Abstract

We propose a novel optical hybrid plasmonic patch nano-antenna for operation at the standard telecommunication wavelength of 1550 nm. The nano-antenna is designed to be compatible with a hybrid plasmonic waveguide through matching of both the operational mode and the wave impedance. The antenna is designed to receive the optical signal from a planar waveguide and redirect the signal out of plane, and is therefore useful for inter- or intra-chip optical communications and sensing. The transmission line model in conjunction with surface plasmon theory is used to develop analytical formulas for design and analysis, and a 3-dimensional full-wave numerical method is used to validate the design. The proposed device provides a bandwidth of more than 15 THz, a gain of 5.6 dB, and an efficiency of 87%. Furthermore, by designing an 8 × 8 array of the proposed antenna, a directivity of 20 dBi and steering of the beam angle are achieved by controlling the relative phase shift between elements of the array.

© 2012 OSA

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2012 (3)

A. Yaacobi, E. Timurdogan, and M. R. Watts, “Vertical emitting aperture nanoantennas,” Opt. Letters 37, 1454–1456 (2012).
[CrossRef]

R. F. Oulton, “Surface plasmon lasers: sources of nanoscopic light 15,” Materials Today 15, 26–34 (2012).
[CrossRef]

J. Pfeifle, L. Alloatti, W. Freude, J. Leuthold, and C. Koos, “Silicon-organic hybrid phase shifter based on a slot waveguide with a liquid crystal cladding,” Opt. Express 20, 15359–15376 (2012).
[CrossRef] [PubMed]

2011 (8)

Q. Song, S. Campione, O. Boyraz, and F. Capolino, “Silicon-based optical leaky wave antenna with narrow beam radiation,” Opt. Express 19, 8735–8749 (2011).
[CrossRef] [PubMed]

D. Dregely, R. Taubert, J. Dorfmuller, R. Vogelgesang, K. Kern, and H. Giessen, “3d optical yagi-uda nanoantenna array,” Nat Commun 2, 10.1038 (2011).
[CrossRef]

K. J. A. Ooi, P. Bai, M. X. Gu, and L. K. Ang, “Design of a monopole-antenna-based resonant nanocavity for detection of optical power from hybrid plasmonic waveguides,” Opt. Express 19, 17075–17085 (2011).
[CrossRef] [PubMed]

L. Novotny and N. F. van Hulst, “Antennas for light,” Nat Photon 5, 83–90 (2011).
[CrossRef]

T. Shegai, S. Chen, V. D. Miljkovic, G. Zengin, P. Johansson, and M. Kall, “A bimetallic nanoantenna for directional colour routing,” Nat Commun 2, 481–486 (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, 333–337 (2011).
[CrossRef] [PubMed]

S. Sederberg and A. Elezzabi, “Sierpiski fractal plasmonic antenna: a fractal abstraction of the plasmonic bowtie antenna,” Opt. Express 19, 10456–10461 (2011).
[CrossRef] [PubMed]

S. Sederberg and A. Y. Elezzabi, “Nanoscale plasmonic contour bowtie antenna operating in the mid-infrared,” Opt. Express 19, 15532–15537 (2011).
[CrossRef] [PubMed]

2010 (5)

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, 930–933 (2010).
[CrossRef] [PubMed]

M. W. Maqsood, R. Mehfuz, and K. J. Chau, “Design and optimization of a high-efficiency nanoscale ± 90 degree light-bending structure by mode selection and tailoring,” Appl. Phys. Lett. 97, 151111 (2010).
[CrossRef]

L. Cao, J. S. Park, P. Fan, B. Clemens, and M. L. Brongersma, “Resonant germanium nanoantenna photodetectors,” Nano Lett. 10, 1229–1233 (2010).
[CrossRef] [PubMed]

I. Avrutsky, R. Soref, and W. Buchwald, “Sub-wavelength plasmonic modes in a conductor-gap-dielectric system with a nanoscale gap,” Opt. Express 18, 348–363 (2010).
[CrossRef] [PubMed]

M. Wu, Z. Han, and V. Van, “Conductor-gap-silicon plasmonic waveguides and passive components at subwavelength scale,” Opt. Express 18, 11728–11736 (2010).
[CrossRef] [PubMed]

2009 (3)

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009).
[CrossRef] [PubMed]

J. A. Schuller, T. Taubner, and M. L. Brongersma, “Optical antenna thermal emitters,” Nat Photon 3, 658–661 (2009).
[CrossRef]

D. Dai and S. He, “A silicon-based hybrid plasmonic waveguide with a metal cap for a nano-scale light confinement,” Opt. Express 17, 16646–16653 (2009).
[CrossRef] [PubMed]

2008 (8)

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat Mater 7, 442–453 (2008).
[CrossRef] [PubMed]

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for sub-wavelength confinement and long-range propagation,” Nat Photon 2, 496–500 (2008).
[CrossRef]

J. Guo and R. Adato, “Control of 2d plasmon-polariton mode with dielectric nanolayers,” Opt. Express 16, 1232–1237 (2008).
[CrossRef] [PubMed]

R. Salvador, A. Martinez, C. Garcia-Meca, R. Ortuno, and J. Marti, “Analysis of hybrid dielectric plasmonic waveguides,” Selected Topics in Quantum Electronics, IEEE Journal 14, 1496–1501 (2008).
[CrossRef]

H. Taminiau, D. Stefani, B. Segerink, and N. F. van Hulst, “Optical antennas direct single-molecule emission,” Nat Photon 2, 234–237 (2008).
[CrossRef]

T. H. Taminiau, F. D. Stefani, and N. F. van Hulst, “Enhanced directional excitation and emission of single emitters by a nano-optical yagi-uda antenna,” Opt. Express 16, 10858–10866 (2008).
[CrossRef] [PubMed]

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

A. Alu and N. Engheta, “Input impedance, nanocircuit loading, and radiation tuning of optical nanoantennas,” Phys. Rev. Lett. 101, 043901 (2008).
[CrossRef] [PubMed]

2007 (2)

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

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Reports on Progress in Physics 70, 1–88 (2007).
[CrossRef]

2006 (2)

Y. D. Wilde, F. Formanek, R. Carminati, B. Gralak, P. A. Lemoine, K. Joulain, J. P. Mulet, Y. Chen, and J. J. Greffet, “Thermal radiation scanning tunnelling microscopy,” Nature 444, 740–743 (2006).
[CrossRef] [PubMed]

L. Novotny and S. J. Stranick, “Near-field optical microscopy and spectroscopy with pointed probes,” Ann. Rev. Phys. Chem. 57, 303–331 (2006).
[CrossRef]

2005 (3)

J. Alda, J. M. Rico-Garca, J. M. Lpez-Alonso, and G. Boreman, “Optical antennas for nano-photonic applications,” Nanotechnology 16, S230 (2005).
[CrossRef]

F. Gonzlez and G. Boreman, “Comparison of dipole, bowtie, spiral and log-periodic ir antennas,” Infrared Physics & Technology 46, 418–428 (2005).
[CrossRef] [PubMed]

J. N. Farahani, D. W. Pohl, H. J. Eisler, and B. Hecht, “Single quantum dot coupled to a scanning optical antenna: A tunable superemitter,” Phys. Rev. Lett. 95, 017402 (2005).
[CrossRef] [PubMed]

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, 200801 (2004).
[CrossRef] [PubMed]

2002 (1)

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[CrossRef] [PubMed]

1997 (1)

R. D. Grober, R. J. Schoelkopf, and D. E. Prober, “Optical antenna: Towards a unity efficiency near-field optical probe,” Appl. Phys. Lett. 70, 1354–1356 (1997).
[CrossRef]

1989 (1)

U. C. Fischer and D. W. Pohl, “Observation of single-particle plasmons by near-field optical microscopy,” Phys. Rev. Lett. 62, 458–461 (1989).
[CrossRef] [PubMed]

1985 (1)

1972 (1)

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

1951 (1)

A. Alu and N. Engheta, “Hertzian plasmonic nanodimer as an efficient optical nanoantenna,” Phys. Rev. B 78, 195111 (2008).

Adato, R.

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]

Alda, J.

J. Alda, J. M. Rico-Garca, J. M. Lpez-Alonso, and G. Boreman, “Optical antennas for nano-photonic applications,” Nanotechnology 16, S230 (2005).
[CrossRef]

Alloatti, L.

Alu, A.

A. Alu and N. Engheta, “Input impedance, nanocircuit loading, and radiation tuning of optical nanoantennas,” Phys. Rev. Lett. 101, 043901 (2008).
[CrossRef] [PubMed]

A. Alu and N. Engheta, “Hertzian plasmonic nanodimer as an efficient optical nanoantenna,” Phys. Rev. B 78, 195111 (2008).

Amzajerdian, F.

F. Amzajerdian, D. F. Pierrottet, L. B. Petway, G. D. Hines, and V. E. Roback, “Lidar systems for precision navigation and safe landing on planetary bodies,” NASA. Technical Reports (2011).

Ang, L. K.

Anker, J. N.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat Mater 7, 442–453 (2008).
[CrossRef] [PubMed]

Avrutsky, I.

Bai, P.

Balanis, C. A.

C. A. Balanis, Antenna Theory: Analysis and Design, 3rd Edition (Wiley, 2005).

Bartal, G.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009).
[CrossRef] [PubMed]

Boreman, G.

F. Gonzlez and G. Boreman, “Comparison of dipole, bowtie, spiral and log-periodic ir antennas,” Infrared Physics & Technology 46, 418–428 (2005).
[CrossRef] [PubMed]

J. Alda, J. M. Rico-Garca, J. M. Lpez-Alonso, and G. Boreman, “Optical antennas for nano-photonic applications,” Nanotechnology 16, S230 (2005).
[CrossRef]

Boyraz, O.

Brongersma, M. L.

L. Cao, J. S. Park, P. Fan, B. Clemens, and M. L. Brongersma, “Resonant germanium nanoantenna photodetectors,” Nano Lett. 10, 1229–1233 (2010).
[CrossRef] [PubMed]

J. A. Schuller, T. Taubner, and M. L. Brongersma, “Optical antenna thermal emitters,” Nat Photon 3, 658–661 (2009).
[CrossRef]

Buchwald, W.

Campione, S.

Cao, L.

L. Cao, J. S. Park, P. Fan, B. Clemens, and M. L. Brongersma, “Resonant germanium nanoantenna photodetectors,” Nano Lett. 10, 1229–1233 (2010).
[CrossRef] [PubMed]

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]

Capolino, F.

Carminati, R.

Y. D. Wilde, F. Formanek, R. Carminati, B. Gralak, P. A. Lemoine, K. Joulain, J. P. Mulet, Y. Chen, and J. J. Greffet, “Thermal radiation scanning tunnelling microscopy,” Nature 444, 740–743 (2006).
[CrossRef] [PubMed]

Chau, K. J.

M. W. Maqsood, R. Mehfuz, and K. J. Chau, “Design and optimization of a high-efficiency nanoscale ± 90 degree light-bending structure by mode selection and tailoring,” Appl. Phys. Lett. 97, 151111 (2010).
[CrossRef]

Chen, S.

T. Shegai, S. Chen, V. D. Miljkovic, G. Zengin, P. Johansson, and M. Kall, “A bimetallic nanoantenna for directional colour routing,” Nat Commun 2, 481–486 (2011).
[CrossRef] [PubMed]

Chen, Y.

Y. D. Wilde, F. Formanek, R. Carminati, B. Gralak, P. A. Lemoine, K. Joulain, J. P. Mulet, Y. Chen, and J. J. Greffet, “Thermal radiation scanning tunnelling microscopy,” Nature 444, 740–743 (2006).
[CrossRef] [PubMed]

Christy, R. W.

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

Chulkov, E. V.

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Reports on Progress in Physics 70, 1–88 (2007).
[CrossRef]

Clemens, B.

L. Cao, J. S. Park, P. Fan, B. Clemens, and M. L. Brongersma, “Resonant germanium nanoantenna photodetectors,” Nano Lett. 10, 1229–1233 (2010).
[CrossRef] [PubMed]

Curto, A. G.

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, 930–933 (2010).
[CrossRef] [PubMed]

Dai, D.

Dai, L.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009).
[CrossRef] [PubMed]

Degiron, A.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[CrossRef] [PubMed]

Devaux, E.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[CrossRef] [PubMed]

Dorfmuller, J.

D. Dregely, R. Taubert, J. Dorfmuller, R. Vogelgesang, K. Kern, and H. Giessen, “3d optical yagi-uda nanoantenna array,” Nat Commun 2, 10.1038 (2011).
[CrossRef]

Dregely, D.

D. Dregely, R. Taubert, J. Dorfmuller, R. Vogelgesang, K. Kern, and H. Giessen, “3d optical yagi-uda nanoantenna array,” Nat Commun 2, 10.1038 (2011).
[CrossRef]

Ebbesen, T. W.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[CrossRef] [PubMed]

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T. Shegai, S. Chen, V. D. Miljkovic, G. Zengin, P. Johansson, and M. Kall, “A bimetallic nanoantenna for directional colour routing,” Nat Commun 2, 481–486 (2011).
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H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
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T. Shegai, S. Chen, V. D. Miljkovic, G. Zengin, P. Johansson, and M. Kall, “A bimetallic nanoantenna for directional colour routing,” Nat Commun 2, 481–486 (2011).
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L. Tang, S. E. Kocabas, S. Latif, A. K. Okyay, D. Ly-Gagnon, K. C. Saraswat, and D. A. B. Miller, “Nanometre-scale germanium photodetector enhanced by a near-infrared dipole antenna,” Nat Photon 2, 226–229 (2008).
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R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for sub-wavelength confinement and long-range propagation,” Nat Photon 2, 496–500 (2008).
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L. Cao, J. S. Park, P. Fan, B. Clemens, and M. L. Brongersma, “Resonant germanium nanoantenna photodetectors,” Nano Lett. 10, 1229–1233 (2010).
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Pierrottet, D. F.

F. Amzajerdian, D. F. Pierrottet, L. B. Petway, G. D. Hines, and V. E. Roback, “Lidar systems for precision navigation and safe landing on planetary bodies,” NASA. Technical Reports (2011).

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R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for sub-wavelength confinement and long-range propagation,” Nat Photon 2, 496–500 (2008).
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J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Reports on Progress in Physics 70, 1–88 (2007).
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J. N. Farahani, D. W. Pohl, H. J. Eisler, and B. Hecht, “Single quantum dot coupled to a scanning optical antenna: A tunable superemitter,” Phys. Rev. Lett. 95, 017402 (2005).
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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, 930–933 (2010).
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J. Alda, J. M. Rico-Garca, J. M. Lpez-Alonso, and G. Boreman, “Optical antennas for nano-photonic applications,” Nanotechnology 16, S230 (2005).
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F. Amzajerdian, D. F. Pierrottet, L. B. Petway, G. D. Hines, and V. E. Roback, “Lidar systems for precision navigation and safe landing on planetary bodies,” NASA. Technical Reports (2011).

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R. Salvador, A. Martinez, C. Garcia-Meca, R. Ortuno, and J. Marti, “Analysis of hybrid dielectric plasmonic waveguides,” Selected Topics in Quantum Electronics, IEEE Journal 14, 1496–1501 (2008).
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L. Tang, S. E. Kocabas, S. Latif, A. K. Okyay, D. Ly-Gagnon, K. C. Saraswat, and D. A. B. Miller, “Nanometre-scale germanium photodetector enhanced by a near-infrared dipole antenna,” Nat Photon 2, 226–229 (2008).
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J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat Mater 7, 442–453 (2008).
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T. Shegai, S. Chen, V. D. Miljkovic, G. Zengin, P. Johansson, and M. Kall, “A bimetallic nanoantenna for directional colour routing,” Nat Commun 2, 481–486 (2011).
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J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Reports on Progress in Physics 70, 1–88 (2007).
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Soref, R.

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R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009).
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H. Taminiau, D. Stefani, B. Segerink, and N. F. van Hulst, “Optical antennas direct single-molecule emission,” Nat Photon 2, 234–237 (2008).
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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, 930–933 (2010).
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T. H. Taminiau, F. D. Stefani, and N. F. van Hulst, “Enhanced directional excitation and emission of single emitters by a nano-optical yagi-uda antenna,” Opt. Express 16, 10858–10866 (2008).
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L. Tang, S. E. Kocabas, S. Latif, A. K. Okyay, D. Ly-Gagnon, K. C. Saraswat, and D. A. B. Miller, “Nanometre-scale germanium photodetector enhanced by a near-infrared dipole antenna,” Nat Photon 2, 226–229 (2008).
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D. Dregely, R. Taubert, J. Dorfmuller, R. Vogelgesang, K. Kern, and H. Giessen, “3d optical yagi-uda nanoantenna array,” Nat Commun 2, 10.1038 (2011).
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J. A. Schuller, T. Taubner, and M. L. Brongersma, “Optical antenna thermal emitters,” Nat Photon 3, 658–661 (2009).
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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, 333–337 (2011).
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J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat Mater 7, 442–453 (2008).
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L. Novotny and N. F. van Hulst, “Antennas for light,” Nat Photon 5, 83–90 (2011).
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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, 930–933 (2010).
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D. Dregely, R. Taubert, J. Dorfmuller, R. Vogelgesang, K. Kern, and H. Giessen, “3d optical yagi-uda nanoantenna array,” Nat Commun 2, 10.1038 (2011).
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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, 930–933 (2010).
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Figures (8)

Fig. 1
Fig. 1

Patch nano-antenna fed by a plasmonic hybrid waveguide (a) Perspective view (b) Cross-sectional schematic.

Fig. 2
Fig. 2

Numerically calculated real component of the effective refractive index, neff.

Fig. 3
Fig. 3

Numerically calculated y-component of electric field, |Ey| (a) in two dimensions at the cross section of the hybrid plasmonic waveguide that feeds the nano-antenna and (b) in one dimension when x = 0.

Fig. 4
Fig. 4

The magnitude of the different components of the electric field at the center of the SiO2 layer (x = 0 and y = −105 nm) for different values of z, and at the wavelength of 1550 nm.

Fig. 5
Fig. 5

Numerically calculated ratio of the reflected wave to the incident wave, S11, versus operation frequency and wavelength.

Fig. 6
Fig. 6

3-D Radiation gain plot, (a) Radiation pattern alone (b) Radiation pattern with the nano-antenna structure superimposed for reference.

Fig. 7
Fig. 7

3-D Radiation pattern of a 8x8 array of the designed patch antenna.

Fig. 8
Fig. 8

Using the designed antenna for beam-steering applications (a) The resultant pattern when Δϕ = −90°, (b) The resultant pattern when Δϕ = +90°.

Equations (4)

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

E y E z = K z K y = ω c ε m ε d ε m + ε d ω c ε d 2 ε m + ε d = ε m ε d
Z antenna = 1 Y in = 1 2 G , G = W 2 120 λ 0 [ 1 1 24 ( 2 π h λ 0 ) 2 ]
Z Waveguide = Z 0 n eff = 377 n eff
n eff = ε d ε m ε d + ε m F ( W , h ) , F ( W , h ) = 1 + 1798 W + 3114 h + 10.55 W h 32300 + 759.7 W + 3337 h + 10.55 W h

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