Abstract

We study optical second harmonic generation from metallic dipole antennas with narrow gaps. Enhancement of the fundamental-frequency field in the gap region plays a marginal role on conversion efficiency. In the symmetric configuration, i.e., with the gap located at the center of the antenna axis, reducing gap size induces a significant red-shift of the maximum conversion efficiency peak. Either enhancement or inhibition of second-harmonic emission may be observed as gap size is decreased, depending on the antenna mode excited at the harmonic frequency. The second-harmonic signal is extremely sensitive to the asymmetry introduced by gap’s displacements with respect to the antenna center. In this situation, second-harmonic light can couple to all the available antenna modes. We perform a multipolar analysis that allows engineering the far-field SH emission and find that the interaction with quasi-odd-symmetry modes generates radiation patterns with a strong dipolar component.

© 2015 Optical Society of America

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References

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2014 (4)

2013 (3)

J. Butet, K. Thyagarajan, and O. J. F. Martin, “Ultrasensitive Optical Shape Characterization of Gold Nanoantennas Using Second Harmonic Generation,” Nano Lett. 13(4), 1787–1792 (2013).
[PubMed]

D. de Ceglia, S. Campione, M. A. Vincenti, F. Capolino, and M. Scalora, “Low-damping epsilon-near-zero slabs: Nonlinear and nonlocal optical properties,” Phys. Rev. B 87(15), 155140 (2013).
[Crossref]

M. A. Vincenti, D. de Ceglia, M. Grande, A. D’Orazio, and M. Scalora, “Tailoring Absorption in Metal Gratings with Resonant Ultrathin Bridges,” Plasmonics 8(3), 1445–1456 (2013).
[Crossref]

2012 (9)

R. Esteban, A. G. Borisov, P. Nordlander, and J. Aizpurua, “Bridging quantum and classical plasmonics with a quantum-corrected model,” Nat. Commun. 3, 825 (2012).
[Crossref] [PubMed]

P. Grahn, A. Shevchenko, and M. Kaivola, “Electromagnetic multipole theory for optical nanomaterials,” New J. Phys. 14(9), 093033 (2012).
[Crossref]

M. A. Vincenti, S. Campione, D. de Ceglia, F. Capolino, and M. Scalora, “Gain-assisted harmonic generation in near-zero permittivity metamaterials made of plasmonic nanoshells,” New J. Phys. 14(10), 103016 (2012).
[Crossref]

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the Ultimate Limits of Plasmonic Enhancement,” Science 337(6098), 1072–1074 (2012).
[Crossref] [PubMed]

M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6(11), 737–748 (2012).
[Crossref]

P. Biagioni, D. Brida, J.-S. Huang, J. Kern, L. Duò, B. Hecht, M. Finazzi, and G. Cerullo, “Dynamics of four-photon photoluminescence in gold nanoantennas,” Nano Lett. 12(6), 2941–2947 (2012).
[Crossref] [PubMed]

A. Slablab, L. Le Xuan, M. Zielinski, Y. de Wilde, V. Jacques, D. Chauvat, and J. F. Roch, “Second-harmonic generation from coupled plasmon modes in a single dimer of gold nanospheres,” Opt. Express 20(1), 220–227 (2012).
[Crossref] [PubMed]

J. Berthelot, G. Bachelier, M. Song, P. Rai, G. Colas des Francs, A. Dereux, and A. Bouhelier, “Silencing and enhancement of second-harmonic generation in optical gap antennas,” Opt. Express 20(10), 10498–10508 (2012).
[PubMed]

K. Thyagarajan, S. Rivier, A. Lovera, and O. J. F. Martin, “Enhanced second-harmonic generation from double resonant plasmonic antennae,” Opt. Express 20(12), 12860–12865 (2012).
[Crossref] [PubMed]

2011 (4)

A. Benedetti, M. Centini, M. Bertolotti, and C. Sibilia, “Second harmonic generation from 3D nanoantennas: on the surface and bulk contributions by far-field pattern analysis,” Opt. Express 19(27), 26752–26767 (2011).
[Crossref] [PubMed]

R. Czaplicki, M. Zdanowicz, K. Koskinen, J. Laukkanen, M. Kuittinen, and M. Kauranen, “Dipole limit in second-harmonic generation from arrays of gold nanoparticles,” Opt. Express 19(27), 26866–26871 (2011).
[Crossref] [PubMed]

M. Castro-Lopez, D. Brinks, R. Sapienza, and N. F. van Hulst, “Aluminum for nonlinear plasmonics: Resonance-driven polarized luminescence of Al, Ag, and Au nanoantennas,” Nano Lett. 11(11), 4674–4678 (2011).
[Crossref] [PubMed]

C. David and F. J. García de Abajo, “Spatial Nonlocality in the Optical Response of Metal Nanoparticles,” J. Phys. Chem. C 115(40), 19470–19475 (2011).
[Crossref]

2010 (4)

2009 (3)

2008 (4)

M. Larciprete, A. Belardini, M. Cappeddu, D. De Ceglia, M. Centini, E. Fazio, C. Sibilia, M. Bloemer, and M. Scalora, “Second-harmonic generation from metallodielectric multilayer photonic-band-gap structures,” Phys. Rev. A 77(1), 013809 (2008).
[Crossref]

H. Husu, B. Canfield, J. Laukkanen, B. Bai, M. Kuittinen, J. Turunen, and M. Kauranen, “Local-field effects in the nonlinear optical response of metamaterials,” Metamaterials (Amst.) 2(2-3), 155–168 (2008).
[Crossref]

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

A. Alù and N. Engheta, “Input Impedance, Nanocircuit Loading, and Radiation Tuning of Optical Nanoantennas,” Phys. Rev. Lett. 101(4), 043901 (2008).
[Crossref] [PubMed]

2007 (2)

M. Danckwerts and L. Novotny, “Optical frequency mixing at coupled gold nanoparticles,” Phys. Rev. Lett. 98(2), 026104 (2007).
[Crossref] [PubMed]

B. K. Canfield, H. Husu, J. Laukkanen, B. Bai, M. Kuittinen, J. Turunen, and M. Kauranen, “Local Field Asymmetry Drives Second-Harmonic Generation in Non-Centrosymmetric Nanodimers,” Nano Lett. 7(5), 1251–1255 (2007).
[Crossref] [PubMed]

2005 (4)

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

P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, “Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas,” Phys. Rev. Lett. 94(1), 017402 (2005).
[Crossref] [PubMed]

M. Lippitz, M. A. van Dijk, and M. Orrit, “Third-harmonic generation from single gold nanoparticles,” Nano Lett. 5(4), 799–802 (2005).
[Crossref] [PubMed]

J. Aizpurua, G. W. Bryant, L. J. Richter, F. J. García de Abajo, B. K. Kelley, and T. Mallouk, “Optical properties of coupled metallic nanorods for field-enhanced spectroscopy,” Phys. Rev. B 71(23), 235420 (2005).
[Crossref]

2004 (2)

1999 (1)

B. Lamprecht, J. Krenn, A. Leitner, and F. Aussenegg, “Resonant and off-resonant light-driven plasmons in metal nanoparticles studied by femtosecond-resolution third-harmonic generation,” Phys. Rev. Lett. 83(21), 4421–4424 (1999).
[Crossref]

1998 (1)

1988 (1)

R. Rojas, F. Claro, and R. Fuchs, “Nonlocal response of a small coated sphere,” Phys. Rev. B Condens. Matter 37(12), 6799–6807 (1988).
[Crossref] [PubMed]

1987 (2)

M. Weber and A. Liebsch, “Density-functional approach to second-harmonic generation at metal surfaces,” Phys. Rev. B Condens. Matter 35(14), 7411–7416 (1987).
[Crossref] [PubMed]

J. E. Sipe, D. J. Moss, and H. M. van Driel, “Phenomenological theory of optical second- and third-harmonic generation from cubic centrosymmetric crystals,” Phys. Rev. B Condens. Matter 35(3), 1129–1141 (1987).
[Crossref] [PubMed]

1986 (1)

D. Maystre, M. Neviere, and R. Reinisch, “Nonlinear polarisation inside metals: A mathematical study of the free-electron model,” Appl. Phys., A Mater. Sci. Process. 39(2), 115–121 (1986).
[Crossref]

1985 (1)

J. L. Coutaz, M. Neviere, E. Pic, and R. Reinisch, “Experimental study of surface-enhanced second-harmonic generation on silver gratings,” Phys. Rev. B Condens. Matter 32(4), 2227–2232 (1985).
[Crossref] [PubMed]

1980 (1)

J. E. Sipe, V. C. Y. So, M. Fukui, and G. I. Stegeman, “Analysis of second-harmonic generation at metal surfaces,” Phys. Rev. B 21(10), 4389–4402 (1980).
[Crossref]

1971 (1)

J. Rudnick and E. A. Stern, “Second-Harmonic Radiation from Metal Surfaces,” Phys. Rev. B 4(12), 4274–4290 (1971).
[Crossref]

1962 (1)

N. Bloembergen and P. S. Pershan, “Light Waves at the Boundary of Nonlinear Media,” Phys. Rev. 128(2), 606–622 (1962).
[Crossref]

Aizpurua, J.

R. Esteban, A. G. Borisov, P. Nordlander, and J. Aizpurua, “Bridging quantum and classical plasmonics with a quantum-corrected model,” Nat. Commun. 3, 825 (2012).
[Crossref] [PubMed]

J. Aizpurua, G. W. Bryant, L. J. Richter, F. J. García de Abajo, B. K. Kelley, and T. Mallouk, “Optical properties of coupled metallic nanorods for field-enhanced spectroscopy,” Phys. Rev. B 71(23), 235420 (2005).
[Crossref]

Akozbek, N.

M. Scalora, M. A. Vincenti, D. de Ceglia, V. Roppo, M. Centini, N. Akozbek, and M. J. Bloemer, “Second- and third-harmonic generation in metal-based structures,” Phys. Rev. A 82(4), 043828 (2010).
[Crossref]

Alù, A.

A. Alù and N. Engheta, “Input Impedance, Nanocircuit Loading, and Radiation Tuning of Optical Nanoantennas,” Phys. Rev. Lett. 101(4), 043901 (2008).
[Crossref] [PubMed]

Aussenegg, F.

B. Lamprecht, J. Krenn, A. Leitner, and F. Aussenegg, “Resonant and off-resonant light-driven plasmons in metal nanoparticles studied by femtosecond-resolution third-harmonic generation,” Phys. Rev. Lett. 83(21), 4421–4424 (1999).
[Crossref]

Bachelier, G.

Bai, B.

H. Husu, B. Canfield, J. Laukkanen, B. Bai, M. Kuittinen, J. Turunen, and M. Kauranen, “Local-field effects in the nonlinear optical response of metamaterials,” Metamaterials (Amst.) 2(2-3), 155–168 (2008).
[Crossref]

B. K. Canfield, H. Husu, J. Laukkanen, B. Bai, M. Kuittinen, J. Turunen, and M. Kauranen, “Local Field Asymmetry Drives Second-Harmonic Generation in Non-Centrosymmetric Nanodimers,” Nano Lett. 7(5), 1251–1255 (2007).
[Crossref] [PubMed]

Belardini, A.

M. Larciprete, A. Belardini, M. Cappeddu, D. De Ceglia, M. Centini, E. Fazio, C. Sibilia, M. Bloemer, and M. Scalora, “Second-harmonic generation from metallodielectric multilayer photonic-band-gap structures,” Phys. Rev. A 77(1), 013809 (2008).
[Crossref]

Benedetti, A.

Berthelot, J.

Bertolotti, M.

Bharadwaj, P.

Biagioni, P.

P. Biagioni, D. Brida, J.-S. Huang, J. Kern, L. Duò, B. Hecht, M. Finazzi, and G. Cerullo, “Dynamics of four-photon photoluminescence in gold nanoantennas,” Nano Lett. 12(6), 2941–2947 (2012).
[Crossref] [PubMed]

Bloembergen, N.

N. Bloembergen and P. S. Pershan, “Light Waves at the Boundary of Nonlinear Media,” Phys. Rev. 128(2), 606–622 (1962).
[Crossref]

Bloemer, M.

M. Larciprete, A. Belardini, M. Cappeddu, D. De Ceglia, M. Centini, E. Fazio, C. Sibilia, M. Bloemer, and M. Scalora, “Second-harmonic generation from metallodielectric multilayer photonic-band-gap structures,” Phys. Rev. A 77(1), 013809 (2008).
[Crossref]

Bloemer, M. J.

M. Scalora, M. A. Vincenti, D. de Ceglia, V. Roppo, M. Centini, N. Akozbek, and M. J. Bloemer, “Second- and third-harmonic generation in metal-based structures,” Phys. Rev. A 82(4), 043828 (2010).
[Crossref]

Borisov, A. G.

R. Esteban, A. G. Borisov, P. Nordlander, and J. Aizpurua, “Bridging quantum and classical plasmonics with a quantum-corrected model,” Nat. Commun. 3, 825 (2012).
[Crossref] [PubMed]

Boscolo, S.

Bouhelier, A.

Brida, D.

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Moerner, W. E.

P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, “Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas,” Phys. Rev. Lett. 94(1), 017402 (2005).
[Crossref] [PubMed]

Moss, D. J.

J. E. Sipe, D. J. Moss, and H. M. van Driel, “Phenomenological theory of optical second- and third-harmonic generation from cubic centrosymmetric crystals,” Phys. Rev. B Condens. Matter 35(3), 1129–1141 (1987).
[Crossref] [PubMed]

Mühlschlegel, P.

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

Neviere, M.

D. Maystre, M. Neviere, and R. Reinisch, “Nonlinear polarisation inside metals: A mathematical study of the free-electron model,” Appl. Phys., A Mater. Sci. Process. 39(2), 115–121 (1986).
[Crossref]

J. L. Coutaz, M. Neviere, E. Pic, and R. Reinisch, “Experimental study of surface-enhanced second-harmonic generation on silver gratings,” Phys. Rev. B Condens. Matter 32(4), 2227–2232 (1985).
[Crossref] [PubMed]

Nordlander, P.

R. Esteban, A. G. Borisov, P. Nordlander, and J. Aizpurua, “Bridging quantum and classical plasmonics with a quantum-corrected model,” Nat. Commun. 3, 825 (2012).
[Crossref] [PubMed]

Novotny, L.

P. Bharadwaj, B. Deutsch, and L. Novotny, “Optical antennas,” Adv. Opt. Photon. 1(3), 438–483 (2009).
[Crossref]

M. Danckwerts and L. Novotny, “Optical frequency mixing at coupled gold nanoparticles,” Phys. Rev. Lett. 98(2), 026104 (2007).
[Crossref] [PubMed]

Orrit, M.

M. Lippitz, M. A. van Dijk, and M. Orrit, “Third-harmonic generation from single gold nanoparticles,” Nano Lett. 5(4), 799–802 (2005).
[Crossref] [PubMed]

Osgood, R. M.

Panoiu, N. C.

Park, I.-Y.

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

Pelton, M.

M. Liu, T.-W. Lee, S. K. Gray, P. Guyot-Sionnest, and M. Pelton, “Excitation of Dark Plasmons in Metal Nanoparticles by a Localized Emitter,” Phys. Rev. Lett. 102(10), 107401 (2009).
[Crossref] [PubMed]

Pendry, J. B.

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the Ultimate Limits of Plasmonic Enhancement,” Science 337(6098), 1072–1074 (2012).
[Crossref] [PubMed]

Pershan, P. S.

N. Bloembergen and P. S. Pershan, “Light Waves at the Boundary of Nonlinear Media,” Phys. Rev. 128(2), 606–622 (1962).
[Crossref]

Pertsch, T.

Petschulat, J.

Pic, E.

J. L. Coutaz, M. Neviere, E. Pic, and R. Reinisch, “Experimental study of surface-enhanced second-harmonic generation on silver gratings,” Phys. Rev. B Condens. Matter 32(4), 2227–2232 (1985).
[Crossref] [PubMed]

Pigozzo, F. M.

Pohl, D. W.

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

Rai, P.

Rakic, A. D.

Reinisch, R.

D. Maystre, M. Neviere, and R. Reinisch, “Nonlinear polarisation inside metals: A mathematical study of the free-electron model,” Appl. Phys., A Mater. Sci. Process. 39(2), 115–121 (1986).
[Crossref]

J. L. Coutaz, M. Neviere, E. Pic, and R. Reinisch, “Experimental study of surface-enhanced second-harmonic generation on silver gratings,” Phys. Rev. B Condens. Matter 32(4), 2227–2232 (1985).
[Crossref] [PubMed]

Richter, L. J.

J. Aizpurua, G. W. Bryant, L. J. Richter, F. J. García de Abajo, B. K. Kelley, and T. Mallouk, “Optical properties of coupled metallic nanorods for field-enhanced spectroscopy,” Phys. Rev. B 71(23), 235420 (2005).
[Crossref]

Rivier, S.

Roch, J. F.

Rockstuhl, C.

Rojas, R.

R. Rojas, F. Claro, and R. Fuchs, “Nonlocal response of a small coated sphere,” Phys. Rev. B Condens. Matter 37(12), 6799–6807 (1988).
[Crossref] [PubMed]

Roppo, V.

M. Scalora, M. A. Vincenti, D. de Ceglia, V. Roppo, M. Centini, N. Akozbek, and M. J. Bloemer, “Second- and third-harmonic generation in metal-based structures,” Phys. Rev. A 82(4), 043828 (2010).
[Crossref]

Rudnick, J.

J. Rudnick and E. A. Stern, “Second-Harmonic Radiation from Metal Surfaces,” Phys. Rev. B 4(12), 4274–4290 (1971).
[Crossref]

Sacchetto, F.

Sapienza, R.

M. Castro-Lopez, D. Brinks, R. Sapienza, and N. F. van Hulst, “Aluminum for nonlinear plasmonics: Resonance-driven polarized luminescence of Al, Ag, and Au nanoantennas,” Nano Lett. 11(11), 4674–4678 (2011).
[Crossref] [PubMed]

Scalora, M.

J. W. Haus, D. de Ceglia, M. A. Vincenti, and M. Scalora, “Nonlinear quantum tunneling effects in nanoplasmonic environments: two-photon absorption and harmonic generation,” J. Opt. Soc. Am. B 31(6), A13–A19 (2014).
[Crossref]

J. W. Haus, D. de Ceglia, M. A. Vincenti, and M. Scalora, “Quantum conductivity for metal-insulator-metal nanostructures,” J. Opt. Soc. Am. B 31(2), 259–269 (2014).
[Crossref]

D. de Ceglia, S. Campione, M. A. Vincenti, F. Capolino, and M. Scalora, “Low-damping epsilon-near-zero slabs: Nonlinear and nonlocal optical properties,” Phys. Rev. B 87(15), 155140 (2013).
[Crossref]

M. A. Vincenti, D. de Ceglia, M. Grande, A. D’Orazio, and M. Scalora, “Tailoring Absorption in Metal Gratings with Resonant Ultrathin Bridges,” Plasmonics 8(3), 1445–1456 (2013).
[Crossref]

M. A. Vincenti, S. Campione, D. de Ceglia, F. Capolino, and M. Scalora, “Gain-assisted harmonic generation in near-zero permittivity metamaterials made of plasmonic nanoshells,” New J. Phys. 14(10), 103016 (2012).
[Crossref]

M. Scalora, M. A. Vincenti, D. de Ceglia, V. Roppo, M. Centini, N. Akozbek, and M. J. Bloemer, “Second- and third-harmonic generation in metal-based structures,” Phys. Rev. A 82(4), 043828 (2010).
[Crossref]

M. Larciprete, A. Belardini, M. Cappeddu, D. De Ceglia, M. Centini, E. Fazio, C. Sibilia, M. Bloemer, and M. Scalora, “Second-harmonic generation from metallodielectric multilayer photonic-band-gap structures,” Phys. Rev. A 77(1), 013809 (2008).
[Crossref]

Schuck, P. J.

P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, “Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas,” Phys. Rev. Lett. 94(1), 017402 (2005).
[Crossref] [PubMed]

Shan, J.

Shevchenko, A.

P. Grahn, A. Shevchenko, and M. Kaivola, “Electromagnetic multipole theory for optical nanomaterials,” New J. Phys. 14(9), 093033 (2012).
[Crossref]

Sibilia, C.

Sipe, J. E.

J. E. Sipe, D. J. Moss, and H. M. van Driel, “Phenomenological theory of optical second- and third-harmonic generation from cubic centrosymmetric crystals,” Phys. Rev. B Condens. Matter 35(3), 1129–1141 (1987).
[Crossref] [PubMed]

J. E. Sipe, V. C. Y. So, M. Fukui, and G. I. Stegeman, “Analysis of second-harmonic generation at metal surfaces,” Phys. Rev. B 21(10), 4389–4402 (1980).
[Crossref]

Slablab, A.

Smith, D. R.

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the Ultimate Limits of Plasmonic Enhancement,” Science 337(6098), 1072–1074 (2012).
[Crossref] [PubMed]

So, V. C. Y.

J. E. Sipe, V. C. Y. So, M. Fukui, and G. I. Stegeman, “Analysis of second-harmonic generation at metal surfaces,” Phys. Rev. B 21(10), 4389–4402 (1980).
[Crossref]

Someda, C. G.

Song, M.

Stegeman, G. I.

J. E. Sipe, V. C. Y. So, M. Fukui, and G. I. Stegeman, “Analysis of second-harmonic generation at metal surfaces,” Phys. Rev. B 21(10), 4389–4402 (1980).
[Crossref]

Stern, E. A.

J. Rudnick and E. A. Stern, “Second-Harmonic Radiation from Metal Surfaces,” Phys. Rev. B 4(12), 4274–4290 (1971).
[Crossref]

Sundaramurthy, A.

P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, “Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas,” Phys. Rev. Lett. 94(1), 017402 (2005).
[Crossref] [PubMed]

Thyagarajan, K.

J. Butet, K. Thyagarajan, and O. J. F. Martin, “Ultrasensitive Optical Shape Characterization of Gold Nanoantennas Using Second Harmonic Generation,” Nano Lett. 13(4), 1787–1792 (2013).
[PubMed]

K. Thyagarajan, S. Rivier, A. Lovera, and O. J. F. Martin, “Enhanced second-harmonic generation from double resonant plasmonic antennae,” Opt. Express 20(12), 12860–12865 (2012).
[Crossref] [PubMed]

Tüennermann, A.

Turunen, J.

H. Husu, B. Canfield, J. Laukkanen, B. Bai, M. Kuittinen, J. Turunen, and M. Kauranen, “Local-field effects in the nonlinear optical response of metamaterials,” Metamaterials (Amst.) 2(2-3), 155–168 (2008).
[Crossref]

B. K. Canfield, H. Husu, J. Laukkanen, B. Bai, M. Kuittinen, J. Turunen, and M. Kauranen, “Local Field Asymmetry Drives Second-Harmonic Generation in Non-Centrosymmetric Nanodimers,” Nano Lett. 7(5), 1251–1255 (2007).
[Crossref] [PubMed]

B. Canfield, S. Kujala, K. Jefimovs, J. Turunen, and M. Kauranen, “Linear and nonlinear optical responses influenced by broken symmetry in an array of gold nanoparticles,” Opt. Express 12(22), 5418–5423 (2004).
[Crossref] [PubMed]

Urzhumov, Y.

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the Ultimate Limits of Plasmonic Enhancement,” Science 337(6098), 1072–1074 (2012).
[Crossref] [PubMed]

van Dijk, M. A.

M. Lippitz, M. A. van Dijk, and M. Orrit, “Third-harmonic generation from single gold nanoparticles,” Nano Lett. 5(4), 799–802 (2005).
[Crossref] [PubMed]

van Driel, H. M.

J. E. Sipe, D. J. Moss, and H. M. van Driel, “Phenomenological theory of optical second- and third-harmonic generation from cubic centrosymmetric crystals,” Phys. Rev. B Condens. Matter 35(3), 1129–1141 (1987).
[Crossref] [PubMed]

van Hulst, N. F.

M. Castro-Lopez, D. Brinks, R. Sapienza, and N. F. van Hulst, “Aluminum for nonlinear plasmonics: Resonance-driven polarized luminescence of Al, Ag, and Au nanoantennas,” Nano Lett. 11(11), 4674–4678 (2011).
[Crossref] [PubMed]

Vincenti, M. A.

J. W. Haus, D. de Ceglia, M. A. Vincenti, and M. Scalora, “Quantum conductivity for metal-insulator-metal nanostructures,” J. Opt. Soc. Am. B 31(2), 259–269 (2014).
[Crossref]

J. W. Haus, D. de Ceglia, M. A. Vincenti, and M. Scalora, “Nonlinear quantum tunneling effects in nanoplasmonic environments: two-photon absorption and harmonic generation,” J. Opt. Soc. Am. B 31(6), A13–A19 (2014).
[Crossref]

M. A. Vincenti, D. de Ceglia, M. Grande, A. D’Orazio, and M. Scalora, “Tailoring Absorption in Metal Gratings with Resonant Ultrathin Bridges,” Plasmonics 8(3), 1445–1456 (2013).
[Crossref]

D. de Ceglia, S. Campione, M. A. Vincenti, F. Capolino, and M. Scalora, “Low-damping epsilon-near-zero slabs: Nonlinear and nonlocal optical properties,” Phys. Rev. B 87(15), 155140 (2013).
[Crossref]

M. A. Vincenti, S. Campione, D. de Ceglia, F. Capolino, and M. Scalora, “Gain-assisted harmonic generation in near-zero permittivity metamaterials made of plasmonic nanoshells,” New J. Phys. 14(10), 103016 (2012).
[Crossref]

M. Scalora, M. A. Vincenti, D. de Ceglia, V. Roppo, M. Centini, N. Akozbek, and M. J. Bloemer, “Second- and third-harmonic generation in metal-based structures,” Phys. Rev. A 82(4), 043828 (2010).
[Crossref]

Weber, M.

M. Weber and A. Liebsch, “Density-functional approach to second-harmonic generation at metal surfaces,” Phys. Rev. B Condens. Matter 35(14), 7411–7416 (1987).
[Crossref] [PubMed]

Yang, J.

Zayats, A. V.

M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6(11), 737–748 (2012).
[Crossref]

Zdanowicz, M.

Zielinski, M.

Adv. Opt. Photon. (1)

Appl. Opt. (1)

Appl. Phys., A Mater. Sci. Process. (1)

D. Maystre, M. Neviere, and R. Reinisch, “Nonlinear polarisation inside metals: A mathematical study of the free-electron model,” Appl. Phys., A Mater. Sci. Process. 39(2), 115–121 (1986).
[Crossref]

J. Opt. Soc. Am. B (4)

J. Phys. Chem. C (1)

C. David and F. J. García de Abajo, “Spatial Nonlocality in the Optical Response of Metal Nanoparticles,” J. Phys. Chem. C 115(40), 19470–19475 (2011).
[Crossref]

Metamaterials (Amst.) (1)

H. Husu, B. Canfield, J. Laukkanen, B. Bai, M. Kuittinen, J. Turunen, and M. Kauranen, “Local-field effects in the nonlinear optical response of metamaterials,” Metamaterials (Amst.) 2(2-3), 155–168 (2008).
[Crossref]

Nano Lett. (5)

B. K. Canfield, H. Husu, J. Laukkanen, B. Bai, M. Kuittinen, J. Turunen, and M. Kauranen, “Local Field Asymmetry Drives Second-Harmonic Generation in Non-Centrosymmetric Nanodimers,” Nano Lett. 7(5), 1251–1255 (2007).
[Crossref] [PubMed]

P. Biagioni, D. Brida, J.-S. Huang, J. Kern, L. Duò, B. Hecht, M. Finazzi, and G. Cerullo, “Dynamics of four-photon photoluminescence in gold nanoantennas,” Nano Lett. 12(6), 2941–2947 (2012).
[Crossref] [PubMed]

M. Castro-Lopez, D. Brinks, R. Sapienza, and N. F. van Hulst, “Aluminum for nonlinear plasmonics: Resonance-driven polarized luminescence of Al, Ag, and Au nanoantennas,” Nano Lett. 11(11), 4674–4678 (2011).
[Crossref] [PubMed]

M. Lippitz, M. A. van Dijk, and M. Orrit, “Third-harmonic generation from single gold nanoparticles,” Nano Lett. 5(4), 799–802 (2005).
[Crossref] [PubMed]

J. Butet, K. Thyagarajan, and O. J. F. Martin, “Ultrasensitive Optical Shape Characterization of Gold Nanoantennas Using Second Harmonic Generation,” Nano Lett. 13(4), 1787–1792 (2013).
[PubMed]

Nat. Commun. (1)

R. Esteban, A. G. Borisov, P. Nordlander, and J. Aizpurua, “Bridging quantum and classical plasmonics with a quantum-corrected model,” Nat. Commun. 3, 825 (2012).
[Crossref] [PubMed]

Nat. Photonics (1)

M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6(11), 737–748 (2012).
[Crossref]

Nature (1)

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

New J. Phys. (2)

M. A. Vincenti, S. Campione, D. de Ceglia, F. Capolino, and M. Scalora, “Gain-assisted harmonic generation in near-zero permittivity metamaterials made of plasmonic nanoshells,” New J. Phys. 14(10), 103016 (2012).
[Crossref]

P. Grahn, A. Shevchenko, and M. Kaivola, “Electromagnetic multipole theory for optical nanomaterials,” New J. Phys. 14(9), 093033 (2012).
[Crossref]

Opt. Express (10)

X. Meng, R. R. Grote, J. I. Dadap, N. C. Panoiu, and R. M. Osgood, “Engineering metal-nanoantennae/dye complexes for maximum fluorescence enhancement,” Opt. Express 22(18), 22018–22030 (2014).
[Crossref] [PubMed]

A. Locatelli, C. De Angelis, D. Modotto, S. Boscolo, F. Sacchetto, M. Midrio, A.-D. Capobianco, F. M. Pigozzo, and C. G. Someda, “Modeling of enhanced field confinement and scattering by optical wire antennas,” Opt. Express 17(19), 16792–16800 (2009).
[Crossref] [PubMed]

A. Locatelli, “Analysis of the optical properties of wire antennas with displaced terminals,” Opt. Express 18(9), 9504–9510 (2010).
[Crossref] [PubMed]

J. Petschulat, J. Yang, C. Menzel, C. Rockstuhl, A. Chipouline, P. Lalanne, A. Tüennermann, F. Lederer, and T. Pertsch, “Understanding the electric and magnetic response of isolated metaatoms by means of a multipolar field decomposition,” Opt. Express 18(14), 14454–14466 (2010).
[Crossref] [PubMed]

A. Benedetti, M. Centini, M. Bertolotti, and C. Sibilia, “Second harmonic generation from 3D nanoantennas: on the surface and bulk contributions by far-field pattern analysis,” Opt. Express 19(27), 26752–26767 (2011).
[Crossref] [PubMed]

R. Czaplicki, M. Zdanowicz, K. Koskinen, J. Laukkanen, M. Kuittinen, and M. Kauranen, “Dipole limit in second-harmonic generation from arrays of gold nanoparticles,” Opt. Express 19(27), 26866–26871 (2011).
[Crossref] [PubMed]

A. Slablab, L. Le Xuan, M. Zielinski, Y. de Wilde, V. Jacques, D. Chauvat, and J. F. Roch, “Second-harmonic generation from coupled plasmon modes in a single dimer of gold nanospheres,” Opt. Express 20(1), 220–227 (2012).
[Crossref] [PubMed]

J. Berthelot, G. Bachelier, M. Song, P. Rai, G. Colas des Francs, A. Dereux, and A. Bouhelier, “Silencing and enhancement of second-harmonic generation in optical gap antennas,” Opt. Express 20(10), 10498–10508 (2012).
[PubMed]

K. Thyagarajan, S. Rivier, A. Lovera, and O. J. F. Martin, “Enhanced second-harmonic generation from double resonant plasmonic antennae,” Opt. Express 20(12), 12860–12865 (2012).
[Crossref] [PubMed]

B. Canfield, S. Kujala, K. Jefimovs, J. Turunen, and M. Kauranen, “Linear and nonlinear optical responses influenced by broken symmetry in an array of gold nanoparticles,” Opt. Express 12(22), 5418–5423 (2004).
[Crossref] [PubMed]

Phys. Rev. (1)

N. Bloembergen and P. S. Pershan, “Light Waves at the Boundary of Nonlinear Media,” Phys. Rev. 128(2), 606–622 (1962).
[Crossref]

Phys. Rev. A (2)

M. Larciprete, A. Belardini, M. Cappeddu, D. De Ceglia, M. Centini, E. Fazio, C. Sibilia, M. Bloemer, and M. Scalora, “Second-harmonic generation from metallodielectric multilayer photonic-band-gap structures,” Phys. Rev. A 77(1), 013809 (2008).
[Crossref]

M. Scalora, M. A. Vincenti, D. de Ceglia, V. Roppo, M. Centini, N. Akozbek, and M. J. Bloemer, “Second- and third-harmonic generation in metal-based structures,” Phys. Rev. A 82(4), 043828 (2010).
[Crossref]

Phys. Rev. B (5)

J. Butet, S. Dutta-Gupta, and O. J. F. Martin, “Surface second-harmonic generation from coupled spherical plasmonic nanoparticles: Eigenmode analysis and symmetry properties,” Phys. Rev. B 89(24), 245449 (2014).
[Crossref]

J. E. Sipe, V. C. Y. So, M. Fukui, and G. I. Stegeman, “Analysis of second-harmonic generation at metal surfaces,” Phys. Rev. B 21(10), 4389–4402 (1980).
[Crossref]

J. Aizpurua, G. W. Bryant, L. J. Richter, F. J. García de Abajo, B. K. Kelley, and T. Mallouk, “Optical properties of coupled metallic nanorods for field-enhanced spectroscopy,” Phys. Rev. B 71(23), 235420 (2005).
[Crossref]

D. de Ceglia, S. Campione, M. A. Vincenti, F. Capolino, and M. Scalora, “Low-damping epsilon-near-zero slabs: Nonlinear and nonlocal optical properties,” Phys. Rev. B 87(15), 155140 (2013).
[Crossref]

J. Rudnick and E. A. Stern, “Second-Harmonic Radiation from Metal Surfaces,” Phys. Rev. B 4(12), 4274–4290 (1971).
[Crossref]

Phys. Rev. B Condens. Matter (4)

R. Rojas, F. Claro, and R. Fuchs, “Nonlocal response of a small coated sphere,” Phys. Rev. B Condens. Matter 37(12), 6799–6807 (1988).
[Crossref] [PubMed]

M. Weber and A. Liebsch, “Density-functional approach to second-harmonic generation at metal surfaces,” Phys. Rev. B Condens. Matter 35(14), 7411–7416 (1987).
[Crossref] [PubMed]

J. E. Sipe, D. J. Moss, and H. M. van Driel, “Phenomenological theory of optical second- and third-harmonic generation from cubic centrosymmetric crystals,” Phys. Rev. B Condens. Matter 35(3), 1129–1141 (1987).
[Crossref] [PubMed]

J. L. Coutaz, M. Neviere, E. Pic, and R. Reinisch, “Experimental study of surface-enhanced second-harmonic generation on silver gratings,” Phys. Rev. B Condens. Matter 32(4), 2227–2232 (1985).
[Crossref] [PubMed]

Phys. Rev. Lett. (5)

P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, “Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas,” Phys. Rev. Lett. 94(1), 017402 (2005).
[Crossref] [PubMed]

B. Lamprecht, J. Krenn, A. Leitner, and F. Aussenegg, “Resonant and off-resonant light-driven plasmons in metal nanoparticles studied by femtosecond-resolution third-harmonic generation,” Phys. Rev. Lett. 83(21), 4421–4424 (1999).
[Crossref]

M. Danckwerts and L. Novotny, “Optical frequency mixing at coupled gold nanoparticles,” Phys. Rev. Lett. 98(2), 026104 (2007).
[Crossref] [PubMed]

A. Alù and N. Engheta, “Input Impedance, Nanocircuit Loading, and Radiation Tuning of Optical Nanoantennas,” Phys. Rev. Lett. 101(4), 043901 (2008).
[Crossref] [PubMed]

M. Liu, T.-W. Lee, S. K. Gray, P. Guyot-Sionnest, and M. Pelton, “Excitation of Dark Plasmons in Metal Nanoparticles by a Localized Emitter,” Phys. Rev. Lett. 102(10), 107401 (2009).
[Crossref] [PubMed]

Plasmonics (1)

M. A. Vincenti, D. de Ceglia, M. Grande, A. D’Orazio, and M. Scalora, “Tailoring Absorption in Metal Gratings with Resonant Ultrathin Bridges,” Plasmonics 8(3), 1445–1456 (2013).
[Crossref]

Science (2)

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the Ultimate Limits of Plasmonic Enhancement,” Science 337(6098), 1072–1074 (2012).
[Crossref] [PubMed]

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

Other (4)

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

E. D. Palik and G. Ghosh, Handbook of optical constants of solids (Academic Press, 1998).

J. D. Jackson, Classical Electrodynamics (Wiley, 1999).

R. E. Raab and O. L. de Lange, Multipole Theory in Electromagnetism (Oxford, 2005).

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Figures (8)

Fig. 1
Fig. 1

Plane wave illumination of symmetric (a) and asymmetric (b) dipole nanoantennas. (E)FF,0 is the input FF electric field polarized along the antenna axis (y-axis). The input wavevector kFF,0 points in the x direction. The red shadow symbolizes the FF field enhancement in the middle of the gap. Green arrows indicate scattering of SH light.

Fig. 2
Fig. 2

Field enhancement |(E)|/E0 spectra evaluated at the gap center of symmetric antennas (as illustrated in Fig. 1(a)) as a function of gap size s. Input field is polarized along the antenna axis, as shown in the inset.

Fig. 3
Fig. 3

(a) Normalized extinction cross section, ECS, as a function of input frequency and gap size. The inset shows the excitation scheme. (b) Spectra of radiative decay of a dipole emitting in proximity of a symmetric dipole antenna for different gap sizes. The dipole’s location (10 nm away from the lower edge of the antenna) is shown in the inset. For illustration purposes, an offset of 2.5 dB is used to distinguish spectra corresponding to different gap sizes. (c) Distribution of the real part of the electric field component parallel to the antenna axis (Re[Ey]) for the first four modes supported by the dipole nanoantenna. The color scale is normalized to the field maximum for each mode. The modes are probed with the dipole excitation technique using a gap size s = 10 nm, at frequencies 0.34 PHz for mode M1, 0.46 PHz for M2, 0.6 PHz for M3 and 0.68 PHz for M4, as indicated by the green triangles and squares in (b).

Fig. 4
Fig. 4

(a) Normalized extinction cross section, ECS, as a function of input frequency and gap displacement d. The inset shows the plane wave excitation scheme. (b) Spectra of radiative decay of a dipole emitting in proximity of symmetric dipole antenna. The dipole’s location (10 nm far from the lower edge of the antenna) is shown in the inset. The blue curves are guides for the eye to indicate the antenna modes excited by a plane wave (a) and a point dipole (b). (c) Distribution of the real part of the electric field component parallel to the antenna axis (Re[Ey]) for the first four modes supported by the asymmetric dipole nanoantenna. The modes are probed with the dipole excitation technique using a displacement d = 50 nm, at frequencies 0.3 PHz for mode M ˜ 1 , 0.5 PHz for M ˜ 2 , 0.6 PHz for M ˜ 3 and 0.68 PHz for M ˜ 4 , as indicated by the green triangles and squares in (b).

Fig. 5
Fig. 5

(a) SH conversion efficiency η SH for the symmetric (d = 0) dipole nanoantenna as a function of FF and SH frequency, and gap size s. The color map is reported on a logarithmic scale. (b) Ey field distributions for SH light when mode M2 is excited by a pump tuned at ~0.23 PHz and mode M4 is excited by a pump tuned at ~0.32 PHz. (c) Spectrum of SH conversion efficiency η SH for the nanoantenna without gap (s = 0, as shown in the inset).

Fig. 6
Fig. 6

Pump field enhancement on the metal surface evaluated on the air side (a) and metal side (b). The black (blue) curve refers to an antenna with a gap size of s = 1 nm (s = 10 nm) pumped at a frequency of 0.23 PHz (0.32 PHz), where mode M2 (M4) enhances SH scattering. The shaded areas represent the approximate location of the metallic antenna.

Fig. 7
Fig. 7

(a) SH conversion efficiency η SH for asymmetric dipole nanoantenna as a function of fundamental/SH frequency and gap displacement d. The gap size is s = 10 nm. The color map is reported on a logarithmic scale. (b) Distributions of the real part of the ESH,y field for three scenarios: (i) when mode M ˜ 2 is excited by a pump tuned at ~0.26 PHz with d = 90 nm (left), (ii) mode M ˜ 3 is excited by a pump tuned at ~0.29 PHz with d = 45 nm, and (iii) mode M ˜ 4 M 4 is excited by a pump tuned at ~0.33 PHz with d = 0. The black curves are the SH, far-field radiation patterns associated to the three cases mentioned above.

Fig. 8
Fig. 8

SH scattering efficiency spectra η SH,m mapped for m = 1,2,3 as a function of the gap displacement d. η SH,m is the efficiency of the m-th order of cylindrical harmonic expansion.

Equations (5)

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n ^ J surf =i n 0 e 3 2 m * 2 3+ ε FF ( ω+i γ 0 ) 2 ( 2ω+i γ 0 ) E FF, 2
t ^ J surf =i 2 n 0 e 3 m * 2 1 ( ω+i γ 0 ) 2 ( 2ω+i γ 0 ) E FF, E FF,//
J vol = n 0 e 3 m * 2 1 ω( ω+i γ 0 )( 2ω+i γ 0 ) [ γ 0 ω+i γ 0 ( E FF ) E FF i 2 ( E FF E FF ) ]
H z = m=0 [ a m + i m cos(mφ)+ a m i m+1 sin(mφ) ] H m (2) (kr)
a 0 =Ak/2( Q yx Q xy ) a 1 + =iA[ p y k 2 /4( O yyy 2 O xxy +3 O yxx )], a 1 =A[ p x + k 2 /4(2 O yxy O xxx 3 O xyy )] a 2 + =Ak/2( Q yx + Q xy ), a 2 =iAk/2( Q yy Q xx ) a 3 + =iA k 2 /4( O yxx O yyy +2 O xxy ), a 3 =A k 2 /4(2 O yxy O xxx + O xyy )

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