Abstract

We report on the possibility of realizing adiabatic compression of polaritonic wave on a metallic conical nano-structure through an oscillating electric potential (quasi dynamic regime). By comparing this result with an electromagnetic wave excitation, we were able to relate the classical lighting-rod effect to adiabatic compression. Furthermore, we show that while the magnetic contribution plays a marginal role in the formation of adiabatic compression, it provides a blue shift in the spectral region. In particular, magnetic permeability can be used as a free parameter for tuning the polaritonic resonances. The peculiar form of adiabatic compression is instead dictated by both the source and the metal permittivity. The analysis is performed by starting from a simple electrostatic system to end with the complete electromagnetic one through intermediate situations such as the quasi-electrostatic and quasi-dynamic regimes. Each configuration is defined by a particular set of equations which allows to clearly determine the individual role played by the electric and magnetic contribution in the generation of adiabatic compression. We notice that these findings can be applied for the realization of a THz nano-metric generator.

© 2013 OSA

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2012 (3)

S. V. Boriskina and M. R. Bjorn, “Molding the flow of light on the nanoscale: from vortex nanogears to phase-operated plasmonic machinery,” Nanoscale4, 76–90 (2012).
[CrossRef]

R. Proietti Zaccaria, A. Alabastri, F. De Angelis, G. Das, C. Liberale, A. Toma, A. Giugni, L. Razzari, M. Malerba, H. B. Sun, and E. Di Fabrizio, “Fully analytical description of adiabatic compression in dissipative polaritonic structures,” Phys. Rev. B86, 035410 (2012).
[CrossRef]

R. Proietti Zaccaria, F. De Angelis, A. Toma, L. Razzari, A. Alabastri, G. Das, C. Liberale, and E. Di Fabrizio, “Surface plasmon polariton compression through radially and linearly polarized source,” Opt. Lett.37, 545–547 (2012).
[CrossRef]

2011 (9)

M. I. Stockman, “Nanoplasmonics: past, present, and glimpse into future,” Opt. Express19, 22029–22106 (2011).
[CrossRef] [PubMed]

P. Bharadwaj, A. Bouhelier, and L. Novotny, “Electrical excitation of surface plasmons,” Phys. Rev. Lett.106, 226802 (2011).
[CrossRef] [PubMed]

J. S. Lee, S. Han, J. Shirdel, S. Koo, D. Sadiq, C. Lienau, and N. Park, “Superfocusing of electric or magnetic fields using conical metal tips: effect of mode symmetry on the plasmon excitation method,” Opt. Express19, 12342–12347 (2011).
[CrossRef] [PubMed]

F. De Angelis, R. Proietti Zaccaria, M. Francardi, C. Liberale, and E. Di Fabrizio, “Multi-scheme approach for efficient surface plasmon polariton generation in metallic conical tips on AFM-based cantilevers,” Opt. Express19, 22268–22279 (2011).
[CrossRef] [PubMed]

B. Fazio, C. D’Andrea, F. Bonaccorso, A. Irrera, G. Calogero, C. Vasi, P. G. Gucciardi, M. Allegrini, A. Toma, D. Chiappe, C. Martella, and F. Buatier de Mongeot, “Re-radiation enhancement in polarized surface-enhanced resonant raman scattering of randomly oriented molecules on self-organized gold nanowires,” ACS Nano5, 5945–5956 (2011).
[CrossRef] [PubMed]

J. Song, R. Proietti Zaccaria, G. Dong, E. Di Fabrizio, M. B. Yu, and G. Q. Lo, “Evolution of modes in a metal-coated nano-fiber,” Opt. Express19, 25206–25221 (2011).
[CrossRef]

A. Belardini, M. C. Larciprete, M. Centini, E. Fazio, C. Sibilia, D. Chiappe, C. Martella, A. Toma, M. Giordano, and F. Buatier de Mongeot, “Circular dichroism in the optical second-harmonic emission of curved gold metal nanowires,” Phys. Rev. Lett.107, 257401 (2011).
[CrossRef]

L. Razzari, A. Toma, M. Shalaby, M. Clerici, R. Proietti Zaccaria, C. Liberale, S. Marras, I.A.I. Al-Naib, G. Das, F. De Angelis, M. Peccianti, A. Falqui, T. Ozaki, R. Morandotti, and E. Di Fabrizio, “Extremely large extinction efficiency and field enhancement in terahertz resonant dipole nanoantennas,” Opt. Express19, 26088–26094 (2011).
[CrossRef]

F. De Angelis, F. Gentile, F. Mecarini, G. Das, M. Moretti, P. Candeloro, M. L. Coluccio, G. Cojoc, A. Accardo, C. Liberale, R. Proietti Zaccaria, G. Perozziello, L. Tirinato, A. Toma, G. Cuda, R. Cingolani, and E. Di Fabrizio, “Breaking the diffusion limit with super-hydrophobic delivery of molecules to plasmonic nanofocusing SERS structures,” Nat. Photon.5, 682–687 (2011).
[CrossRef]

2010 (4)

T. J. Davis, D. E. Gomez, and K. C. Vernon, “Evanescent coupling between a Raman-active molecule and surface plasmons in ensembles of metallic nanoparticles,” Phys. Rev. B82, 205434 (2010).
[CrossRef]

F. De Angelis, G. Das, P. Candeloro, M. Patrini, M. Galli, A. Bek, M. Lazzarino, I. Maksymov, C. Liberale, L. C. Andreani, and E. Di Fabrizio, “Nanoscale chemical mapping using three-dimensional adiabatic compression of surface plasmon polaritons,” Nat. Nanotech.5, 67–72 (2010).
[CrossRef]

P. I. Geshev, U. Fischer, and H. Fuchs, “Calculation of tip enhanced Raman scattering caused by nanoparticle plasmons acting on a molecule placed near a metallic film,” Phys. Rev. B81, 125441 (2010).
[CrossRef]

C. C. Neacsu, S. Bergewer, R. L. Olmon, L. V. Saraf, C. Ropers, and M. B. Raschke, “Near-field localization in plasmonic superfocusing: a nanoemitter on a tip,” Nano Lett.10, 592–596 (2010).
[CrossRef] [PubMed]

2009 (4)

C. Huang, X. Yin, H. Huang, and Y. Zhu, “Study of plasmon resonance in a gold nanorod with an LC circuit model,” Opt. Express17, 6407–6413 (2009).
[CrossRef] [PubMed]

W. Zhang, X. Cui, and O. J. F. Martin, “Local field enhancement of an infinite conical metal tip illuminated by a focused beam,” J. Raman Spectrosc.40, 1338–1342 (2009).
[CrossRef]

A. Belardini, M. C. Larciprete, M. Centini, E. Fazio, C. Sibilia, M. Bertolotti, A. Toma, D. Chiappe, and F. Buatier de Mongeot, “Tailored second harmonic generation from self-organized metal nano-wires arrays,” Opt. Express17, 3603–3609 (2009).
[CrossRef] [PubMed]

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterials as broadband circular polarizer,” Science325, 1513–1515 (2009).
[CrossRef] [PubMed]

2008 (4)

F. De Angelis, M. Patrini, G. Das, I. Maksymov, M. Galli, L. Businaro, L. C. Andreani, and E. Di Fabrizio, “A hybrid plasmonic-photonic nanodevice for label-free detection of a few molecules,” Nano Lett.8, 2321–2327 (2008).
[CrossRef] [PubMed]

D. K. Gramotnev, M. W. Vogel, and M. I. Stockman, “Optimized nonadiabatic nanofocusing of plasmons by tapered metal rods,” J. Appl. Phys.104, 034311 (2008).
[CrossRef]

G. W. Bryant, F. J. Garca de Abajo, and J. Aizpurua, “Mapping the plasmon resonances of metallic nanoantennas,” Nano Lett.8, 631–636 (2008).
[CrossRef] [PubMed]

E. S. Barnard, J. S. White, A. Chandran, and M. L. Brongersma, “Spectral properties of plasmonic resonator antennas,” Opt. Express16, 16529–16537 (2008).
[CrossRef] [PubMed]

2007 (4)

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

T. Sondergaard and S. Bozhevolnyi, “Slow-plasmon resonant nanostructures: scattering and field enhancements,” Phys. Rev. B75, 073402 (2007).
[CrossRef]

E. J. Smythe, E. Cubukcu, and F. Capasso, “Optical properties of surface plasmon resonances of coupled metallic nanorods,” Opt. Express15, 7439–7447 (2007).
[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. A75, 063822 (2007).
[CrossRef]

2006 (3)

M. I. Haftel, C. Schlockermann, and G. Blumberg, “Role of cylindrical surface plasmons in enhanced transmission,” Appl. Phys. Lett.88, 193104 (2006).
[CrossRef]

J. A. H. van Nieuwstadt, M. Sandtke, R. H. Harmsen, F. B. Segerink, J. C. Prangsma, S. Enoch, and L. Kuipers, “Strong modification of the nonlinear optical response of metallic subwavelength hole arrays,” Phys. Rev. Lett.97, 146102 (2006).
[CrossRef] [PubMed]

S. Linden, C. Enkrich, G. Dolling, M. W. Klein, J. Zhou, T. Koschny, C. M. Soukoulis, S. Burger, F. Schmidt, and M. Wegener, “Photonic metamaterials: magnetism at optical frequencies,” IEEE J. Sel. Top. Quantum Electron.12, 1097–1105 (2006).
[CrossRef]

2005 (3)

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett.95, 223902 (2005).
[CrossRef] [PubMed]

N. A. Janunts, K. S. Baghdasaryan, Kh. V. Nerkararyan, and B. Hecht, “Excitation and superfocusing of surface plasmon polaritons on a silver-coated optical fiber tip,” Opt. Commun.253, 118–124 (2005).
[CrossRef]

R. Ruppin, “Effect of non-locality on nanofocusing of surface plasmon field intensity in a conical tip,” Phys. Lett. A340, 299–302 (2005).
[CrossRef]

2004 (1)

M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett.93, 137404 (2004).
[CrossRef] [PubMed]

2003 (3)

L. Vaccaro, L. Aeschimann, U. Staufer, H. P. Herzig, and R. Dandliker, “Propagation of the electromagnetic field in fully coated near-field optical probes,” Appl. Phys. Lett.83, 584–586 (2003).
[CrossRef]

P. A. Belov, R. Marques, S. I. Maslovski, I. S. Nefedov, M. Silveirinha, C. R. Simovski, and S. A. Tretyakov, “Strong spatial dispersion in wire media in the very large wavelength limit,” Phys. Rev. B67, 113103 (2003).
[CrossRef]

K. B. Crozier, A. Sundaramurthy, G. S. Kino, and C. F. Quate, “Optical antennas: resonator for local field enhancement,” J. Appl. Phys.94, 4632 (2003).
[CrossRef]

2000 (2)

A. J. Babadjanyan, N. L. Margaryan, and Kh. V. Nerkararyan, “Superfocusing of surface polaritons in the conical structure,” J. Appl. Phys.87, 3785–3788 (2000).
[CrossRef]

P. Corio, S. D.M. Brown, A. Marucci, M. A. Pimenta, K. Kneipp, G. Dresselhaus, and M. S. Dresselhaus, “Surface-enhanced resonant Raman spectroscopy of single-wall carbon nanotubes adsorbed on silver and gold surfaces,” Phys. Rev. B61, 13202–13211 (2000).
[CrossRef]

1998 (1)

Accardo, A.

F. De Angelis, F. Gentile, F. Mecarini, G. Das, M. Moretti, P. Candeloro, M. L. Coluccio, G. Cojoc, A. Accardo, C. Liberale, R. Proietti Zaccaria, G. Perozziello, L. Tirinato, A. Toma, G. Cuda, R. Cingolani, and E. Di Fabrizio, “Breaking the diffusion limit with super-hydrophobic delivery of molecules to plasmonic nanofocusing SERS structures,” Nat. Photon.5, 682–687 (2011).
[CrossRef]

Aeschimann, L.

L. Vaccaro, L. Aeschimann, U. Staufer, H. P. Herzig, and R. Dandliker, “Propagation of the electromagnetic field in fully coated near-field optical probes,” Appl. Phys. Lett.83, 584–586 (2003).
[CrossRef]

Aizpurua, J.

G. W. Bryant, F. J. Garca de Abajo, and J. Aizpurua, “Mapping the plasmon resonances of metallic nanoantennas,” Nano Lett.8, 631–636 (2008).
[CrossRef] [PubMed]

Alabastri, A.

R. Proietti Zaccaria, A. Alabastri, F. De Angelis, G. Das, C. Liberale, A. Toma, A. Giugni, L. Razzari, M. Malerba, H. B. Sun, and E. Di Fabrizio, “Fully analytical description of adiabatic compression in dissipative polaritonic structures,” Phys. Rev. B86, 035410 (2012).
[CrossRef]

R. Proietti Zaccaria, F. De Angelis, A. Toma, L. Razzari, A. Alabastri, G. Das, C. Liberale, and E. Di Fabrizio, “Surface plasmon polariton compression through radially and linearly polarized source,” Opt. Lett.37, 545–547 (2012).
[CrossRef]

Allegrini, M.

B. Fazio, C. D’Andrea, F. Bonaccorso, A. Irrera, G. Calogero, C. Vasi, P. G. Gucciardi, M. Allegrini, A. Toma, D. Chiappe, C. Martella, and F. Buatier de Mongeot, “Re-radiation enhancement in polarized surface-enhanced resonant raman scattering of randomly oriented molecules on self-organized gold nanowires,” ACS Nano5, 5945–5956 (2011).
[CrossRef] [PubMed]

Al-Naib, I.A.I.

Andreani, L. C.

F. De Angelis, G. Das, P. Candeloro, M. Patrini, M. Galli, A. Bek, M. Lazzarino, I. Maksymov, C. Liberale, L. C. Andreani, and E. Di Fabrizio, “Nanoscale chemical mapping using three-dimensional adiabatic compression of surface plasmon polaritons,” Nat. Nanotech.5, 67–72 (2010).
[CrossRef]

F. De Angelis, M. Patrini, G. Das, I. Maksymov, M. Galli, L. Businaro, L. C. Andreani, and E. Di Fabrizio, “A hybrid plasmonic-photonic nanodevice for label-free detection of a few molecules,” Nano Lett.8, 2321–2327 (2008).
[CrossRef] [PubMed]

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. A75, 063822 (2007).
[CrossRef]

Babadjanyan, A. J.

A. J. Babadjanyan, N. L. Margaryan, and Kh. V. Nerkararyan, “Superfocusing of surface polaritons in the conical structure,” J. Appl. Phys.87, 3785–3788 (2000).
[CrossRef]

Bade, K.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterials as broadband circular polarizer,” Science325, 1513–1515 (2009).
[CrossRef] [PubMed]

Baghdasaryan, K. S.

N. A. Janunts, K. S. Baghdasaryan, Kh. V. Nerkararyan, and B. Hecht, “Excitation and superfocusing of surface plasmon polaritons on a silver-coated optical fiber tip,” Opt. Commun.253, 118–124 (2005).
[CrossRef]

Barnard, E. S.

Bek, A.

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A. Belardini, M. C. Larciprete, M. Centini, E. Fazio, C. Sibilia, M. Bertolotti, A. Toma, D. Chiappe, and F. Buatier de Mongeot, “Tailored second harmonic generation from self-organized metal nano-wires arrays,” Opt. Express17, 3603–3609 (2009).
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[CrossRef]

F. De Angelis, G. Das, P. Candeloro, M. Patrini, M. Galli, A. Bek, M. Lazzarino, I. Maksymov, C. Liberale, L. C. Andreani, and E. Di Fabrizio, “Nanoscale chemical mapping using three-dimensional adiabatic compression of surface plasmon polaritons,” Nat. Nanotech.5, 67–72 (2010).
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A. Belardini, M. C. Larciprete, M. Centini, E. Fazio, C. Sibilia, D. Chiappe, C. Martella, A. Toma, M. Giordano, and F. Buatier de Mongeot, “Circular dichroism in the optical second-harmonic emission of curved gold metal nanowires,” Phys. Rev. Lett.107, 257401 (2011).
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A. Belardini, M. C. Larciprete, M. Centini, E. Fazio, C. Sibilia, M. Bertolotti, A. Toma, D. Chiappe, and F. Buatier de Mongeot, “Tailored second harmonic generation from self-organized metal nano-wires arrays,” Opt. Express17, 3603–3609 (2009).
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B. Fazio, C. D’Andrea, F. Bonaccorso, A. Irrera, G. Calogero, C. Vasi, P. G. Gucciardi, M. Allegrini, A. Toma, D. Chiappe, C. Martella, and F. Buatier de Mongeot, “Re-radiation enhancement in polarized surface-enhanced resonant raman scattering of randomly oriented molecules on self-organized gold nanowires,” ACS Nano5, 5945–5956 (2011).
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A. Belardini, M. C. Larciprete, M. Centini, E. Fazio, C. Sibilia, M. Bertolotti, A. Toma, D. Chiappe, and F. Buatier de Mongeot, “Tailored second harmonic generation from self-organized metal nano-wires arrays,” Opt. Express17, 3603–3609 (2009).
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F. De Angelis, F. Gentile, F. Mecarini, G. Das, M. Moretti, P. Candeloro, M. L. Coluccio, G. Cojoc, A. Accardo, C. Liberale, R. Proietti Zaccaria, G. Perozziello, L. Tirinato, A. Toma, G. Cuda, R. Cingolani, and E. Di Fabrizio, “Breaking the diffusion limit with super-hydrophobic delivery of molecules to plasmonic nanofocusing SERS structures,” Nat. Photon.5, 682–687 (2011).
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Cojoc, G.

F. De Angelis, F. Gentile, F. Mecarini, G. Das, M. Moretti, P. Candeloro, M. L. Coluccio, G. Cojoc, A. Accardo, C. Liberale, R. Proietti Zaccaria, G. Perozziello, L. Tirinato, A. Toma, G. Cuda, R. Cingolani, and E. Di Fabrizio, “Breaking the diffusion limit with super-hydrophobic delivery of molecules to plasmonic nanofocusing SERS structures,” Nat. Photon.5, 682–687 (2011).
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F. De Angelis, F. Gentile, F. Mecarini, G. Das, M. Moretti, P. Candeloro, M. L. Coluccio, G. Cojoc, A. Accardo, C. Liberale, R. Proietti Zaccaria, G. Perozziello, L. Tirinato, A. Toma, G. Cuda, R. Cingolani, and E. Di Fabrizio, “Breaking the diffusion limit with super-hydrophobic delivery of molecules to plasmonic nanofocusing SERS structures,” Nat. Photon.5, 682–687 (2011).
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R. Proietti Zaccaria, F. De Angelis, A. Toma, L. Razzari, A. Alabastri, G. Das, C. Liberale, and E. Di Fabrizio, “Surface plasmon polariton compression through radially and linearly polarized source,” Opt. Lett.37, 545–547 (2012).
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F. De Angelis, F. Gentile, F. Mecarini, G. Das, M. Moretti, P. Candeloro, M. L. Coluccio, G. Cojoc, A. Accardo, C. Liberale, R. Proietti Zaccaria, G. Perozziello, L. Tirinato, A. Toma, G. Cuda, R. Cingolani, and E. Di Fabrizio, “Breaking the diffusion limit with super-hydrophobic delivery of molecules to plasmonic nanofocusing SERS structures,” Nat. Photon.5, 682–687 (2011).
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L. Razzari, A. Toma, M. Shalaby, M. Clerici, R. Proietti Zaccaria, C. Liberale, S. Marras, I.A.I. Al-Naib, G. Das, F. De Angelis, M. Peccianti, A. Falqui, T. Ozaki, R. Morandotti, and E. Di Fabrizio, “Extremely large extinction efficiency and field enhancement in terahertz resonant dipole nanoantennas,” Opt. Express19, 26088–26094 (2011).
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F. De Angelis, G. Das, P. Candeloro, M. Patrini, M. Galli, A. Bek, M. Lazzarino, I. Maksymov, C. Liberale, L. C. Andreani, and E. Di Fabrizio, “Nanoscale chemical mapping using three-dimensional adiabatic compression of surface plasmon polaritons,” Nat. Nanotech.5, 67–72 (2010).
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F. De Angelis, M. Patrini, G. Das, I. Maksymov, M. Galli, L. Businaro, L. C. Andreani, and E. Di Fabrizio, “A hybrid plasmonic-photonic nanodevice for label-free detection of a few molecules,” Nano Lett.8, 2321–2327 (2008).
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R. Proietti Zaccaria, A. Alabastri, F. De Angelis, G. Das, C. Liberale, A. Toma, A. Giugni, L. Razzari, M. Malerba, H. B. Sun, and E. Di Fabrizio, “Fully analytical description of adiabatic compression in dissipative polaritonic structures,” Phys. Rev. B86, 035410 (2012).
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F. De Angelis, R. Proietti Zaccaria, M. Francardi, C. Liberale, and E. Di Fabrizio, “Multi-scheme approach for efficient surface plasmon polariton generation in metallic conical tips on AFM-based cantilevers,” Opt. Express19, 22268–22279 (2011).
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F. De Angelis, F. Gentile, F. Mecarini, G. Das, M. Moretti, P. Candeloro, M. L. Coluccio, G. Cojoc, A. Accardo, C. Liberale, R. Proietti Zaccaria, G. Perozziello, L. Tirinato, A. Toma, G. Cuda, R. Cingolani, and E. Di Fabrizio, “Breaking the diffusion limit with super-hydrophobic delivery of molecules to plasmonic nanofocusing SERS structures,” Nat. Photon.5, 682–687 (2011).
[CrossRef]

F. De Angelis, G. Das, P. Candeloro, M. Patrini, M. Galli, A. Bek, M. Lazzarino, I. Maksymov, C. Liberale, L. C. Andreani, and E. Di Fabrizio, “Nanoscale chemical mapping using three-dimensional adiabatic compression of surface plasmon polaritons,” Nat. Nanotech.5, 67–72 (2010).
[CrossRef]

F. De Angelis, M. Patrini, G. Das, I. Maksymov, M. Galli, L. Businaro, L. C. Andreani, and E. Di Fabrizio, “A hybrid plasmonic-photonic nanodevice for label-free detection of a few molecules,” Nano Lett.8, 2321–2327 (2008).
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R. Proietti Zaccaria, F. De Angelis, A. Toma, L. Razzari, A. Alabastri, G. Das, C. Liberale, and E. Di Fabrizio, “Surface plasmon polariton compression through radially and linearly polarized source,” Opt. Lett.37, 545–547 (2012).
[CrossRef]

R. Proietti Zaccaria, A. Alabastri, F. De Angelis, G. Das, C. Liberale, A. Toma, A. Giugni, L. Razzari, M. Malerba, H. B. Sun, and E. Di Fabrizio, “Fully analytical description of adiabatic compression in dissipative polaritonic structures,” Phys. Rev. B86, 035410 (2012).
[CrossRef]

F. De Angelis, R. Proietti Zaccaria, M. Francardi, C. Liberale, and E. Di Fabrizio, “Multi-scheme approach for efficient surface plasmon polariton generation in metallic conical tips on AFM-based cantilevers,” Opt. Express19, 22268–22279 (2011).
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L. Razzari, A. Toma, M. Shalaby, M. Clerici, R. Proietti Zaccaria, C. Liberale, S. Marras, I.A.I. Al-Naib, G. Das, F. De Angelis, M. Peccianti, A. Falqui, T. Ozaki, R. Morandotti, and E. Di Fabrizio, “Extremely large extinction efficiency and field enhancement in terahertz resonant dipole nanoantennas,” Opt. Express19, 26088–26094 (2011).
[CrossRef]

F. De Angelis, F. Gentile, F. Mecarini, G. Das, M. Moretti, P. Candeloro, M. L. Coluccio, G. Cojoc, A. Accardo, C. Liberale, R. Proietti Zaccaria, G. Perozziello, L. Tirinato, A. Toma, G. Cuda, R. Cingolani, and E. Di Fabrizio, “Breaking the diffusion limit with super-hydrophobic delivery of molecules to plasmonic nanofocusing SERS structures,” Nat. Photon.5, 682–687 (2011).
[CrossRef]

F. De Angelis, G. Das, P. Candeloro, M. Patrini, M. Galli, A. Bek, M. Lazzarino, I. Maksymov, C. Liberale, L. C. Andreani, and E. Di Fabrizio, “Nanoscale chemical mapping using three-dimensional adiabatic compression of surface plasmon polaritons,” Nat. Nanotech.5, 67–72 (2010).
[CrossRef]

F. De Angelis, M. Patrini, G. Das, I. Maksymov, M. Galli, L. Businaro, L. C. Andreani, and E. Di Fabrizio, “A hybrid plasmonic-photonic nanodevice for label-free detection of a few molecules,” Nano Lett.8, 2321–2327 (2008).
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P. Corio, S. D.M. Brown, A. Marucci, M. A. Pimenta, K. Kneipp, G. Dresselhaus, and M. S. Dresselhaus, “Surface-enhanced resonant Raman spectroscopy of single-wall carbon nanotubes adsorbed on silver and gold surfaces,” Phys. Rev. B61, 13202–13211 (2000).
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P. Corio, S. D.M. Brown, A. Marucci, M. A. Pimenta, K. Kneipp, G. Dresselhaus, and M. S. Dresselhaus, “Surface-enhanced resonant Raman spectroscopy of single-wall carbon nanotubes adsorbed on silver and gold surfaces,” Phys. Rev. B61, 13202–13211 (2000).
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A. Belardini, M. C. Larciprete, M. Centini, E. Fazio, C. Sibilia, D. Chiappe, C. Martella, A. Toma, M. Giordano, and F. Buatier de Mongeot, “Circular dichroism in the optical second-harmonic emission of curved gold metal nanowires,” Phys. Rev. Lett.107, 257401 (2011).
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A. Belardini, M. C. Larciprete, M. Centini, E. Fazio, C. Sibilia, M. Bertolotti, A. Toma, D. Chiappe, and F. Buatier de Mongeot, “Tailored second harmonic generation from self-organized metal nano-wires arrays,” Opt. Express17, 3603–3609 (2009).
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P. I. Geshev, U. Fischer, and H. Fuchs, “Calculation of tip enhanced Raman scattering caused by nanoparticle plasmons acting on a molecule placed near a metallic film,” Phys. Rev. B81, 125441 (2010).
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Fuchs, H.

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F. De Angelis, G. Das, P. Candeloro, M. Patrini, M. Galli, A. Bek, M. Lazzarino, I. Maksymov, C. Liberale, L. C. Andreani, and E. Di Fabrizio, “Nanoscale chemical mapping using three-dimensional adiabatic compression of surface plasmon polaritons,” Nat. Nanotech.5, 67–72 (2010).
[CrossRef]

F. De Angelis, M. Patrini, G. Das, I. Maksymov, M. Galli, L. Businaro, L. C. Andreani, and E. Di Fabrizio, “A hybrid plasmonic-photonic nanodevice for label-free detection of a few molecules,” Nano Lett.8, 2321–2327 (2008).
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G. W. Bryant, F. J. Garca de Abajo, and J. Aizpurua, “Mapping the plasmon resonances of metallic nanoantennas,” Nano Lett.8, 631–636 (2008).
[CrossRef] [PubMed]

Gentile, F.

F. De Angelis, F. Gentile, F. Mecarini, G. Das, M. Moretti, P. Candeloro, M. L. Coluccio, G. Cojoc, A. Accardo, C. Liberale, R. Proietti Zaccaria, G. Perozziello, L. Tirinato, A. Toma, G. Cuda, R. Cingolani, and E. Di Fabrizio, “Breaking the diffusion limit with super-hydrophobic delivery of molecules to plasmonic nanofocusing SERS structures,” Nat. Photon.5, 682–687 (2011).
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L. Vaccaro, L. Aeschimann, U. Staufer, H. P. Herzig, and R. Dandliker, “Propagation of the electromagnetic field in fully coated near-field optical probes,” Appl. Phys. Lett.83, 584–586 (2003).
[CrossRef]

Stockman, M. I.

M. I. Stockman, “Nanoplasmonics: past, present, and glimpse into future,” Opt. Express19, 22029–22106 (2011).
[CrossRef] [PubMed]

D. K. Gramotnev, M. W. Vogel, and M. I. Stockman, “Optimized nonadiabatic nanofocusing of plasmons by tapered metal rods,” J. Appl. Phys.104, 034311 (2008).
[CrossRef]

M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett.93, 137404 (2004).
[CrossRef] [PubMed]

Sun, H. B.

R. Proietti Zaccaria, A. Alabastri, F. De Angelis, G. Das, C. Liberale, A. Toma, A. Giugni, L. Razzari, M. Malerba, H. B. Sun, and E. Di Fabrizio, “Fully analytical description of adiabatic compression in dissipative polaritonic structures,” Phys. Rev. B86, 035410 (2012).
[CrossRef]

Sundaramurthy, A.

K. B. Crozier, A. Sundaramurthy, G. S. Kino, and C. F. Quate, “Optical antennas: resonator for local field enhancement,” J. Appl. Phys.94, 4632 (2003).
[CrossRef]

Thiel, M.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterials as broadband circular polarizer,” Science325, 1513–1515 (2009).
[CrossRef] [PubMed]

Tirinato, L.

F. De Angelis, F. Gentile, F. Mecarini, G. Das, M. Moretti, P. Candeloro, M. L. Coluccio, G. Cojoc, A. Accardo, C. Liberale, R. Proietti Zaccaria, G. Perozziello, L. Tirinato, A. Toma, G. Cuda, R. Cingolani, and E. Di Fabrizio, “Breaking the diffusion limit with super-hydrophobic delivery of molecules to plasmonic nanofocusing SERS structures,” Nat. Photon.5, 682–687 (2011).
[CrossRef]

Toma, A.

R. Proietti Zaccaria, F. De Angelis, A. Toma, L. Razzari, A. Alabastri, G. Das, C. Liberale, and E. Di Fabrizio, “Surface plasmon polariton compression through radially and linearly polarized source,” Opt. Lett.37, 545–547 (2012).
[CrossRef]

R. Proietti Zaccaria, A. Alabastri, F. De Angelis, G. Das, C. Liberale, A. Toma, A. Giugni, L. Razzari, M. Malerba, H. B. Sun, and E. Di Fabrizio, “Fully analytical description of adiabatic compression in dissipative polaritonic structures,” Phys. Rev. B86, 035410 (2012).
[CrossRef]

F. De Angelis, F. Gentile, F. Mecarini, G. Das, M. Moretti, P. Candeloro, M. L. Coluccio, G. Cojoc, A. Accardo, C. Liberale, R. Proietti Zaccaria, G. Perozziello, L. Tirinato, A. Toma, G. Cuda, R. Cingolani, and E. Di Fabrizio, “Breaking the diffusion limit with super-hydrophobic delivery of molecules to plasmonic nanofocusing SERS structures,” Nat. Photon.5, 682–687 (2011).
[CrossRef]

A. Belardini, M. C. Larciprete, M. Centini, E. Fazio, C. Sibilia, D. Chiappe, C. Martella, A. Toma, M. Giordano, and F. Buatier de Mongeot, “Circular dichroism in the optical second-harmonic emission of curved gold metal nanowires,” Phys. Rev. Lett.107, 257401 (2011).
[CrossRef]

L. Razzari, A. Toma, M. Shalaby, M. Clerici, R. Proietti Zaccaria, C. Liberale, S. Marras, I.A.I. Al-Naib, G. Das, F. De Angelis, M. Peccianti, A. Falqui, T. Ozaki, R. Morandotti, and E. Di Fabrizio, “Extremely large extinction efficiency and field enhancement in terahertz resonant dipole nanoantennas,” Opt. Express19, 26088–26094 (2011).
[CrossRef]

B. Fazio, C. D’Andrea, F. Bonaccorso, A. Irrera, G. Calogero, C. Vasi, P. G. Gucciardi, M. Allegrini, A. Toma, D. Chiappe, C. Martella, and F. Buatier de Mongeot, “Re-radiation enhancement in polarized surface-enhanced resonant raman scattering of randomly oriented molecules on self-organized gold nanowires,” ACS Nano5, 5945–5956 (2011).
[CrossRef] [PubMed]

A. Belardini, M. C. Larciprete, M. Centini, E. Fazio, C. Sibilia, M. Bertolotti, A. Toma, D. Chiappe, and F. Buatier de Mongeot, “Tailored second harmonic generation from self-organized metal nano-wires arrays,” Opt. Express17, 3603–3609 (2009).
[CrossRef] [PubMed]

Tretyakov, S. A.

P. A. Belov, R. Marques, S. I. Maslovski, I. S. Nefedov, M. Silveirinha, C. R. Simovski, and S. A. Tretyakov, “Strong spatial dispersion in wire media in the very large wavelength limit,” Phys. Rev. B67, 113103 (2003).
[CrossRef]

Vaccaro, L.

L. Vaccaro, L. Aeschimann, U. Staufer, H. P. Herzig, and R. Dandliker, “Propagation of the electromagnetic field in fully coated near-field optical probes,” Appl. Phys. Lett.83, 584–586 (2003).
[CrossRef]

van Nieuwstadt, J. A. H.

J. A. H. van Nieuwstadt, M. Sandtke, R. H. Harmsen, F. B. Segerink, J. C. Prangsma, S. Enoch, and L. Kuipers, “Strong modification of the nonlinear optical response of metallic subwavelength hole arrays,” Phys. Rev. Lett.97, 146102 (2006).
[CrossRef] [PubMed]

Vasi, C.

B. Fazio, C. D’Andrea, F. Bonaccorso, A. Irrera, G. Calogero, C. Vasi, P. G. Gucciardi, M. Allegrini, A. Toma, D. Chiappe, C. Martella, and F. Buatier de Mongeot, “Re-radiation enhancement in polarized surface-enhanced resonant raman scattering of randomly oriented molecules on self-organized gold nanowires,” ACS Nano5, 5945–5956 (2011).
[CrossRef] [PubMed]

Vernon, K. C.

T. J. Davis, D. E. Gomez, and K. C. Vernon, “Evanescent coupling between a Raman-active molecule and surface plasmons in ensembles of metallic nanoparticles,” Phys. Rev. B82, 205434 (2010).
[CrossRef]

Vogel, M. W.

D. K. Gramotnev, M. W. Vogel, and M. I. Stockman, “Optimized nonadiabatic nanofocusing of plasmons by tapered metal rods,” J. Appl. Phys.104, 034311 (2008).
[CrossRef]

von Freymann, G.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterials as broadband circular polarizer,” Science325, 1513–1515 (2009).
[CrossRef] [PubMed]

Wegener, M.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterials as broadband circular polarizer,” Science325, 1513–1515 (2009).
[CrossRef] [PubMed]

S. Linden, C. Enkrich, G. Dolling, M. W. Klein, J. Zhou, T. Koschny, C. M. Soukoulis, S. Burger, F. Schmidt, and M. Wegener, “Photonic metamaterials: magnetism at optical frequencies,” IEEE J. Sel. Top. Quantum Electron.12, 1097–1105 (2006).
[CrossRef]

White, J. S.

Yin, X.

Yu, M. B.

Zhang, W.

W. Zhang, X. Cui, and O. J. F. Martin, “Local field enhancement of an infinite conical metal tip illuminated by a focused beam,” J. Raman Spectrosc.40, 1338–1342 (2009).
[CrossRef]

Zhou, J.

S. Linden, C. Enkrich, G. Dolling, M. W. Klein, J. Zhou, T. Koschny, C. M. Soukoulis, S. Burger, F. Schmidt, and M. Wegener, “Photonic metamaterials: magnetism at optical frequencies,” IEEE J. Sel. Top. Quantum Electron.12, 1097–1105 (2006).
[CrossRef]

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett.95, 223902 (2005).
[CrossRef] [PubMed]

Zhu, Y.

ACS Nano (1)

B. Fazio, C. D’Andrea, F. Bonaccorso, A. Irrera, G. Calogero, C. Vasi, P. G. Gucciardi, M. Allegrini, A. Toma, D. Chiappe, C. Martella, and F. Buatier de Mongeot, “Re-radiation enhancement in polarized surface-enhanced resonant raman scattering of randomly oriented molecules on self-organized gold nanowires,” ACS Nano5, 5945–5956 (2011).
[CrossRef] [PubMed]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

L. Vaccaro, L. Aeschimann, U. Staufer, H. P. Herzig, and R. Dandliker, “Propagation of the electromagnetic field in fully coated near-field optical probes,” Appl. Phys. Lett.83, 584–586 (2003).
[CrossRef]

M. I. Haftel, C. Schlockermann, and G. Blumberg, “Role of cylindrical surface plasmons in enhanced transmission,” Appl. Phys. Lett.88, 193104 (2006).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

S. Linden, C. Enkrich, G. Dolling, M. W. Klein, J. Zhou, T. Koschny, C. M. Soukoulis, S. Burger, F. Schmidt, and M. Wegener, “Photonic metamaterials: magnetism at optical frequencies,” IEEE J. Sel. Top. Quantum Electron.12, 1097–1105 (2006).
[CrossRef]

J. Appl. Phys. (3)

K. B. Crozier, A. Sundaramurthy, G. S. Kino, and C. F. Quate, “Optical antennas: resonator for local field enhancement,” J. Appl. Phys.94, 4632 (2003).
[CrossRef]

A. J. Babadjanyan, N. L. Margaryan, and Kh. V. Nerkararyan, “Superfocusing of surface polaritons in the conical structure,” J. Appl. Phys.87, 3785–3788 (2000).
[CrossRef]

D. K. Gramotnev, M. W. Vogel, and M. I. Stockman, “Optimized nonadiabatic nanofocusing of plasmons by tapered metal rods,” J. Appl. Phys.104, 034311 (2008).
[CrossRef]

J. Raman Spectrosc. (1)

W. Zhang, X. Cui, and O. J. F. Martin, “Local field enhancement of an infinite conical metal tip illuminated by a focused beam,” J. Raman Spectrosc.40, 1338–1342 (2009).
[CrossRef]

Nano Lett. (3)

F. De Angelis, M. Patrini, G. Das, I. Maksymov, M. Galli, L. Businaro, L. C. Andreani, and E. Di Fabrizio, “A hybrid plasmonic-photonic nanodevice for label-free detection of a few molecules,” Nano Lett.8, 2321–2327 (2008).
[CrossRef] [PubMed]

G. W. Bryant, F. J. Garca de Abajo, and J. Aizpurua, “Mapping the plasmon resonances of metallic nanoantennas,” Nano Lett.8, 631–636 (2008).
[CrossRef] [PubMed]

C. C. Neacsu, S. Bergewer, R. L. Olmon, L. V. Saraf, C. Ropers, and M. B. Raschke, “Near-field localization in plasmonic superfocusing: a nanoemitter on a tip,” Nano Lett.10, 592–596 (2010).
[CrossRef] [PubMed]

Nanoscale (1)

S. V. Boriskina and M. R. Bjorn, “Molding the flow of light on the nanoscale: from vortex nanogears to phase-operated plasmonic machinery,” Nanoscale4, 76–90 (2012).
[CrossRef]

Nat. Nanotech. (1)

F. De Angelis, G. Das, P. Candeloro, M. Patrini, M. Galli, A. Bek, M. Lazzarino, I. Maksymov, C. Liberale, L. C. Andreani, and E. Di Fabrizio, “Nanoscale chemical mapping using three-dimensional adiabatic compression of surface plasmon polaritons,” Nat. Nanotech.5, 67–72 (2010).
[CrossRef]

Nat. Photon. (1)

F. De Angelis, F. Gentile, F. Mecarini, G. Das, M. Moretti, P. Candeloro, M. L. Coluccio, G. Cojoc, A. Accardo, C. Liberale, R. Proietti Zaccaria, G. Perozziello, L. Tirinato, A. Toma, G. Cuda, R. Cingolani, and E. Di Fabrizio, “Breaking the diffusion limit with super-hydrophobic delivery of molecules to plasmonic nanofocusing SERS structures,” Nat. Photon.5, 682–687 (2011).
[CrossRef]

Opt. Commun. (1)

N. A. Janunts, K. S. Baghdasaryan, Kh. V. Nerkararyan, and B. Hecht, “Excitation and superfocusing of surface plasmon polaritons on a silver-coated optical fiber tip,” Opt. Commun.253, 118–124 (2005).
[CrossRef]

Opt. Express (9)

A. Belardini, M. C. Larciprete, M. Centini, E. Fazio, C. Sibilia, M. Bertolotti, A. Toma, D. Chiappe, and F. Buatier de Mongeot, “Tailored second harmonic generation from self-organized metal nano-wires arrays,” Opt. Express17, 3603–3609 (2009).
[CrossRef] [PubMed]

J. Song, R. Proietti Zaccaria, G. Dong, E. Di Fabrizio, M. B. Yu, and G. Q. Lo, “Evolution of modes in a metal-coated nano-fiber,” Opt. Express19, 25206–25221 (2011).
[CrossRef]

L. Razzari, A. Toma, M. Shalaby, M. Clerici, R. Proietti Zaccaria, C. Liberale, S. Marras, I.A.I. Al-Naib, G. Das, F. De Angelis, M. Peccianti, A. Falqui, T. Ozaki, R. Morandotti, and E. Di Fabrizio, “Extremely large extinction efficiency and field enhancement in terahertz resonant dipole nanoantennas,” Opt. Express19, 26088–26094 (2011).
[CrossRef]

E. S. Barnard, J. S. White, A. Chandran, and M. L. Brongersma, “Spectral properties of plasmonic resonator antennas,” Opt. Express16, 16529–16537 (2008).
[CrossRef] [PubMed]

E. J. Smythe, E. Cubukcu, and F. Capasso, “Optical properties of surface plasmon resonances of coupled metallic nanorods,” Opt. Express15, 7439–7447 (2007).
[CrossRef] [PubMed]

J. S. Lee, S. Han, J. Shirdel, S. Koo, D. Sadiq, C. Lienau, and N. Park, “Superfocusing of electric or magnetic fields using conical metal tips: effect of mode symmetry on the plasmon excitation method,” Opt. Express19, 12342–12347 (2011).
[CrossRef] [PubMed]

C. Huang, X. Yin, H. Huang, and Y. Zhu, “Study of plasmon resonance in a gold nanorod with an LC circuit model,” Opt. Express17, 6407–6413 (2009).
[CrossRef] [PubMed]

F. De Angelis, R. Proietti Zaccaria, M. Francardi, C. Liberale, and E. Di Fabrizio, “Multi-scheme approach for efficient surface plasmon polariton generation in metallic conical tips on AFM-based cantilevers,” Opt. Express19, 22268–22279 (2011).
[CrossRef] [PubMed]

M. I. Stockman, “Nanoplasmonics: past, present, and glimpse into future,” Opt. Express19, 22029–22106 (2011).
[CrossRef] [PubMed]

Opt. Lett. (1)

Phys. Lett. A (1)

R. Ruppin, “Effect of non-locality on nanofocusing of surface plasmon field intensity in a conical tip,” Phys. Lett. A340, 299–302 (2005).
[CrossRef]

Phys. Rev. A (1)

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. A75, 063822 (2007).
[CrossRef]

Phys. Rev. B (6)

R. Proietti Zaccaria, A. Alabastri, F. De Angelis, G. Das, C. Liberale, A. Toma, A. Giugni, L. Razzari, M. Malerba, H. B. Sun, and E. Di Fabrizio, “Fully analytical description of adiabatic compression in dissipative polaritonic structures,” Phys. Rev. B86, 035410 (2012).
[CrossRef]

T. Sondergaard and S. Bozhevolnyi, “Slow-plasmon resonant nanostructures: scattering and field enhancements,” Phys. Rev. B75, 073402 (2007).
[CrossRef]

P. Corio, S. D.M. Brown, A. Marucci, M. A. Pimenta, K. Kneipp, G. Dresselhaus, and M. S. Dresselhaus, “Surface-enhanced resonant Raman spectroscopy of single-wall carbon nanotubes adsorbed on silver and gold surfaces,” Phys. Rev. B61, 13202–13211 (2000).
[CrossRef]

P. I. Geshev, U. Fischer, and H. Fuchs, “Calculation of tip enhanced Raman scattering caused by nanoparticle plasmons acting on a molecule placed near a metallic film,” Phys. Rev. B81, 125441 (2010).
[CrossRef]

T. J. Davis, D. E. Gomez, and K. C. Vernon, “Evanescent coupling between a Raman-active molecule and surface plasmons in ensembles of metallic nanoparticles,” Phys. Rev. B82, 205434 (2010).
[CrossRef]

P. A. Belov, R. Marques, S. I. Maslovski, I. S. Nefedov, M. Silveirinha, C. R. Simovski, and S. A. Tretyakov, “Strong spatial dispersion in wire media in the very large wavelength limit,” Phys. Rev. B67, 113103 (2003).
[CrossRef]

Phys. Rev. Lett. (6)

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett.95, 223902 (2005).
[CrossRef] [PubMed]

P. Bharadwaj, A. Bouhelier, and L. Novotny, “Electrical excitation of surface plasmons,” Phys. Rev. Lett.106, 226802 (2011).
[CrossRef] [PubMed]

J. A. H. van Nieuwstadt, M. Sandtke, R. H. Harmsen, F. B. Segerink, J. C. Prangsma, S. Enoch, and L. Kuipers, “Strong modification of the nonlinear optical response of metallic subwavelength hole arrays,” Phys. Rev. Lett.97, 146102 (2006).
[CrossRef] [PubMed]

A. Belardini, M. C. Larciprete, M. Centini, E. Fazio, C. Sibilia, D. Chiappe, C. Martella, A. Toma, M. Giordano, and F. Buatier de Mongeot, “Circular dichroism in the optical second-harmonic emission of curved gold metal nanowires,” Phys. Rev. Lett.107, 257401 (2011).
[CrossRef]

M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett.93, 137404 (2004).
[CrossRef] [PubMed]

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

Science (1)

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterials as broadband circular polarizer,” Science325, 1513–1515 (2009).
[CrossRef] [PubMed]

Other (4)

J. D. Jackson, Classical Electrodynamics (John Wiley & Sons, 1998).

S. A. Mayer, Plasmonics: Fundamentals and Applications (Springer, 2007).

D. Sarid and W. Challener, Modern introduction to Surface Plasmons (Cambridge University Press, 2010).

The Drude-Lorentz model is a commonly adopted method to describe the interaction between a metallic medium and an electromagnetic field. The model itself does not require the definition of any wave vector k⃗, but it just assumes the presence of an oscillating electric field. Ought to this aspect, we will exploit the Drude-Lorentz model in all our numerical analysis except the ES case.

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Figures (5)

Fig. 1
Fig. 1

Spectrum of the norm of the electric field calculated on the cone axis 5 nm off the tip-end. The strongest peak, corresponding to the fundamental dipole mode, is found at 5878 nm (∼ 51 THz). No peaks are found for lower frequencies. The figure shows also the sketch of the the illumination method together with the x-component of the electric field for three frequencies: 10 THz, 93 THz and 147 THz. For each of them the nodal planes are indicated by dashed lines.

Fig. 2
Fig. 2

E-field norm calculated along a line from the base to the apex of the cone. The line is 1 nm above the cone surface (in the dielectric). Three situations are considered: (a) equipotential condition on the cone is assumed (ES case); (b) slowly oscillating field (10 THz) characterized by strongly negative permittivity ε = −17000 (QES case); (c) electromagnetic source with λ = 30 μm (EM case). For the three cases the field amplitude is set at 1 V/m. A common zero is found at ∼ 950 nm from the base. (a), (b) and (c) are the corresponding E-field plots on the xz plane.

Fig. 3
Fig. 3

Spectrum of the norm of the electric field calculated at 5 nm from the tip-apex for the QD case. Strong blue-shift is found with respect to the EM case (Fig. 1). The first three mode profiles for the x-component of the electric field are also shown. The dashed lines represent the nodal planes.

Fig. 4
Fig. 4

x-component of the electric field for a) EM case; b) QD case. For both cases the seventh order peak was considered, corresponding to 315 THz and 528 THz for EM and QD case, respectively (see bottom plots, Fig. 1 (left) and 3 (right)). Adiabatic compression (shrinkage of λeff) is clearly shown through the red/blue scale indicating the nodes positions. c) Radial mode calculated 5 nm off the cone apex.

Fig. 5
Fig. 5

Norm of the electric field calculated at 5 nm off the tip apex by changing the relative magnetic permeability μsm (μcone = 1 unless otherwise specified). The curve with μsm = 1 corresponds to Fig. 1. By decreasing μsm a blue-shift is observed. The QD case is also plotted for comparison with the EM zero limit of both μsm and μcone resulting in a overlapping of the two curves. The first two saturation frequency orders are shown by the two vertical dotted lines. The ordinate is in log scale.

Equations (5)

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ε r = 1 Ω p 2 ω ( ω i Γ 0 ) + j = 1 m f j ω p 2 ( ω j 2 ω 2 ) + i ω Γ j
{ D = ε 0 ε r E D = ρ E = V
× μ r 1 ( × E ) k 0 2 ε r E = 0
{ D = ε 0 ε r E D = ρ E = V J + ρ t = 0 J = i ω D = σ ( ω ) E + ε 0 E t
{ E = V A t A = μ 4 π p ˙ r

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