Grand, S. Kostcheev, L. Billot, A. Vial, R. Bachelot, P. Royer, S.-H. Chang, S. K. Gray, G. P. Wiederrecht, and G. C. Schatz, “Near-field photochemical imaging of noble metal nanostructures,” Nano Lett. 5(4), 615–619 (2005).
[Crossref] [PubMed]

Chen, Y.-H.

W. Ding, Y.-H. Chen, and Z.-Y. Li, “Unidirectional emissions from dielectric photonic circuits decorated with plasmonic phased antenna arrays,” Chin. Phys. B 23(3), 037301 (2014).
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Cherukulappurath, S.

M. Righini, P. Ghenuche, S. Cherukulappurath, V. Myroshnychenko, F. J. García de Abajo, and R. Quidant, “Nano-optical trapping of Rayleigh particles and Escherichia coli bacteria with resonant optical antennas,” Nano Lett. 9(10), 3387–3391 (2009).
[Crossref] [PubMed]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

Ciminelli, C.

D. Conteduca, F. Dell’Olio, C. Ciminelli, T. F. Krauss, and M. N. Armenise, “Design of a high-performance optical tweezer for nanoparticle trapping,” Appl. Phys., A Mater. Sci. Process. 122(4), 1–6 (2016).
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Colin, C.

Collin, S.

Conteduca, D.

D. Conteduca, F. Dell’Olio, C. Ciminelli, T. F. Krauss, and M. N. Armenise, “Design of a high-performance optical tweezer for nanoparticle trapping,” Appl. Phys., A Mater. Sci. Process. 122(4), 1–6 (2016).
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Curto, A. G.

I. M. Hancu, A. G. Curto, M. Castro-López, M. Kuttge, and N. F. van Hulst, “Multipolar interference for directed light emission,” Nano Lett. 14(1), 166–171 (2014).
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A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, “Unidirectional emission of a quantum dot coupled to a nanoantenna,” Science 329(5994), 930–933 (2010).
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de Lustrac, A.

Degiron, A.

Dell’Olio, F.

D. Conteduca, F. Dell’Olio, C. Ciminelli, T. F. Krauss, and M. N. Armenise, “Design of a high-performance optical tweezer for nanoparticle trapping,” Appl. Phys., A Mater. Sci. Process. 122(4), 1–6 (2016).
[Crossref]

Deutsch, B.

P. Bharadwaj, B. Deutsch, and L. Novotny, “Optical Antennas,” Adv. Opt. Photonics 1(3), 438 (2009).
[Crossref]

Dhakal, A.

F. Peyskens, A. Dhakal, P. Van Dorpe, N. Le Thomas, and R. Baets, “Surface Enhanced Raman Spectroscopy Using a Single Mode Nanophotonic-Plasmonic Platform,” ACS Photonics 3(1), 102–108 (2016).
[Crossref]

Di Martino, G.

D. Vercruysse, Y. Sonnefraud, N. Verellen, F. B. Fuchs, G. Di Martino, L. Lagae, V. V. Moshchalkov, S. A. Maier, and P. Van Dorpe, “Unidirectional side scattering of light by a single-element nanoantenna,” Nano Lett. 13(8), 3843–3849 (2013).
[Crossref] [PubMed]

Ding, W.

Y.-Z. Sun, R. Bachelot, S. Blaize, Z.-Y. Li, and W. Ding, “Vector beam generation via micrometer-scale photonic integrated circuits and plasmonic nano-antennae,” J. Opt. Soc. Am. B 33(3), 360 (2016).
[Crossref]

W. Ding, Y.-H. Chen, and Z.-Y. Li, “Unidirectional emissions from dielectric photonic circuits decorated with plasmonic phased antenna arrays,” Chin. Phys. B 23(3), 037301 (2014).
[Crossref]

W. Ding, R. Bachelot, R. Espiau de Lamaestre, D. Macias, A. L. Baudrion, and P. Royer, “Understanding near/far-field engineering of optical dimer antennas through geometry modification,” Opt. Express 17(23), 21228–21239 (2009).
[Crossref] [PubMed]

W. Ding, S. R. Andrews, and S. A. Maier, “Internal excitation and superfocusing of surface plasmon polaritons on a silver-coated optical fiber tip,” Phys. Rev. A 75(6), 063822 (2007).
[Crossref]

Ditlbacher, H.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett. 95(25), 257403 (2005).
[Crossref] [PubMed]

Dorkenoo, K. D.

C. Hubert, L. Billot, P. M. Adam, R. Bachelot, P. Royer, J. Grand, D. Gindre, K. D. Dorkenoo, and A. Fort, “Role of surface plasmon in second harmonic generation from gold nanorods,” Appl. Phys. Lett. 90(18), 181105 (2007).
[Crossref]

Dubrovina, N.

Eisler, H.-J.

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308(5728), 1607–1609 (2005).
[Crossref] [PubMed]

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(6067), 427 (2012).
[Crossref] [PubMed]

Espiau de Lamaestre, R.

Evlyukhin, A. B.

A. B. Evlyukhin, S. I. Bozhevolnyi, A. Pors, M. G. Nielsen, I. P. Radko, M. Willatzen, and O. Albrektsen, “Detuned electrical dipoles for plasmonic sensing,” Nano Lett. 10(11), 4571–4577 (2010).
[Crossref] [PubMed]

Felderer, K.

H. G. Frey, S. Witt, K. Felderer, and R. Guckenberger, “High-resolution imaging of single fluorescent molecules with the optical near-field of a metal tip,” Phys. Rev. Lett. 93(20), 200801 (2004).
[Crossref] [PubMed]

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V. Giannini, A. I. Fernández-Domínguez, S. C. Heck, and S. A. Maier, “Plasmonic nanoantennas: fundamentals and their use in controlling the radiative properties of nanoemitters,” Chem. Rev. 111(6), 3888–3912 (2011).
[Crossref] [PubMed]

Fort, A.

C. Hubert, L. Billot, P. M. Adam, R. Bachelot, P. Royer, J. Grand, D. Gindre, K. D. Dorkenoo, and A. Fort, “Role of surface plasmon in second harmonic generation from gold nanorods,” Appl. Phys. Lett. 90(18), 181105 (2007).
[Crossref]

Frey, H. G.

H. G. Frey, S. Witt, K. Felderer, and R. Guckenberger, “High-resolution imaging of single fluorescent molecules with the optical near-field of a metal tip,” Phys. Rev. Lett. 93(20), 200801 (2004).
[Crossref] [PubMed]

Fuchs, F. B.

D. Vercruysse, Y. Sonnefraud, N. Verellen, F. B. Fuchs, G. Di Martino, L. Lagae, V. V. Moshchalkov, S. A. Maier, and P. Van Dorpe, “Unidirectional side scattering of light by a single-element nanoantenna,” Nano Lett. 13(8), 3843–3849 (2013).
[Crossref] [PubMed]

Gaburro, Z.

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[Crossref] [PubMed]

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12(12), 6328–6333 (2012).
[Crossref] [PubMed]

F. Aieta, P. Genevet, N. Yu, M. A. Kats, Z. Gaburro, and F. Capasso, “Out-of-plane reflection and refraction of light by anisotropic optical antenna metasurfaces with phase discontinuities,” Nano Lett. 12(3), 1702–1706 (2012).
[Crossref] [PubMed]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

García de Abajo, F. J.

M. Righini, P. Ghenuche, S. Cherukulappurath, V. Myroshnychenko, F. J. García de Abajo, and R. Quidant, “Nano-optical trapping of Rayleigh particles and Escherichia coli bacteria with resonant optical antennas,” Nano Lett. 9(10), 3387–3391 (2009).
[Crossref] [PubMed]

Genevet, P.

F. Aieta, P. Genevet, N. Yu, M. A. Kats, Z. Gaburro, and F. Capasso, “Out-of-plane reflection and refraction of light by anisotropic optical antenna metasurfaces with phase discontinuities,” Nano Lett. 12(3), 1702–1706 (2012).
[Crossref] [PubMed]

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12(12), 6328–6333 (2012).
[Crossref] [PubMed]

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[Crossref] [PubMed]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Ghasemi, R.

Ghenuche, P.

M. Righini, P. Ghenuche, S. Cherukulappurath, V. Myroshnychenko, F. J. García de Abajo, and R. Quidant, “Nano-optical trapping of Rayleigh particles and Escherichia coli bacteria with resonant optical antennas,” Nano Lett. 9(10), 3387–3391 (2009).
[Crossref] [PubMed]

Giannini, V.

V. Giannini, A. I. Fernández-Domínguez, S. C. Heck, and S. A. Maier, “Plasmonic nanoantennas: fundamentals and their use in controlling the radiative properties of nanoemitters,” Chem. Rev. 111(6), 3888–3912 (2011).
[Crossref] [PubMed]

Giessen, H.

N. Liu, M. L. Tang, M. Hentschel, H. Giessen, and A. P. Alivisatos, “Nanoantenna-enhanced gas sensing in a single tailored nanofocus,” Nat. Mater. 10(8), 631–636 (2011).
[Crossref] [PubMed]

Gindre, D.

C. Hubert, L. Billot, P. M. Adam, R. Bachelot, P. Royer, J. Grand, D. Gindre, K. D. Dorkenoo, and A. Fort, “Role of surface plasmon in second harmonic generation from gold nanorods,” Appl. Phys. Lett. 90(18), 181105 (2007).
[Crossref]

Grand, J.

C. Hubert, L. Billot, P. M. Adam, R. Bachelot, P. Royer, J. Grand, D. Gindre, K. D. Dorkenoo, and A. Fort, “Role of surface plasmon in second harmonic generation from gold nanorods,” Appl. Phys. Lett. 90(18), 181105 (2007).
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J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493(7431), 195–199 (2013).
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Van Dorpe, P.

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N. Verellen, Y. Sonnefraud, H. Sobhani, F. Hao, V. V. Moshchalkov, P. Van Dorpe, P. Nordlander, and S. A. Maier, “Fano resonances in individual coherent plasmonic nanocavities,” Nano Lett. 9(4), 1663–1667 (2009).
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N. Liu, F. Wen, Y. Zhao, Y. Wang, P. Nordlander, N. J. Halas, and A. Alù, “Individual nanoantennas loaded with three-dimensional optical nanocircuits,” Nano Lett. 13(1), 142–147 (2013).
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J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493(7431), 195–199 (2013).
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F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
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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(6054), 333–337 (2011).
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G. Lerosey, D. F. P. Pile, P. Matheu, G. Bartal, and X. Zhang, “Controlling the phase and amplitude of plasmon sources at a subwavelength scale,” Nano Lett. 9(1), 327–331 (2009).
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N. Liu, F. Wen, Y. Zhao, Y. Wang, P. Nordlander, N. J. Halas, and A. Alù, “Individual nanoantennas loaded with three-dimensional optical nanocircuits,” Nano Lett. 13(1), 142–147 (2013).
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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(5), 426–431 (2012).
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ACS Photonics (1)

F. Peyskens, A. Dhakal, P. Van Dorpe, N. Le Thomas, and R. Baets, “Surface Enhanced Raman Spectroscopy Using a Single Mode Nanophotonic-Plasmonic Platform,” ACS Photonics 3(1), 102–108 (2016).
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P. Bharadwaj, B. Deutsch, and L. Novotny, “Optical Antennas,” Adv. Opt. Photonics 1(3), 438 (2009).
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C. Hubert, L. Billot, P. M. Adam, R. Bachelot, P. Royer, J. Grand, D. Gindre, K. D. Dorkenoo, and A. Fort, “Role of surface plasmon in second harmonic generation from gold nanorods,” Appl. Phys. Lett. 90(18), 181105 (2007).
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D. Conteduca, F. Dell’Olio, C. Ciminelli, T. F. Krauss, and M. N. Armenise, “Design of a high-performance optical tweezer for nanoparticle trapping,” Appl. Phys., A Mater. Sci. Process. 122(4), 1–6 (2016).
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V. Giannini, A. I. Fernández-Domínguez, S. C. Heck, and S. A. Maier, “Plasmonic nanoantennas: fundamentals and their use in controlling the radiative properties of nanoemitters,” Chem. Rev. 111(6), 3888–3912 (2011).
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W. Ding, Y.-H. Chen, and Z.-Y. Li, “Unidirectional emissions from dielectric photonic circuits decorated with plasmonic phased antenna arrays,” Chin. Phys. B 23(3), 037301 (2014).
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Y. Yang, W. Wang, P. Moitra, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Dielectric meta-reflectarray for broadband linear polarization conversion and optical vortex generation,” Nano Lett. 14(3), 1394–1399 (2014).
[Crossref] [PubMed]

G. Lerosey, D. F. P. Pile, P. Matheu, G. Bartal, and X. Zhang, “Controlling the phase and amplitude of plasmon sources at a subwavelength scale,” Nano Lett. 9(1), 327–331 (2009).
[Crossref] [PubMed]

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[Crossref] [PubMed]

Y. Luo, M. Chamanzar, A. Apuzzo, R. Salas-Montiel, K. N. Nguyen, S. Blaize, and A. Adibi, “On-chip hybrid photonic-plasmonic light concentrator for nanofocusing in an integrated silicon photonics platform,” Nano Lett. 15(2), 849–856 (2015).
[Crossref] [PubMed]

F. Aieta, P. Genevet, N. Yu, M. A. Kats, Z. Gaburro, and F. Capasso, “Out-of-plane reflection and refraction of light by anisotropic optical antenna metasurfaces with phase discontinuities,” Nano Lett. 12(3), 1702–1706 (2012).
[Crossref] [PubMed]

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12(12), 6328–6333 (2012).
[Crossref] [PubMed]

D. Vercruysse, Y. Sonnefraud, N. Verellen, F. B. Fuchs, G. Di Martino, L. Lagae, V. V. Moshchalkov, S. A. Maier, and P. Van Dorpe, “Unidirectional side scattering of light by a single-element nanoantenna,” Nano Lett. 13(8), 3843–3849 (2013).
[Crossref] [PubMed]

I. M. Hancu, A. G. Curto, M. Castro-López, M. Kuttge, and N. F. van Hulst, “Multipolar interference for directed light emission,” Nano Lett. 14(1), 166–171 (2014).
[Crossref] [PubMed]

M. Righini, P. Ghenuche, S. Cherukulappurath, V. Myroshnychenko, F. J. García de Abajo, and R. Quidant, “Nano-optical trapping of Rayleigh particles and Escherichia coli bacteria with resonant optical antennas,” Nano Lett. 9(10), 3387–3391 (2009).
[Crossref] [PubMed]

A. B. Evlyukhin, S. I. Bozhevolnyi, A. Pors, M. G. Nielsen, I. P. Radko, M. Willatzen, and O. Albrektsen, “Detuned electrical dipoles for plasmonic sensing,” Nano Lett. 10(11), 4571–4577 (2010).
[Crossref] [PubMed]

C. Hubert, A. Rumyantseva, G. Lerondel, J. Grand, S. Kostcheev, L. Billot, A. Vial, R. Bachelot, P. Royer, S.-H. Chang, S. K. Gray, G. P. Wiederrecht, and G. C. Schatz, “Near-field photochemical imaging of noble metal nanostructures,” Nano Lett. 5(4), 615–619 (2005).
[Crossref] [PubMed]

N. Verellen, Y. Sonnefraud, H. Sobhani, F. Hao, V. V. Moshchalkov, P. Van Dorpe, P. Nordlander, and S. A. Maier, “Fano resonances in individual coherent plasmonic nanocavities,” Nano Lett. 9(4), 1663–1667 (2009).
[Crossref] [PubMed]

N. Liu, F. Wen, Y. Zhao, Y. Wang, P. Nordlander, N. J. Halas, and A. Alù, “Individual nanoantennas loaded with three-dimensional optical nanocircuits,” Nano Lett. 13(1), 142–147 (2013).
[Crossref] [PubMed]

Nat. Mater. (3)

N. Liu, M. L. Tang, M. Hentschel, H. Giessen, and A. P. Alivisatos, “Nanoantenna-enhanced gas sensing in a single tailored nanofocus,” Nat. Mater. 10(8), 631–636 (2011).
[Crossref] [PubMed]

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
[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. Mater. 11(5), 426–431 (2012).
[Crossref] [PubMed]

Nat. Nanotechnol. (1)

H. Aouani, M. Rahmani, M. Navarro-Cía, and S. A. Maier, “Third-harmonic-upconversion enhancement from a single semiconductor nanoparticle coupled to a plasmonic antenna,” Nat. Nanotechnol. 9(4), 290–294 (2014).
[Crossref] [PubMed]

Nat. Photonics (3)

L. Tang, S. E. Kocabas, S. Latif, A. K. Okyay, D.-S. Ly-Gagnon, K. C. Saraswat, and D. A. B. Miller, “Nanometre-scale germanium photodetector enhanced by a near-infrared dipole antenna,” Nat. Photonics 2(4), 226–229 (2008).
[Crossref]

L. Novotny and N. van Hulst, “Antennas for light,” Nat. Photonics 5(2), 83–90 (2011).
[Crossref]

T. Kosako, Y. Kadoya, and H. F. Hofmann, “Directional control of light by a nano-optical Yagi–Uda antenna,” Nat. Photonics 4(5), 312–315 (2010).
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Figures (6)

Fig. 1
Fig. 1 (a) Effective mode index of the short-range SPP wave as a function of the gold nanorod width (black and red curve). The effective propagation distance of the SPP (Leff = α−1, blue curve) is normalized with respect to the effective wavelength λ/Re(neff). Here, the loss coefficient is α ≡ -ln[I(x)/I(0)]/x = (4π/λ)·Im(neff) and the working wavelength is λ = 1.55 μm. Insert: square root of intensity profile in y-z plane. (b) Schematic of an LSPR being established in a gold nanorod. (c) Reflectivity of the SPP wave at an open end. (d) Square root of intensity profile (recorded at the substrate interface) and instantaneous charge distributions of electric dipolar, electric quadrupolar, and cascaded gold nanorods, respectively. The dipole and quadrupole resonance natures are clarified by the numbers of the zeros (the white dashed lines). The cross section of the gold nanorod is 80 nm × 80 nm, and the gap is 20 nm. The blue (red) color represents the minimum (maximum) value.
Fig. 2
Fig. 2 (a,b) Schematics of a single gold nanorod (Type-I) and two cascaded gold nanorods (Type-IIa and IIb) being excited by guided wave of a single-mode (quasi-TE) silicon waveguide. (c, d, e) Simulated intensities (in logarithmical scale) and (f, g, h) phases of the far-field radiation (in the substrate normal direction) for, respectively, Type-I, Type-IIa, and Type-IIb radiation pixels as a function of gap distance (g) and nanorod length (l). The sixteen white circles represent a set of radiation pixels with same strength and varied phases covering the 2π range (see Table 1). λ = 1.55 μm.
Fig. 3
Fig. 3 (a) Near-field profile (square root of electric field intensity at the substrate interface) of an assembled device comprised of two pairs of radiation pixels (Type-I + Type-IIa). Far-field intensity patterns (in the substrate side) of (c) one pair of Type-I radiation pixels (g = 40 nm, l = 450 nm), (d) one pair of Type-IIa radiation pixels (g = 100 nm, LQ = 600 nm, l = 200 nm), and (d,e) their assemblies. The parameters in (e) are (g = 40 nm, l = 325 nm, Type-IIa), (g = 40 nm, l = 450 nm, Type-I), and d = 380 nm. In (f), they are (g = 40 nm, l = 450 nm, Type-I), (g = 50 nm, l = 250 nm, Type-IIa), and d = 380 nm. The spherical coordinates (θ, ϕ) is denoted in both (b) and (e).
Fig. 4
Fig. 4 (a) Schematic of an out-of-plane light collimator comprised of four silicon waveguides and a plasmonic nanoantenna array. Far-field patterns of (b,c) the 2 × 2 arrays and (e,f) the 6 × 10 arrays. The results are presented in both 2D and 3D views. (d) The phase profile recorded at z = −5 μm for the main lobe of the radiation in case (e). A planar equal-phase wavefront is manifest.
Fig. 5
Fig. 5 (a) Schematic of a beam focuser with the effective area of ~6 μm × 5.2 μm and the scale of 4 × 14. (b) Required phase distributions at the PIC interface (solid lines) and provided phases by our nanoantennas (square symbols). Insert: the phase distribution at the interface. (c) Full-width at half maximum (FWHM, Δx and Δy) of the focused beam as a function of the working wavelength. (d-f) Simulated intensity distributions at λ = 1550 nm.
Fig. 6
Fig. 6 (a) Schematic of the TM01 vector mode generator constituted by a silicon micro-ring with the radius of 4.15 μm and 15 radiation subunits separated by 4π. (b) The new and (c) the old radiation subunits comprised of four and two radiation pixels, respectively. (d,e) The field profiles (|Ex|2 + |Ey|2) of the radiated beams recorded at z = −5 μm for the two structures. The parameters in (b,c) from top to bottom are (g = 340nm, l = 400nm, Type-I)/(g = 80nm, l = 350nm, Type-IIa)/(g = 220nm, l = 300nm, Type-I)/(g = 80nm, l = 250nm, Type-IIa) and (g = 100nm, l = 320nm, Type-I)/(g = 180nm, l = 400nm, Type-I), respectively.

Tables (3)

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Table 1 Sixteen radiation pixels with the same far-field intensity and different phase shifts, Φ's.

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Table 2 Constituent radiation pixels of the 6 × 2 nanoantenna arrays in Figs. 4(d) and 4(e).

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Table 3 Constituent radiation pixels of the 4 × 14 nanoantenna arrays in Fig. 5.

Equations (8)

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I= I 0 λ 0 2 λ 0 2 +4 Q 2 (λ λ 0 ) 2 ,
φ=atan(2Q λ 0 λ λ 0 ) ,
Δϑ=( 2π/λ )( n eff n Si O 2 sinθcosϕ)Δy+ΔΦ ,
ϑ k =( 2π/λ )[ n eff y k n Si O 2 sinθ( x k sinϕ+ y k cosϕ)]+ Φ k ,
I total = | k A k (θ,φ) e i ϑ k (θ,φ) | 2 .
ϑ k =( 2π/λ )[ n eff y k + n Si O 2 ( x k x 0 ) 2 + ( y k y 0 ) 2 + ( z k z 0 ) 2 ]+ Φ k ,
ϑ required =( 2π/λ ) n Si O 2 X 1,2 2 + y 2 + z 0 2 ,
ϑ k_antenna =( 2π/λ )[ n eff y k + n Si O 2 ( x k 2 + y k 2 + z 0 2 X 1,2 2 + y k 2 + z 0 2 )]+ Φ k .

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