Abstract

In this paper, we theoretically characterize the performance of array of plasmonic core-shell nano-radiators located over layered substrates. Engineered substrates are investigated to manipulate the radiation performance of nanoantennas. A rigorous analytical approach for the problem in hand is developed by applying Green’s function analysis of dipoles located above layered materials. It is illustrated that around the electric scattering resonances of the subwavelength spherical particles, each particle can be viewed as an induced electric dipole which is related to the total electric field upon that particle by a polarizability factor. Utilizing this, we can effectively study the physical performance of such structures. The accuracy of our theoretical model is validated through using a full-wave finite difference time domain (FDTD) numerical technique. It is established that by novel arraying of nano-particles and tailoring their multilayer substrates, one can successfully engineer the radiation patterns and beam angles. Several optical nanoantennas designed on layered substrates are explored. Using the FDTD the effect of finite size substrate is also explored.

© 2009 Optical Society of America

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References

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  1. E. Ozbay, "Plasmonics: Merging photonics and electronics at nanoscale dimensions," Science 311, 189-193 (2006).
    [CrossRef] [PubMed]
  2. S. I. Bozhevolnyi and V. M. Shalaev, "Nanophotonics with surface plasmons Part I," Science,  40, 58-66 (2006).
  3. S. I. Bozhevolnyi and V. M. Shalaev, "Nanophotonics with surface plasmons Part II," Science,  40, 66-72 (2006).
  4. S. A. Maier and H. A. Atwater, "Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures," J. Appl. Phys.  98, 011101 (2005).
    [CrossRef]
  5. L. A. Sweatlock, S. A. Maier, H. A. Atwater, J. J. Penninkhof, and A. Polman, "Highly confined electromagnetic fields in arrays of strongly coupled ag nanoparticles," Phys. Rev. B.  71, 235408 (2005).
    [CrossRef]
  6. V. Podolskiy, A. Sarychev, and V. Shalaev, "Plasmon modes in metal nanowires," J. Nonlinear Opt. Phys. Mater. 11, 65-74 (2002).
    [CrossRef]
  7. J. Li, A. Salandrino, and N. Engheta, "Shaping light beams in the nanometer scale: A yagi-uda nanoantenna in the optical domain," Phys. Rev. B. 76, 245403 (2007).
    [CrossRef]
  8. J. Li, and N. Engheta, "Optical leaky-wave nano-antennas using plasmonic nanowires with periodical variation of permittivity," (presented at the 2005 Annual Meeting of the OSA., Tucson, Arizona, 1620, 2005).
  9. J. Li, A. Salandrino, and N. Engheta, "Radiation characteristics and beam forming of multi-particles nanoantennas at optical frequencies," (iWAT 06: Small Antennas and Novel Metamaterials, White Plains, NY, 432-433, 2006).
  10. P. Muhlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D.W. Pohl, "Resonant optical antennas," Science 308, 1607-1609 (2005).
    [CrossRef]
  11. 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]
  12. D. R. Jackson, T. Zhao, J. T. Williams, A. A. Oliner, "Leaky surface-plasmon theory for dramatically enhanced transmission through a sub-wavelength aperture, Part II: Leaky-wave antenna model," (IEEE International Symposium on Antenna and Propagations, 2, 1095-1098, 2003).
  13. N. C. Panoiu, and R. M. Osgood, "Optical antenna arrays in the visible range," Opt. Lett. 32, 2825 (2007).
    [CrossRef] [PubMed]
  14. H. F. Hofmann, Terukazu, and Y. Kadoya, "Design parameters for a nano-optical yagi-uda antenna," New J. Phys. 9, 217 (2007).
    [CrossRef]
  15. K. Nakayama, K. Tanabe, and H. A. Atwater, "Plasmonic nanoparticle enhanced light absorption in gaas solar cells," Appl. Phys. Lett. 93, 121904 (2008).
    [CrossRef]
  16. D. R. Matthews, H. D. Summers, K. Njoh, S. Chappell, R. Errington, and P. Smith, "Optical antenna arrays in the visible range," Opt. Express 15, 3479-3487 (2007).
    [CrossRef]
  17. D. M. Schaadt, B. Feng, and T. F. Yu, "Optical antenna arrays in the visible range," Appl. Phys. Lett. 86, 063106 (2005).
    [CrossRef]
  18. V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, "Plasmonic nanostructure design for efficient light coupling into solar cells," Nano Lett. 8, 12 (2008).
  19. S. Pillai, K. R. Catchpole, T. Trupke, and M. A. Green, "Surface plasmon enhanced silicon solar cells," J. Appl. Phys. 101, 093105 (2007).
    [CrossRef]
  20. W. C. Chew, Waves and Fields in Inhomogeneous Media (IEEE Press, New York, 1995).
  21. S. Ghadarghadr, and H. Mosallaei, "Array of plasmonic nanoparticles enabling energy coupling-guiding in solar systems: A theoretical analysis," (Optics and Photonics for Advanced Energy Technology, Cambridge, MA, 2009).
  22. S. Ghadarghadr, and H. Mosallaei, "Nanoantennas Array Enabling Optical Communication," (Frontiers in Optics 2009/Laser Science XXV, San Jose, CA, 2009).
  23. H. Mosallaei, "FDTD-PLRC technique for modeling of anisotropic-dispersive media and metamaterial devices," IEEE Trans. Electromagn. Compat. 49, 649-660 (2007).
    [CrossRef]
  24. J. A. Stratton, Electromagnetic Theory (McGraw Hill, New York, 1941).
  25. P. B. Johnson and R. W. Christy, "Optical constants of the nobel metals," Phys. Rev. B 6, 4370-4379 (1972).
  26. L. Novotny and B. Hecht, Principles of Nano-Optics (Cambrdige University Press, United Kingdom, 2006).
  27. C. A. Balanis, Antenna Theory: Analysis and Design (John Wiley & Sons, 2005).

2008 (3)

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]

V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, "Plasmonic nanostructure design for efficient light coupling into solar cells," Nano Lett. 8, 12 (2008).

K. Nakayama, K. Tanabe, and H. A. Atwater, "Plasmonic nanoparticle enhanced light absorption in gaas solar cells," Appl. Phys. Lett. 93, 121904 (2008).
[CrossRef]

2007 (6)

D. R. Matthews, H. D. Summers, K. Njoh, S. Chappell, R. Errington, and P. Smith, "Optical antenna arrays in the visible range," Opt. Express 15, 3479-3487 (2007).
[CrossRef]

S. Pillai, K. R. Catchpole, T. Trupke, and M. A. Green, "Surface plasmon enhanced silicon solar cells," J. Appl. Phys. 101, 093105 (2007).
[CrossRef]

H. Mosallaei, "FDTD-PLRC technique for modeling of anisotropic-dispersive media and metamaterial devices," IEEE Trans. Electromagn. Compat. 49, 649-660 (2007).
[CrossRef]

N. C. Panoiu, and R. M. Osgood, "Optical antenna arrays in the visible range," Opt. Lett. 32, 2825 (2007).
[CrossRef] [PubMed]

H. F. Hofmann, Terukazu, and Y. Kadoya, "Design parameters for a nano-optical yagi-uda antenna," New J. Phys. 9, 217 (2007).
[CrossRef]

H. F. Hofmann, Terukazu, and Y. Kadoya, "Design parameters for a nano-optical yagi-uda antenna," New J. Phys. 9, 217 (2007).
[CrossRef]

J. Li, A. Salandrino, and N. Engheta, "Shaping light beams in the nanometer scale: A yagi-uda nanoantenna in the optical domain," Phys. Rev. B. 76, 245403 (2007).
[CrossRef]

2006 (3)

E. Ozbay, "Plasmonics: Merging photonics and electronics at nanoscale dimensions," Science 311, 189-193 (2006).
[CrossRef] [PubMed]

S. I. Bozhevolnyi and V. M. Shalaev, "Nanophotonics with surface plasmons Part I," Science,  40, 58-66 (2006).

S. I. Bozhevolnyi and V. M. Shalaev, "Nanophotonics with surface plasmons Part II," Science,  40, 66-72 (2006).

2005 (4)

S. A. Maier and H. A. Atwater, "Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures," J. Appl. Phys.  98, 011101 (2005).
[CrossRef]

L. A. Sweatlock, S. A. Maier, H. A. Atwater, J. J. Penninkhof, and A. Polman, "Highly confined electromagnetic fields in arrays of strongly coupled ag nanoparticles," Phys. Rev. B.  71, 235408 (2005).
[CrossRef]

P. Muhlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D.W. Pohl, "Resonant optical antennas," Science 308, 1607-1609 (2005).
[CrossRef]

D. M. Schaadt, B. Feng, and T. F. Yu, "Optical antenna arrays in the visible range," Appl. Phys. Lett. 86, 063106 (2005).
[CrossRef]

2002 (1)

V. Podolskiy, A. Sarychev, and V. Shalaev, "Plasmon modes in metal nanowires," J. Nonlinear Opt. Phys. Mater. 11, 65-74 (2002).
[CrossRef]

1972 (1)

P. B. Johnson and R. W. Christy, "Optical constants of the nobel metals," Phys. Rev. B 6, 4370-4379 (1972).

Atwater, H. A.

K. Nakayama, K. Tanabe, and H. A. Atwater, "Plasmonic nanoparticle enhanced light absorption in gaas solar cells," Appl. Phys. Lett. 93, 121904 (2008).
[CrossRef]

V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, "Plasmonic nanostructure design for efficient light coupling into solar cells," Nano Lett. 8, 12 (2008).

S. A. Maier and H. A. Atwater, "Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures," J. Appl. Phys.  98, 011101 (2005).
[CrossRef]

L. A. Sweatlock, S. A. Maier, H. A. Atwater, J. J. Penninkhof, and A. Polman, "Highly confined electromagnetic fields in arrays of strongly coupled ag nanoparticles," Phys. Rev. B.  71, 235408 (2005).
[CrossRef]

Bozhevolnyi, S. I.

S. I. Bozhevolnyi and V. M. Shalaev, "Nanophotonics with surface plasmons Part I," Science,  40, 58-66 (2006).

S. I. Bozhevolnyi and V. M. Shalaev, "Nanophotonics with surface plasmons Part II," Science,  40, 66-72 (2006).

Catchpole, K. R.

S. Pillai, K. R. Catchpole, T. Trupke, and M. A. Green, "Surface plasmon enhanced silicon solar cells," J. Appl. Phys. 101, 093105 (2007).
[CrossRef]

Chappell, S.

D. R. Matthews, H. D. Summers, K. Njoh, S. Chappell, R. Errington, and P. Smith, "Optical antenna arrays in the visible range," Opt. Express 15, 3479-3487 (2007).
[CrossRef]

Christy, R. W.

P. B. Johnson and R. W. Christy, "Optical constants of the nobel metals," Phys. Rev. B 6, 4370-4379 (1972).

Eisler, H. J.

P. Muhlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D.W. Pohl, "Resonant optical antennas," Science 308, 1607-1609 (2005).
[CrossRef]

Engheta, N.

J. Li, A. Salandrino, and N. Engheta, "Shaping light beams in the nanometer scale: A yagi-uda nanoantenna in the optical domain," Phys. Rev. B. 76, 245403 (2007).
[CrossRef]

Errington, R.

D. R. Matthews, H. D. Summers, K. Njoh, S. Chappell, R. Errington, and P. Smith, "Optical antenna arrays in the visible range," Opt. Express 15, 3479-3487 (2007).
[CrossRef]

Feng, B.

D. M. Schaadt, B. Feng, and T. F. Yu, "Optical antenna arrays in the visible range," Appl. Phys. Lett. 86, 063106 (2005).
[CrossRef]

Ferry, V. E.

V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, "Plasmonic nanostructure design for efficient light coupling into solar cells," Nano Lett. 8, 12 (2008).

Green, M. A.

S. Pillai, K. R. Catchpole, T. Trupke, and M. A. Green, "Surface plasmon enhanced silicon solar cells," J. Appl. Phys. 101, 093105 (2007).
[CrossRef]

Hecht, B.

P. Muhlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D.W. Pohl, "Resonant optical antennas," Science 308, 1607-1609 (2005).
[CrossRef]

Hofmann, H. F.

H. F. Hofmann, Terukazu, and Y. Kadoya, "Design parameters for a nano-optical yagi-uda antenna," New J. Phys. 9, 217 (2007).
[CrossRef]

Johnson, P. B.

P. B. Johnson and R. W. Christy, "Optical constants of the nobel metals," Phys. Rev. B 6, 4370-4379 (1972).

Kadoya, Y.

H. F. Hofmann, Terukazu, and Y. Kadoya, "Design parameters for a nano-optical yagi-uda antenna," New J. Phys. 9, 217 (2007).
[CrossRef]

Li, J.

J. Li, A. Salandrino, and N. Engheta, "Shaping light beams in the nanometer scale: A yagi-uda nanoantenna in the optical domain," Phys. Rev. B. 76, 245403 (2007).
[CrossRef]

Maier, S. A.

S. A. Maier and H. A. Atwater, "Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures," J. Appl. Phys.  98, 011101 (2005).
[CrossRef]

L. A. Sweatlock, S. A. Maier, H. A. Atwater, J. J. Penninkhof, and A. Polman, "Highly confined electromagnetic fields in arrays of strongly coupled ag nanoparticles," Phys. Rev. B.  71, 235408 (2005).
[CrossRef]

Martin, O. J. F.

P. Muhlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D.W. Pohl, "Resonant optical antennas," Science 308, 1607-1609 (2005).
[CrossRef]

Matthews, D. R.

D. R. Matthews, H. D. Summers, K. Njoh, S. Chappell, R. Errington, and P. Smith, "Optical antenna arrays in the visible range," Opt. Express 15, 3479-3487 (2007).
[CrossRef]

Mosallaei, H.

H. Mosallaei, "FDTD-PLRC technique for modeling of anisotropic-dispersive media and metamaterial devices," IEEE Trans. Electromagn. Compat. 49, 649-660 (2007).
[CrossRef]

Muhlschlegel, P.

P. Muhlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D.W. Pohl, "Resonant optical antennas," Science 308, 1607-1609 (2005).
[CrossRef]

Nakayama, K.

K. Nakayama, K. Tanabe, and H. A. Atwater, "Plasmonic nanoparticle enhanced light absorption in gaas solar cells," Appl. Phys. Lett. 93, 121904 (2008).
[CrossRef]

Njoh, K.

D. R. Matthews, H. D. Summers, K. Njoh, S. Chappell, R. Errington, and P. Smith, "Optical antenna arrays in the visible range," Opt. Express 15, 3479-3487 (2007).
[CrossRef]

Osgood, R. M.

Ozbay, E.

E. Ozbay, "Plasmonics: Merging photonics and electronics at nanoscale dimensions," Science 311, 189-193 (2006).
[CrossRef] [PubMed]

Pacifici, D.

V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, "Plasmonic nanostructure design for efficient light coupling into solar cells," Nano Lett. 8, 12 (2008).

Panoiu, N. C.

Penninkhof, J. J.

L. A. Sweatlock, S. A. Maier, H. A. Atwater, J. J. Penninkhof, and A. Polman, "Highly confined electromagnetic fields in arrays of strongly coupled ag nanoparticles," Phys. Rev. B.  71, 235408 (2005).
[CrossRef]

Pillai, S.

S. Pillai, K. R. Catchpole, T. Trupke, and M. A. Green, "Surface plasmon enhanced silicon solar cells," J. Appl. Phys. 101, 093105 (2007).
[CrossRef]

Podolskiy, V.

V. Podolskiy, A. Sarychev, and V. Shalaev, "Plasmon modes in metal nanowires," J. Nonlinear Opt. Phys. Mater. 11, 65-74 (2002).
[CrossRef]

Pohl, D.W.

P. Muhlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D.W. Pohl, "Resonant optical antennas," Science 308, 1607-1609 (2005).
[CrossRef]

Polman, A.

L. A. Sweatlock, S. A. Maier, H. A. Atwater, J. J. Penninkhof, and A. Polman, "Highly confined electromagnetic fields in arrays of strongly coupled ag nanoparticles," Phys. Rev. B.  71, 235408 (2005).
[CrossRef]

Salandrino, A.

J. Li, A. Salandrino, and N. Engheta, "Shaping light beams in the nanometer scale: A yagi-uda nanoantenna in the optical domain," Phys. Rev. B. 76, 245403 (2007).
[CrossRef]

Sarychev, A.

V. Podolskiy, A. Sarychev, and V. Shalaev, "Plasmon modes in metal nanowires," J. Nonlinear Opt. Phys. Mater. 11, 65-74 (2002).
[CrossRef]

Schaadt, D. M.

D. M. Schaadt, B. Feng, and T. F. Yu, "Optical antenna arrays in the visible range," Appl. Phys. Lett. 86, 063106 (2005).
[CrossRef]

Shalaev, V.

V. Podolskiy, A. Sarychev, and V. Shalaev, "Plasmon modes in metal nanowires," J. Nonlinear Opt. Phys. Mater. 11, 65-74 (2002).
[CrossRef]

Shalaev, V. M.

S. I. Bozhevolnyi and V. M. Shalaev, "Nanophotonics with surface plasmons Part II," Science,  40, 66-72 (2006).

S. I. Bozhevolnyi and V. M. Shalaev, "Nanophotonics with surface plasmons Part I," Science,  40, 58-66 (2006).

Smith, P.

D. R. Matthews, H. D. Summers, K. Njoh, S. Chappell, R. Errington, and P. Smith, "Optical antenna arrays in the visible range," Opt. Express 15, 3479-3487 (2007).
[CrossRef]

Stefani, F. D.

Summers, H. D.

D. R. Matthews, H. D. Summers, K. Njoh, S. Chappell, R. Errington, and P. Smith, "Optical antenna arrays in the visible range," Opt. Express 15, 3479-3487 (2007).
[CrossRef]

Sweatlock, L. A.

V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, "Plasmonic nanostructure design for efficient light coupling into solar cells," Nano Lett. 8, 12 (2008).

L. A. Sweatlock, S. A. Maier, H. A. Atwater, J. J. Penninkhof, and A. Polman, "Highly confined electromagnetic fields in arrays of strongly coupled ag nanoparticles," Phys. Rev. B.  71, 235408 (2005).
[CrossRef]

Taminiau, T. H.

Tanabe, K.

K. Nakayama, K. Tanabe, and H. A. Atwater, "Plasmonic nanoparticle enhanced light absorption in gaas solar cells," Appl. Phys. Lett. 93, 121904 (2008).
[CrossRef]

Terukazu, H. F.

H. F. Hofmann, Terukazu, and Y. Kadoya, "Design parameters for a nano-optical yagi-uda antenna," New J. Phys. 9, 217 (2007).
[CrossRef]

Trupke, T.

S. Pillai, K. R. Catchpole, T. Trupke, and M. A. Green, "Surface plasmon enhanced silicon solar cells," J. Appl. Phys. 101, 093105 (2007).
[CrossRef]

van Hulst, N. F.

Yu, T. F.

D. M. Schaadt, B. Feng, and T. F. Yu, "Optical antenna arrays in the visible range," Appl. Phys. Lett. 86, 063106 (2005).
[CrossRef]

Appl. Phys. Lett. (2)

K. Nakayama, K. Tanabe, and H. A. Atwater, "Plasmonic nanoparticle enhanced light absorption in gaas solar cells," Appl. Phys. Lett. 93, 121904 (2008).
[CrossRef]

D. M. Schaadt, B. Feng, and T. F. Yu, "Optical antenna arrays in the visible range," Appl. Phys. Lett. 86, 063106 (2005).
[CrossRef]

IEEE Trans. Electromagn. Compat. (1)

H. Mosallaei, "FDTD-PLRC technique for modeling of anisotropic-dispersive media and metamaterial devices," IEEE Trans. Electromagn. Compat. 49, 649-660 (2007).
[CrossRef]

J. Appl. Phys. (2)

S. Pillai, K. R. Catchpole, T. Trupke, and M. A. Green, "Surface plasmon enhanced silicon solar cells," J. Appl. Phys. 101, 093105 (2007).
[CrossRef]

S. A. Maier and H. A. Atwater, "Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures," J. Appl. Phys.  98, 011101 (2005).
[CrossRef]

J. Nonlinear Opt. Phys. Mater. (1)

V. Podolskiy, A. Sarychev, and V. Shalaev, "Plasmon modes in metal nanowires," J. Nonlinear Opt. Phys. Mater. 11, 65-74 (2002).
[CrossRef]

Nano Lett. (1)

V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, "Plasmonic nanostructure design for efficient light coupling into solar cells," Nano Lett. 8, 12 (2008).

New J. Phys. (1)

H. F. Hofmann, Terukazu, and Y. Kadoya, "Design parameters for a nano-optical yagi-uda antenna," New J. Phys. 9, 217 (2007).
[CrossRef]

Opt. Express (2)

D. R. Matthews, H. D. Summers, K. Njoh, S. Chappell, R. Errington, and P. Smith, "Optical antenna arrays in the visible range," Opt. Express 15, 3479-3487 (2007).
[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]

Opt. Lett. (1)

Phys. Rev. B (1)

P. B. Johnson and R. W. Christy, "Optical constants of the nobel metals," Phys. Rev. B 6, 4370-4379 (1972).

Phys. Rev. B. (2)

J. Li, A. Salandrino, and N. Engheta, "Shaping light beams in the nanometer scale: A yagi-uda nanoantenna in the optical domain," Phys. Rev. B. 76, 245403 (2007).
[CrossRef]

L. A. Sweatlock, S. A. Maier, H. A. Atwater, J. J. Penninkhof, and A. Polman, "Highly confined electromagnetic fields in arrays of strongly coupled ag nanoparticles," Phys. Rev. B.  71, 235408 (2005).
[CrossRef]

Science (4)

E. Ozbay, "Plasmonics: Merging photonics and electronics at nanoscale dimensions," Science 311, 189-193 (2006).
[CrossRef] [PubMed]

S. I. Bozhevolnyi and V. M. Shalaev, "Nanophotonics with surface plasmons Part I," Science,  40, 58-66 (2006).

S. I. Bozhevolnyi and V. M. Shalaev, "Nanophotonics with surface plasmons Part II," Science,  40, 66-72 (2006).

P. Muhlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D.W. Pohl, "Resonant optical antennas," Science 308, 1607-1609 (2005).
[CrossRef]

Other (9)

D. R. Jackson, T. Zhao, J. T. Williams, A. A. Oliner, "Leaky surface-plasmon theory for dramatically enhanced transmission through a sub-wavelength aperture, Part II: Leaky-wave antenna model," (IEEE International Symposium on Antenna and Propagations, 2, 1095-1098, 2003).

J. Li, and N. Engheta, "Optical leaky-wave nano-antennas using plasmonic nanowires with periodical variation of permittivity," (presented at the 2005 Annual Meeting of the OSA., Tucson, Arizona, 1620, 2005).

J. Li, A. Salandrino, and N. Engheta, "Radiation characteristics and beam forming of multi-particles nanoantennas at optical frequencies," (iWAT 06: Small Antennas and Novel Metamaterials, White Plains, NY, 432-433, 2006).

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambrdige University Press, United Kingdom, 2006).

C. A. Balanis, Antenna Theory: Analysis and Design (John Wiley & Sons, 2005).

J. A. Stratton, Electromagnetic Theory (McGraw Hill, New York, 1941).

W. C. Chew, Waves and Fields in Inhomogeneous Media (IEEE Press, New York, 1995).

S. Ghadarghadr, and H. Mosallaei, "Array of plasmonic nanoparticles enabling energy coupling-guiding in solar systems: A theoretical analysis," (Optics and Photonics for Advanced Energy Technology, Cambridge, MA, 2009).

S. Ghadarghadr, and H. Mosallaei, "Nanoantennas Array Enabling Optical Communication," (Frontiers in Optics 2009/Laser Science XXV, San Jose, CA, 2009).

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Figures (17)

Fig. 1.
Fig. 1.

Array of plasmonic nanoantennas located above a layered substrate.

Fig. 2.
Fig. 2.

Magnitude and phase of normalized polarizability of a plasmonic core-shell sphere versus r 1/r 2 ratio for different frequencies for a structure with r 2=0.1λ, εrc =2.2+0.01i and silver coating. (a) Polarization magnitude, and (b) Polarization phase, (c) Silver permittivity behavior.

Fig. 3.
Fig. 3.

Maximum percentage of error in obtaining the integrals in (7) and (8) using our theoretical model compared to their exact values for different observation points. ρ and z0 denote the location of the observation point.

Fig. 4.
Fig. 4.

(a) A Yagi-Uda type antenna constructed from a dipole source exciting two nano core-shells, operating at frequency f=650 THz. The reflector’s radii ratio is r 1r /r 2r =0.75 and the radii ratio of the director is r 1d /r 2d =0.65. Both core-shells have core made of SiO 2(εrc =2.2+0.01i) and shell made of silver (εrs =-8.06+0.175i). The normalized radiated power obtained by theory and FDTD, (b) in xy plane, and (c) in yz plane. A good comparison is observed. Note that FDTD characterizes the actual plasmonic core-shell structure whereas in theoretical model we approximate them with dipole modes.

Fig. 5.
Fig. 5.

Magnitude of Ez (dB) for the nanoantenna in Fig. 4(a) in xy (z=0) plane and yz (x=0) plane. (a) Theory, (b) FDTD. It is worth highlighting again, that in our theory each nano core-shell is modeled with an electric dipole, where FDTD calculates the field for the actual structure. Outside the plasmonic core-shells one can expect the similar performance.

Fig. 6.
Fig. 6.

(a) Nanoantenna configuration in Fig. 4(a) located above a slab of InGaAs with the thickness of 0.35λ 0. (b) The 3D radiation pattern of the radiated power. The substrate considerably degrades the antenna radiation pattern.

Fig. 7.
Fig. 7.

Near field distribution for the antenna in Fig. 6(a) obtained by using the theoretical approach of this paper, (a) The magnitude of Ey (dB) in xy plane, (b) The magnitude of Ez (dB) in yz plane. Field penetration and propagation through the substrate is illustrated.

Fig. 8.
Fig. 8.

Near field distribution for the antenna in Fig. 6(a) obtained utilizing FDTD numerical technique, (a) The magnitude of Ey (dB) in xy plane, (b) The magnitude of Ez (dB) in yz plane.

Fig. 9.
Fig. 9.

(a) A nanoantenna array of a horizontal dipole, px, and two nano core-shells located above a InGaAs slab of 0.35λ0 thickness. (b) The 3D radiation pattern. (c) The magnitude of Ex (dB) in yz plane.

Fig. 10.
Fig. 10.

(a) Configuration of the nanoantenna in Fig. 4(a) where the nano core-shells are located above a InGaAs slab of 0.35λ 0 which its top surface is coated with 0.2λ 0 of silver. (b) The 3D radiation pattern. The silver layer suppresses the back radiation.

Fig. 11.
Fig. 11.

Near field distribution for the antenna in Fig. 10(a). (a) The magnitude of Ey (dB) in xy plane, (b) The magnitude of Ez (dB) in yz plane.

Fig. 12.
Fig. 12.

(a) A vertical dipole located at the top of a planar layered material. The layered substrate includes a slab of InGaAs with thickness of 0.35λ 0 where its top surface is coated with silver of thickness 0.2λ 0. A third layer of dielectric ε r2 is deposited at top of the silver. (b) The angle of maximum radiation in the yz plane vs. the thickness of the dielectric layer. The jump in angle is because the maximum radiation occurs in another direction.

Fig. 13.
Fig. 13.

(a) Nanoantenna configuration in Fig. 4(a) located above a 3 layered substrate including InGaAs slab of 0.35λ 0, silver with thickness of 0.2λ 0 and a 0.1λ 0 layer of SiO 2. (b) The 3D radiation pattern of the radiated power. Adding a third layer controls better the radiation pattern.

Fig. 14.
Fig. 14.

Near field distribution for the antenna in Fig. 13(a), (a) The magnitude of Ey (dB) in xy plane, (b) The magnitude of Ez (dB) in yz plane.

Fig. 15.
Fig. 15.

(a) 4-particle nanoantenna array with an engineered substrate demonstrating a broadside radiation characteristic. The radii ratio for the particles are r 1 r/r 2r =0.72 and r 1d /r 2d =0.69, and dref=0.25λ 0 while ddir =0.65λ 0. The layered material includes 0.5λ 0 of InGaAs, 0.2λ 0 of silver coating and a dielectric layer (SiO 2) with the thickness of 0.1λ 0. (b) The 3D radiation pattern.

Fig. 16.
Fig. 16.

Radiation pattern sensitivity to the change of r 1r for the configuration shown in Fig. 13(a). The radiation performance in yz plane, where r 2r =r 2d =46 nm and r 1d =30 nm.

Fig. 17.
Fig. 17.

(a) 4-particle nanoantenna array located above a finite-size substrate. In this case the radii ratios are r 1r /r 2r =0.75 and r 1d /r 2d =0.65. (a) The radiation pattern in xy and yz planes, (b) The near-field distribution of Ez (dB) in yz plane. The FDTD technique demonstrates the effect of finite-size substrate on the field penetration through the substrate and the edge diffractions (as this will establish different radiation characteristic compared to what is obtained for the infinite-size substrate model).

Equations (25)

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p = α . Etotal = i 6πε0k03 Γ1(e) . Etotal ,
Γn(e) = Un(e)Un(e)+iVn(e) ,
Un(e) = jn(kcr1)jn(ksr1)yn(ksr1)0jn(k˜cr1)εcjn(k˜sr1)εsyn(k˜sr1)εs00jn(ksr2)yn(ksr2)jn(k0r2)0j˜n(ksr2)y˜n(ksrs)εsj˜n(k0r2)ε0,
Vn(e) = jn(kcr1)jn(ksr1)yn(ksr1)0jn(k˜cr1)εcjn(k˜sr1)εsyn(k˜sr1)εp00jn(ksr2)yn(ksr2)yn(k0r2)0j˜n(ksr2)y˜n(ksrs)εsy˜n(k0r2)ε0.
εrs = 1 1.513×1032ω(ω+i7.9×1013) .
pl = αl (Einctotal(rl)+q,qlG̿dipolel(rl,rq)pq+qG̿reflectedl(rl,rq)pq) ,
G̿dipolel (rl,rq)=[(k12+22x)2xy2xz2xy(k12+22y)2yz2xz2yz(k12+22z)] eik1rlrq4πε1rlrq ,
G̿reflectedl (rlrq)=[Gerxlx(rlrq)Gerylx(rlrq)Gerzlx(rlrq)Gerxly(rlrq)Geryly(rlrq)Gerzly(rlrq)Gerxlz(rlrq)Gerylz(rlrq)Gerzlz(rlrq)].
G erxlz = 18πε1 cos ϕ dkρkρ2H1(1)(kρρ)R˜1,2TMeik1z(z+2d1),
G erylz = 18πε1 sin ϕ dkρkρ2H1(1)(kρρ)R˜1,2TMeik1z(z+2d1),
G erzlz = i8πε1 dkρkρ3k1zH0(1)(kρρ)R˜1,2TMeik1z(z+2d1),
G˜ erwls (kρ)=1kρ2[zG˜erwls(kρ)zμẑ×sG˜hrwlz(kρ)],
R˜i,i+1TMTE = Ri,i+1TMTE+R˜i+1,i+2TMTEe2iki+1,z(di+1di)1+Ri,i+1TMTER˜i+1,i+2TMTEe2iki+1,z(di+1di) ,
Ri,jTMTE = (εjμj)kiz(εiμi)kjz(εjμj)kiz+(εiμi)kjz ,
kiz = ki2kρ2 .
p = (I̿αG̿reflected)1 α Etotal ,
E = EθEϕ=kJ24πεJeikJrr(pxcosϕ+pysinϕ)cosθΦJ2pzsinθΦJ1(pxsinϕpysinϕ)ΦJ3.
Φ11 = eik1r [1+R˜1,2TM(θ)eik1z0],
Φ12 = eik1r [1R˜1,2TM(θ)eik1z0],
Φ13 = eik1r [1+R˜1,2TM(θ)eik1z0],
ΦN1 = ΦN2 = nNn1 cosθs˜z TTM (θ)eikN[z0s˜z+(dNd1)cosθ],
ΦN3 = cosθs˜z TTM (θ)eikN[z0s˜z+(dNd1)cosθ],
kJ r = kJ [x0cosϕsinθ+y0sinϕsinθ+z0cosθ] ,
kJ z = 2 kJ (z0+d1)cosθ,
s˜z = k1zkN = (n1nN)2sin2θ .

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