Abstract

We develop a coherent hyperspectral near-field microscope using a combined nano-Fourier Transform Infra-Red (FTIR) spectroscope and a scattering Scanning Near-field Optical Microscope (s-SNOM) illuminated by an ultra-broadband few-cycle femtosecond source, spanning a spectrum from 660 to 1050 nm. Using this spatio-spectral approach, we resolve hyperspectral near-field response of a single plasmonic nano-antennas over 450 nm bandwidth with a spatial resolution of 40 nm and a spectral resolution of 50 cm−1. In particular, we identify the electric near-field spatial distribution of the dipole resonant mode of various nano-antennas and observe, in accordance with previous theoretical reports, that those are spectrally red-shifted from their far-field response. Moreover, we are able to spectrally and spatially differentiate the near-field distribution of the dipole and quadrupole modes at the single nanoparticle level. Being coherent and short-pulsed, our technique opens the path for optical ultrafast characterization and control of light-matter interaction at the nanoscale.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  22. J. W. Gadzuk, “Hot-electron femtochemistry at surfaces: on the role of multiple electron processes in desorption,” Chem. Phys. 251(1–3), 87–97 (2000).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]

2018 (1)

K. Xu, L. Huang, Z. Zhang, J. Zhao, Z. Zhang, L. W. Snyman, and J. W. Swart, “Light emission from a poly-silicon device with carrier injection engineering,” Mater. Sci. Eng. B 231, 28–31 (2018).
[Crossref]

2017 (1)

A. Peer, Z. Hu, A. Singh, J. A. Hollingsworth, R. Biswas, and H. Htoon, “Photoluminescence enhancement of CuInS2 quantum dots in solution coupled to plasmonic gold nanocup array,” Small 13(33), 1700660 (2017).
[Crossref] [PubMed]

2015 (1)

2014 (3)

H. A. Bechtel, E. A. Muller, R. L. Olmon, M. C. Martin, and M. B. Raschke, “Ultrabroadband infrared nanospectroscopic imaging,” Proc. Natl. Acad. Sci. U.S.A. 111(20), 7191–7196 (2014).
[Crossref] [PubMed]

M. Wagner, Z. Fei, A. S. McLeod, A. S. Rodin, W. Bao, E. G. Iwinski, Z. Zhao, M. Goldflam, M. Liu, G. Dominguez, M. Thiemens, M. M. Fogler, A. H. Castro Neto, C. N. Lau, S. Amarie, F. Keilmann, and D. N. Basov, “Ultrafast and nanoscale plasmonic phenomena in exfoliated graphene revealed by infrared pump-probe nanoscopy,” Nano Lett. 14(2), 894–900 (2014).
[Crossref] [PubMed]

X. Yin, Z. Ye, D. A. Chenet, Y. Ye, K. O’Brien, J. C. Hone, and X. Zhang, “Edge nonlinear optics on a MoS2 atomic monolayer,” Science 344(6183), 488–490 (2014).
[Crossref] [PubMed]

2013 (1)

P. Alonso-González, P. Albella, F. Neubrech, C. Huck, J. Chen, F. Golmar, F. Casanova, L. E. Hueso, A. Pucci, J. Aizpurua, and R. Hillenbrand, “Experimental verification of the spectral shift between near- and far-field peak intensities of plasmonic infrared nanoantennas,” Phys. Rev. Lett. 110(20), 203902 (2013).
[Crossref] [PubMed]

2012 (2)

F. Huth, A. Govyadinov, S. Amarie, W. Nuansing, F. Keilmann, and R. Hillenbrand, “Nano-FTIR absorption spectroscopy of molecular fingerprints at 20 nm spatial resolution,” Nano Lett. 12(8), 3973–3978 (2012).
[Crossref] [PubMed]

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

2011 (3)

J. Zuloaga and P. Nordlander, “On the energy shift between near-field and far-field peak intensities in localized plasmon systems,” Nano Lett. 11(3), 1280–1283 (2011).
[Crossref] [PubMed]

M. Aeschlimann, T. Brixner, A. Fischer, C. Kramer, P. Melchior, W. Pfeiffer, C. Schneider, C. Strüber, P. Tuchscherer, and D. V. Voronine, “Coherent two-dimensional nanoscopy,” Science 333(6050), 1723–1726 (2011).
[Crossref] [PubMed]

J. Ye and P. Van Dorpe, “Improvement of figure of merit for gold nanobar array plasmonic sensors,” Plasmonics 6(4), 665–671 (2011).
[Crossref]

2010 (2)

S. Aksu, A. A. Yanik, R. Adato, A. Artar, M. Huang, and H. Altug, “High-throughput nanofabrication of infrared plasmonic nanoantenna arrays for vibrational nanospectroscopy,” Nano Lett. 10(7), 2511–2518 (2010).
[Crossref] [PubMed]

L. W. Snyman, M. du Plessis, and E. Bellotti, “Photonic transitions (1.4 eV-2.8 eV) in silicon p+np+ injection-avalanche CMOS LEDs as function of depletion layer profiling and defect engineering,” IEEE J. Quantum Electron. 46(6), 906–919 (2010).
[Crossref]

2009 (2)

A. García-Etxarri, I. Romero, F. J. García de Abajo, R. Hillenbrand, and J. Aizpurua, “Influence of the tip in near-field imaging of nanoparticle plasmonic modes: Weak and strong coupling regimes,” Phys. Rev. B Condens. Matter Mater. Phys. 79(12), 125439 (2009).
[Crossref]

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, and A. V. Zayats, “Plasmonic nanorod metamaterials for biosensing,” Nat. Mater. 8(11), 867–871 (2009).
[Crossref] [PubMed]

2008 (3)

Z. Liu, A. Boltasseva, R. H. Pedersen, R. Bakker, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Plasmonic nanoantenna arrays for the visible,” Metamaterials (Amst.) 2(1), 45–51 (2008).
[Crossref]

M. I. Stockman, “Ultrafast nanoplasmonics under coherent control,” New J. Phys. 10(2), 025031 (2008).
[Crossref]

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
[Crossref] [PubMed]

2007 (1)

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B Condens. Matter Mater. Phys. 75(15), 155410 (2007).
[Crossref]

2006 (1)

M. Brehm, T. Taubner, R. Hillenbrand, and F. Keilmann, “Infrared spectroscopic mapping of single nanoparticles and viruses at nanoscale resolution,” Nano Lett. 6(7), 1307–1310 (2006).
[Crossref] [PubMed]

2000 (1)

J. W. Gadzuk, “Hot-electron femtochemistry at surfaces: on the role of multiple electron processes in desorption,” Chem. Phys. 251(1–3), 87–97 (2000).
[Crossref]

Adato, R.

S. Aksu, A. A. Yanik, R. Adato, A. Artar, M. Huang, and H. Altug, “High-throughput nanofabrication of infrared plasmonic nanoantenna arrays for vibrational nanospectroscopy,” Nano Lett. 10(7), 2511–2518 (2010).
[Crossref] [PubMed]

Aeschlimann, M.

M. Aeschlimann, T. Brixner, A. Fischer, C. Kramer, P. Melchior, W. Pfeiffer, C. Schneider, C. Strüber, P. Tuchscherer, and D. V. Voronine, “Coherent two-dimensional nanoscopy,” Science 333(6050), 1723–1726 (2011).
[Crossref] [PubMed]

Aizpurua, J.

P. Alonso-González, P. Albella, F. Neubrech, C. Huck, J. Chen, F. Golmar, F. Casanova, L. E. Hueso, A. Pucci, J. Aizpurua, and R. Hillenbrand, “Experimental verification of the spectral shift between near- and far-field peak intensities of plasmonic infrared nanoantennas,” Phys. Rev. Lett. 110(20), 203902 (2013).
[Crossref] [PubMed]

A. García-Etxarri, I. Romero, F. J. García de Abajo, R. Hillenbrand, and J. Aizpurua, “Influence of the tip in near-field imaging of nanoparticle plasmonic modes: Weak and strong coupling regimes,” Phys. Rev. B Condens. Matter Mater. Phys. 79(12), 125439 (2009).
[Crossref]

Aksu, S.

S. Aksu, A. A. Yanik, R. Adato, A. Artar, M. Huang, and H. Altug, “High-throughput nanofabrication of infrared plasmonic nanoantenna arrays for vibrational nanospectroscopy,” Nano Lett. 10(7), 2511–2518 (2010).
[Crossref] [PubMed]

Albella, P.

P. Alonso-González, P. Albella, F. Neubrech, C. Huck, J. Chen, F. Golmar, F. Casanova, L. E. Hueso, A. Pucci, J. Aizpurua, and R. Hillenbrand, “Experimental verification of the spectral shift between near- and far-field peak intensities of plasmonic infrared nanoantennas,” Phys. Rev. Lett. 110(20), 203902 (2013).
[Crossref] [PubMed]

Alonso-González, P.

P. Alonso-González, P. Albella, F. Neubrech, C. Huck, J. Chen, F. Golmar, F. Casanova, L. E. Hueso, A. Pucci, J. Aizpurua, and R. Hillenbrand, “Experimental verification of the spectral shift between near- and far-field peak intensities of plasmonic infrared nanoantennas,” Phys. Rev. Lett. 110(20), 203902 (2013).
[Crossref] [PubMed]

Altug, H.

S. Aksu, A. A. Yanik, R. Adato, A. Artar, M. Huang, and H. Altug, “High-throughput nanofabrication of infrared plasmonic nanoantenna arrays for vibrational nanospectroscopy,” Nano Lett. 10(7), 2511–2518 (2010).
[Crossref] [PubMed]

Alù, A.

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B Condens. Matter Mater. Phys. 75(15), 155410 (2007).
[Crossref]

Amarie, S.

M. Wagner, Z. Fei, A. S. McLeod, A. S. Rodin, W. Bao, E. G. Iwinski, Z. Zhao, M. Goldflam, M. Liu, G. Dominguez, M. Thiemens, M. M. Fogler, A. H. Castro Neto, C. N. Lau, S. Amarie, F. Keilmann, and D. N. Basov, “Ultrafast and nanoscale plasmonic phenomena in exfoliated graphene revealed by infrared pump-probe nanoscopy,” Nano Lett. 14(2), 894–900 (2014).
[Crossref] [PubMed]

F. Huth, A. Govyadinov, S. Amarie, W. Nuansing, F. Keilmann, and R. Hillenbrand, “Nano-FTIR absorption spectroscopy of molecular fingerprints at 20 nm spatial resolution,” Nano Lett. 12(8), 3973–3978 (2012).
[Crossref] [PubMed]

Artar, A.

S. Aksu, A. A. Yanik, R. Adato, A. Artar, M. Huang, and H. Altug, “High-throughput nanofabrication of infrared plasmonic nanoantenna arrays for vibrational nanospectroscopy,” Nano Lett. 10(7), 2511–2518 (2010).
[Crossref] [PubMed]

Atkinson, R.

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, and A. V. Zayats, “Plasmonic nanorod metamaterials for biosensing,” Nat. Mater. 8(11), 867–871 (2009).
[Crossref] [PubMed]

Bakker, R.

Z. Liu, A. Boltasseva, R. H. Pedersen, R. Bakker, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Plasmonic nanoantenna arrays for the visible,” Metamaterials (Amst.) 2(1), 45–51 (2008).
[Crossref]

Bao, W.

M. Wagner, Z. Fei, A. S. McLeod, A. S. Rodin, W. Bao, E. G. Iwinski, Z. Zhao, M. Goldflam, M. Liu, G. Dominguez, M. Thiemens, M. M. Fogler, A. H. Castro Neto, C. N. Lau, S. Amarie, F. Keilmann, and D. N. Basov, “Ultrafast and nanoscale plasmonic phenomena in exfoliated graphene revealed by infrared pump-probe nanoscopy,” Nano Lett. 14(2), 894–900 (2014).
[Crossref] [PubMed]

Bartal, G.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
[Crossref] [PubMed]

Basov, D. N.

M. Wagner, Z. Fei, A. S. McLeod, A. S. Rodin, W. Bao, E. G. Iwinski, Z. Zhao, M. Goldflam, M. Liu, G. Dominguez, M. Thiemens, M. M. Fogler, A. H. Castro Neto, C. N. Lau, S. Amarie, F. Keilmann, and D. N. Basov, “Ultrafast and nanoscale plasmonic phenomena in exfoliated graphene revealed by infrared pump-probe nanoscopy,” Nano Lett. 14(2), 894–900 (2014).
[Crossref] [PubMed]

Bechtel, H. A.

H. A. Bechtel, E. A. Muller, R. L. Olmon, M. C. Martin, and M. B. Raschke, “Ultrabroadband infrared nanospectroscopic imaging,” Proc. Natl. Acad. Sci. U.S.A. 111(20), 7191–7196 (2014).
[Crossref] [PubMed]

Bellotti, E.

L. W. Snyman, M. du Plessis, and E. Bellotti, “Photonic transitions (1.4 eV-2.8 eV) in silicon p+np+ injection-avalanche CMOS LEDs as function of depletion layer profiling and defect engineering,” IEEE J. Quantum Electron. 46(6), 906–919 (2010).
[Crossref]

Biswas, R.

A. Peer, Z. Hu, A. Singh, J. A. Hollingsworth, R. Biswas, and H. Htoon, “Photoluminescence enhancement of CuInS2 quantum dots in solution coupled to plasmonic gold nanocup array,” Small 13(33), 1700660 (2017).
[Crossref] [PubMed]

Boltasseva, A.

Z. Liu, A. Boltasseva, R. H. Pedersen, R. Bakker, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Plasmonic nanoantenna arrays for the visible,” Metamaterials (Amst.) 2(1), 45–51 (2008).
[Crossref]

Brehm, M.

M. Brehm, T. Taubner, R. Hillenbrand, and F. Keilmann, “Infrared spectroscopic mapping of single nanoparticles and viruses at nanoscale resolution,” Nano Lett. 6(7), 1307–1310 (2006).
[Crossref] [PubMed]

Brixner, T.

M. Aeschlimann, T. Brixner, A. Fischer, C. Kramer, P. Melchior, W. Pfeiffer, C. Schneider, C. Strüber, P. Tuchscherer, and D. V. Voronine, “Coherent two-dimensional nanoscopy,” Science 333(6050), 1723–1726 (2011).
[Crossref] [PubMed]

Casanova, F.

P. Alonso-González, P. Albella, F. Neubrech, C. Huck, J. Chen, F. Golmar, F. Casanova, L. E. Hueso, A. Pucci, J. Aizpurua, and R. Hillenbrand, “Experimental verification of the spectral shift between near- and far-field peak intensities of plasmonic infrared nanoantennas,” Phys. Rev. Lett. 110(20), 203902 (2013).
[Crossref] [PubMed]

Castro Neto, A. H.

M. Wagner, Z. Fei, A. S. McLeod, A. S. Rodin, W. Bao, E. G. Iwinski, Z. Zhao, M. Goldflam, M. Liu, G. Dominguez, M. Thiemens, M. M. Fogler, A. H. Castro Neto, C. N. Lau, S. Amarie, F. Keilmann, and D. N. Basov, “Ultrafast and nanoscale plasmonic phenomena in exfoliated graphene revealed by infrared pump-probe nanoscopy,” Nano Lett. 14(2), 894–900 (2014).
[Crossref] [PubMed]

Chen, J.

P. Alonso-González, P. Albella, F. Neubrech, C. Huck, J. Chen, F. Golmar, F. Casanova, L. E. Hueso, A. Pucci, J. Aizpurua, and R. Hillenbrand, “Experimental verification of the spectral shift between near- and far-field peak intensities of plasmonic infrared nanoantennas,” Phys. Rev. Lett. 110(20), 203902 (2013).
[Crossref] [PubMed]

Chenet, D. A.

X. Yin, Z. Ye, D. A. Chenet, Y. Ye, K. O’Brien, J. C. Hone, and X. Zhang, “Edge nonlinear optics on a MoS2 atomic monolayer,” Science 344(6183), 488–490 (2014).
[Crossref] [PubMed]

Dominguez, G.

M. Wagner, Z. Fei, A. S. McLeod, A. S. Rodin, W. Bao, E. G. Iwinski, Z. Zhao, M. Goldflam, M. Liu, G. Dominguez, M. Thiemens, M. M. Fogler, A. H. Castro Neto, C. N. Lau, S. Amarie, F. Keilmann, and D. N. Basov, “Ultrafast and nanoscale plasmonic phenomena in exfoliated graphene revealed by infrared pump-probe nanoscopy,” Nano Lett. 14(2), 894–900 (2014).
[Crossref] [PubMed]

Drachev, V. P.

Z. Liu, A. Boltasseva, R. H. Pedersen, R. Bakker, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Plasmonic nanoantenna arrays for the visible,” Metamaterials (Amst.) 2(1), 45–51 (2008).
[Crossref]

du Plessis, M.

L. W. Snyman, M. du Plessis, and E. Bellotti, “Photonic transitions (1.4 eV-2.8 eV) in silicon p+np+ injection-avalanche CMOS LEDs as function of depletion layer profiling and defect engineering,” IEEE J. Quantum Electron. 46(6), 906–919 (2010).
[Crossref]

Engheta, N.

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B Condens. Matter Mater. Phys. 75(15), 155410 (2007).
[Crossref]

Evans, P.

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, and A. V. Zayats, “Plasmonic nanorod metamaterials for biosensing,” Nat. Mater. 8(11), 867–871 (2009).
[Crossref] [PubMed]

Fei, Z.

M. Wagner, Z. Fei, A. S. McLeod, A. S. Rodin, W. Bao, E. G. Iwinski, Z. Zhao, M. Goldflam, M. Liu, G. Dominguez, M. Thiemens, M. M. Fogler, A. H. Castro Neto, C. N. Lau, S. Amarie, F. Keilmann, and D. N. Basov, “Ultrafast and nanoscale plasmonic phenomena in exfoliated graphene revealed by infrared pump-probe nanoscopy,” Nano Lett. 14(2), 894–900 (2014).
[Crossref] [PubMed]

Fischer, A.

M. Aeschlimann, T. Brixner, A. Fischer, C. Kramer, P. Melchior, W. Pfeiffer, C. Schneider, C. Strüber, P. Tuchscherer, and D. V. Voronine, “Coherent two-dimensional nanoscopy,” Science 333(6050), 1723–1726 (2011).
[Crossref] [PubMed]

Fogler, M. M.

M. Wagner, Z. Fei, A. S. McLeod, A. S. Rodin, W. Bao, E. G. Iwinski, Z. Zhao, M. Goldflam, M. Liu, G. Dominguez, M. Thiemens, M. M. Fogler, A. H. Castro Neto, C. N. Lau, S. Amarie, F. Keilmann, and D. N. Basov, “Ultrafast and nanoscale plasmonic phenomena in exfoliated graphene revealed by infrared pump-probe nanoscopy,” Nano Lett. 14(2), 894–900 (2014).
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A. García-Etxarri, I. Romero, F. J. García de Abajo, R. Hillenbrand, and J. Aizpurua, “Influence of the tip in near-field imaging of nanoparticle plasmonic modes: Weak and strong coupling regimes,” Phys. Rev. B Condens. Matter Mater. Phys. 79(12), 125439 (2009).
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García-Etxarri, A.

A. García-Etxarri, I. Romero, F. J. García de Abajo, R. Hillenbrand, and J. Aizpurua, “Influence of the tip in near-field imaging of nanoparticle plasmonic modes: Weak and strong coupling regimes,” Phys. Rev. B Condens. Matter Mater. Phys. 79(12), 125439 (2009).
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J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
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M. Wagner, Z. Fei, A. S. McLeod, A. S. Rodin, W. Bao, E. G. Iwinski, Z. Zhao, M. Goldflam, M. Liu, G. Dominguez, M. Thiemens, M. M. Fogler, A. H. Castro Neto, C. N. Lau, S. Amarie, F. Keilmann, and D. N. Basov, “Ultrafast and nanoscale plasmonic phenomena in exfoliated graphene revealed by infrared pump-probe nanoscopy,” Nano Lett. 14(2), 894–900 (2014).
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Golmar, F.

P. Alonso-González, P. Albella, F. Neubrech, C. Huck, J. Chen, F. Golmar, F. Casanova, L. E. Hueso, A. Pucci, J. Aizpurua, and R. Hillenbrand, “Experimental verification of the spectral shift between near- and far-field peak intensities of plasmonic infrared nanoantennas,” Phys. Rev. Lett. 110(20), 203902 (2013).
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F. Huth, A. Govyadinov, S. Amarie, W. Nuansing, F. Keilmann, and R. Hillenbrand, “Nano-FTIR absorption spectroscopy of molecular fingerprints at 20 nm spatial resolution,” Nano Lett. 12(8), 3973–3978 (2012).
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A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, and A. V. Zayats, “Plasmonic nanorod metamaterials for biosensing,” Nat. Mater. 8(11), 867–871 (2009).
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P. Alonso-González, P. Albella, F. Neubrech, C. Huck, J. Chen, F. Golmar, F. Casanova, L. E. Hueso, A. Pucci, J. Aizpurua, and R. Hillenbrand, “Experimental verification of the spectral shift between near- and far-field peak intensities of plasmonic infrared nanoantennas,” Phys. Rev. Lett. 110(20), 203902 (2013).
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F. Huth, A. Govyadinov, S. Amarie, W. Nuansing, F. Keilmann, and R. Hillenbrand, “Nano-FTIR absorption spectroscopy of molecular fingerprints at 20 nm spatial resolution,” Nano Lett. 12(8), 3973–3978 (2012).
[Crossref] [PubMed]

A. García-Etxarri, I. Romero, F. J. García de Abajo, R. Hillenbrand, and J. Aizpurua, “Influence of the tip in near-field imaging of nanoparticle plasmonic modes: Weak and strong coupling regimes,” Phys. Rev. B Condens. Matter Mater. Phys. 79(12), 125439 (2009).
[Crossref]

M. Brehm, T. Taubner, R. Hillenbrand, and F. Keilmann, “Infrared spectroscopic mapping of single nanoparticles and viruses at nanoscale resolution,” Nano Lett. 6(7), 1307–1310 (2006).
[Crossref] [PubMed]

Hollingsworth, J. A.

A. Peer, Z. Hu, A. Singh, J. A. Hollingsworth, R. Biswas, and H. Htoon, “Photoluminescence enhancement of CuInS2 quantum dots in solution coupled to plasmonic gold nanocup array,” Small 13(33), 1700660 (2017).
[Crossref] [PubMed]

Hone, J. C.

X. Yin, Z. Ye, D. A. Chenet, Y. Ye, K. O’Brien, J. C. Hone, and X. Zhang, “Edge nonlinear optics on a MoS2 atomic monolayer,” Science 344(6183), 488–490 (2014).
[Crossref] [PubMed]

Htoon, H.

A. Peer, Z. Hu, A. Singh, J. A. Hollingsworth, R. Biswas, and H. Htoon, “Photoluminescence enhancement of CuInS2 quantum dots in solution coupled to plasmonic gold nanocup array,” Small 13(33), 1700660 (2017).
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Hu, Z.

A. Peer, Z. Hu, A. Singh, J. A. Hollingsworth, R. Biswas, and H. Htoon, “Photoluminescence enhancement of CuInS2 quantum dots in solution coupled to plasmonic gold nanocup array,” Small 13(33), 1700660 (2017).
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K. Xu, L. Huang, Z. Zhang, J. Zhao, Z. Zhang, L. W. Snyman, and J. W. Swart, “Light emission from a poly-silicon device with carrier injection engineering,” Mater. Sci. Eng. B 231, 28–31 (2018).
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Huang, M.

S. Aksu, A. A. Yanik, R. Adato, A. Artar, M. Huang, and H. Altug, “High-throughput nanofabrication of infrared plasmonic nanoantenna arrays for vibrational nanospectroscopy,” Nano Lett. 10(7), 2511–2518 (2010).
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P. Alonso-González, P. Albella, F. Neubrech, C. Huck, J. Chen, F. Golmar, F. Casanova, L. E. Hueso, A. Pucci, J. Aizpurua, and R. Hillenbrand, “Experimental verification of the spectral shift between near- and far-field peak intensities of plasmonic infrared nanoantennas,” Phys. Rev. Lett. 110(20), 203902 (2013).
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Hueso, L. E.

P. Alonso-González, P. Albella, F. Neubrech, C. Huck, J. Chen, F. Golmar, F. Casanova, L. E. Hueso, A. Pucci, J. Aizpurua, and R. Hillenbrand, “Experimental verification of the spectral shift between near- and far-field peak intensities of plasmonic infrared nanoantennas,” Phys. Rev. Lett. 110(20), 203902 (2013).
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F. Huth, A. Govyadinov, S. Amarie, W. Nuansing, F. Keilmann, and R. Hillenbrand, “Nano-FTIR absorption spectroscopy of molecular fingerprints at 20 nm spatial resolution,” Nano Lett. 12(8), 3973–3978 (2012).
[Crossref] [PubMed]

Iwinski, E. G.

M. Wagner, Z. Fei, A. S. McLeod, A. S. Rodin, W. Bao, E. G. Iwinski, Z. Zhao, M. Goldflam, M. Liu, G. Dominguez, M. Thiemens, M. M. Fogler, A. H. Castro Neto, C. N. Lau, S. Amarie, F. Keilmann, and D. N. Basov, “Ultrafast and nanoscale plasmonic phenomena in exfoliated graphene revealed by infrared pump-probe nanoscopy,” Nano Lett. 14(2), 894–900 (2014).
[Crossref] [PubMed]

Kabashin, A. V.

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, and A. V. Zayats, “Plasmonic nanorod metamaterials for biosensing,” Nat. Mater. 8(11), 867–871 (2009).
[Crossref] [PubMed]

Kauranen, M.

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

M. Wagner, Z. Fei, A. S. McLeod, A. S. Rodin, W. Bao, E. G. Iwinski, Z. Zhao, M. Goldflam, M. Liu, G. Dominguez, M. Thiemens, M. M. Fogler, A. H. Castro Neto, C. N. Lau, S. Amarie, F. Keilmann, and D. N. Basov, “Ultrafast and nanoscale plasmonic phenomena in exfoliated graphene revealed by infrared pump-probe nanoscopy,” Nano Lett. 14(2), 894–900 (2014).
[Crossref] [PubMed]

F. Huth, A. Govyadinov, S. Amarie, W. Nuansing, F. Keilmann, and R. Hillenbrand, “Nano-FTIR absorption spectroscopy of molecular fingerprints at 20 nm spatial resolution,” Nano Lett. 12(8), 3973–3978 (2012).
[Crossref] [PubMed]

M. Brehm, T. Taubner, R. Hillenbrand, and F. Keilmann, “Infrared spectroscopic mapping of single nanoparticles and viruses at nanoscale resolution,” Nano Lett. 6(7), 1307–1310 (2006).
[Crossref] [PubMed]

Kildishev, A. V.

Z. Liu, A. Boltasseva, R. H. Pedersen, R. Bakker, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Plasmonic nanoantenna arrays for the visible,” Metamaterials (Amst.) 2(1), 45–51 (2008).
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Kramer, C.

M. Aeschlimann, T. Brixner, A. Fischer, C. Kramer, P. Melchior, W. Pfeiffer, C. Schneider, C. Strüber, P. Tuchscherer, and D. V. Voronine, “Coherent two-dimensional nanoscopy,” Science 333(6050), 1723–1726 (2011).
[Crossref] [PubMed]

Lau, C. N.

M. Wagner, Z. Fei, A. S. McLeod, A. S. Rodin, W. Bao, E. G. Iwinski, Z. Zhao, M. Goldflam, M. Liu, G. Dominguez, M. Thiemens, M. M. Fogler, A. H. Castro Neto, C. N. Lau, S. Amarie, F. Keilmann, and D. N. Basov, “Ultrafast and nanoscale plasmonic phenomena in exfoliated graphene revealed by infrared pump-probe nanoscopy,” Nano Lett. 14(2), 894–900 (2014).
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Liu, M.

M. Wagner, Z. Fei, A. S. McLeod, A. S. Rodin, W. Bao, E. G. Iwinski, Z. Zhao, M. Goldflam, M. Liu, G. Dominguez, M. Thiemens, M. M. Fogler, A. H. Castro Neto, C. N. Lau, S. Amarie, F. Keilmann, and D. N. Basov, “Ultrafast and nanoscale plasmonic phenomena in exfoliated graphene revealed by infrared pump-probe nanoscopy,” Nano Lett. 14(2), 894–900 (2014).
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Liu, Z.

Z. Liu, A. Boltasseva, R. H. Pedersen, R. Bakker, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Plasmonic nanoantenna arrays for the visible,” Metamaterials (Amst.) 2(1), 45–51 (2008).
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Lu, X.

Martin, M. C.

H. A. Bechtel, E. A. Muller, R. L. Olmon, M. C. Martin, and M. B. Raschke, “Ultrabroadband infrared nanospectroscopic imaging,” Proc. Natl. Acad. Sci. U.S.A. 111(20), 7191–7196 (2014).
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McLeod, A. S.

M. Wagner, Z. Fei, A. S. McLeod, A. S. Rodin, W. Bao, E. G. Iwinski, Z. Zhao, M. Goldflam, M. Liu, G. Dominguez, M. Thiemens, M. M. Fogler, A. H. Castro Neto, C. N. Lau, S. Amarie, F. Keilmann, and D. N. Basov, “Ultrafast and nanoscale plasmonic phenomena in exfoliated graphene revealed by infrared pump-probe nanoscopy,” Nano Lett. 14(2), 894–900 (2014).
[Crossref] [PubMed]

Melchior, P.

M. Aeschlimann, T. Brixner, A. Fischer, C. Kramer, P. Melchior, W. Pfeiffer, C. Schneider, C. Strüber, P. Tuchscherer, and D. V. Voronine, “Coherent two-dimensional nanoscopy,” Science 333(6050), 1723–1726 (2011).
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Muller, E. A.

H. A. Bechtel, E. A. Muller, R. L. Olmon, M. C. Martin, and M. B. Raschke, “Ultrabroadband infrared nanospectroscopic imaging,” Proc. Natl. Acad. Sci. U.S.A. 111(20), 7191–7196 (2014).
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Neubrech, F.

P. Alonso-González, P. Albella, F. Neubrech, C. Huck, J. Chen, F. Golmar, F. Casanova, L. E. Hueso, A. Pucci, J. Aizpurua, and R. Hillenbrand, “Experimental verification of the spectral shift between near- and far-field peak intensities of plasmonic infrared nanoantennas,” Phys. Rev. Lett. 110(20), 203902 (2013).
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J. Zuloaga and P. Nordlander, “On the energy shift between near-field and far-field peak intensities in localized plasmon systems,” Nano Lett. 11(3), 1280–1283 (2011).
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F. Huth, A. Govyadinov, S. Amarie, W. Nuansing, F. Keilmann, and R. Hillenbrand, “Nano-FTIR absorption spectroscopy of molecular fingerprints at 20 nm spatial resolution,” Nano Lett. 12(8), 3973–3978 (2012).
[Crossref] [PubMed]

O’Brien, K.

X. Yin, Z. Ye, D. A. Chenet, Y. Ye, K. O’Brien, J. C. Hone, and X. Zhang, “Edge nonlinear optics on a MoS2 atomic monolayer,” Science 344(6183), 488–490 (2014).
[Crossref] [PubMed]

Olmon, R. L.

H. A. Bechtel, E. A. Muller, R. L. Olmon, M. C. Martin, and M. B. Raschke, “Ultrabroadband infrared nanospectroscopic imaging,” Proc. Natl. Acad. Sci. U.S.A. 111(20), 7191–7196 (2014).
[Crossref] [PubMed]

Pastkovsky, S.

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, and A. V. Zayats, “Plasmonic nanorod metamaterials for biosensing,” Nat. Mater. 8(11), 867–871 (2009).
[Crossref] [PubMed]

Pedersen, R. H.

Z. Liu, A. Boltasseva, R. H. Pedersen, R. Bakker, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Plasmonic nanoantenna arrays for the visible,” Metamaterials (Amst.) 2(1), 45–51 (2008).
[Crossref]

Peer, A.

A. Peer, Z. Hu, A. Singh, J. A. Hollingsworth, R. Biswas, and H. Htoon, “Photoluminescence enhancement of CuInS2 quantum dots in solution coupled to plasmonic gold nanocup array,” Small 13(33), 1700660 (2017).
[Crossref] [PubMed]

Pfeiffer, W.

M. Aeschlimann, T. Brixner, A. Fischer, C. Kramer, P. Melchior, W. Pfeiffer, C. Schneider, C. Strüber, P. Tuchscherer, and D. V. Voronine, “Coherent two-dimensional nanoscopy,” Science 333(6050), 1723–1726 (2011).
[Crossref] [PubMed]

Podolskiy, V. A.

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, and A. V. Zayats, “Plasmonic nanorod metamaterials for biosensing,” Nat. Mater. 8(11), 867–871 (2009).
[Crossref] [PubMed]

Pollard, R.

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, and A. V. Zayats, “Plasmonic nanorod metamaterials for biosensing,” Nat. Mater. 8(11), 867–871 (2009).
[Crossref] [PubMed]

Pucci, A.

P. Alonso-González, P. Albella, F. Neubrech, C. Huck, J. Chen, F. Golmar, F. Casanova, L. E. Hueso, A. Pucci, J. Aizpurua, and R. Hillenbrand, “Experimental verification of the spectral shift between near- and far-field peak intensities of plasmonic infrared nanoantennas,” Phys. Rev. Lett. 110(20), 203902 (2013).
[Crossref] [PubMed]

Raschke, M. B.

H. A. Bechtel, E. A. Muller, R. L. Olmon, M. C. Martin, and M. B. Raschke, “Ultrabroadband infrared nanospectroscopic imaging,” Proc. Natl. Acad. Sci. U.S.A. 111(20), 7191–7196 (2014).
[Crossref] [PubMed]

Rodin, A. S.

M. Wagner, Z. Fei, A. S. McLeod, A. S. Rodin, W. Bao, E. G. Iwinski, Z. Zhao, M. Goldflam, M. Liu, G. Dominguez, M. Thiemens, M. M. Fogler, A. H. Castro Neto, C. N. Lau, S. Amarie, F. Keilmann, and D. N. Basov, “Ultrafast and nanoscale plasmonic phenomena in exfoliated graphene revealed by infrared pump-probe nanoscopy,” Nano Lett. 14(2), 894–900 (2014).
[Crossref] [PubMed]

Romero, I.

A. García-Etxarri, I. Romero, F. J. García de Abajo, R. Hillenbrand, and J. Aizpurua, “Influence of the tip in near-field imaging of nanoparticle plasmonic modes: Weak and strong coupling regimes,” Phys. Rev. B Condens. Matter Mater. Phys. 79(12), 125439 (2009).
[Crossref]

Salandrino, A.

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B Condens. Matter Mater. Phys. 75(15), 155410 (2007).
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Schneider, C.

M. Aeschlimann, T. Brixner, A. Fischer, C. Kramer, P. Melchior, W. Pfeiffer, C. Schneider, C. Strüber, P. Tuchscherer, and D. V. Voronine, “Coherent two-dimensional nanoscopy,” Science 333(6050), 1723–1726 (2011).
[Crossref] [PubMed]

Shalaev, V. M.

Z. Liu, A. Boltasseva, R. H. Pedersen, R. Bakker, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Plasmonic nanoantenna arrays for the visible,” Metamaterials (Amst.) 2(1), 45–51 (2008).
[Crossref]

Silveirinha, M. G.

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B Condens. Matter Mater. Phys. 75(15), 155410 (2007).
[Crossref]

Singh, A.

A. Peer, Z. Hu, A. Singh, J. A. Hollingsworth, R. Biswas, and H. Htoon, “Photoluminescence enhancement of CuInS2 quantum dots in solution coupled to plasmonic gold nanocup array,” Small 13(33), 1700660 (2017).
[Crossref] [PubMed]

Snyman, L. W.

K. Xu, L. Huang, Z. Zhang, J. Zhao, Z. Zhang, L. W. Snyman, and J. W. Swart, “Light emission from a poly-silicon device with carrier injection engineering,” Mater. Sci. Eng. B 231, 28–31 (2018).
[Crossref]

L. W. Snyman, M. du Plessis, and E. Bellotti, “Photonic transitions (1.4 eV-2.8 eV) in silicon p+np+ injection-avalanche CMOS LEDs as function of depletion layer profiling and defect engineering,” IEEE J. Quantum Electron. 46(6), 906–919 (2010).
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Stockman, M. I.

M. I. Stockman, “Ultrafast nanoplasmonics under coherent control,” New J. Phys. 10(2), 025031 (2008).
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Strüber, C.

M. Aeschlimann, T. Brixner, A. Fischer, C. Kramer, P. Melchior, W. Pfeiffer, C. Schneider, C. Strüber, P. Tuchscherer, and D. V. Voronine, “Coherent two-dimensional nanoscopy,” Science 333(6050), 1723–1726 (2011).
[Crossref] [PubMed]

Swart, J. W.

K. Xu, L. Huang, Z. Zhang, J. Zhao, Z. Zhang, L. W. Snyman, and J. W. Swart, “Light emission from a poly-silicon device with carrier injection engineering,” Mater. Sci. Eng. B 231, 28–31 (2018).
[Crossref]

Taubner, T.

M. Brehm, T. Taubner, R. Hillenbrand, and F. Keilmann, “Infrared spectroscopic mapping of single nanoparticles and viruses at nanoscale resolution,” Nano Lett. 6(7), 1307–1310 (2006).
[Crossref] [PubMed]

Thiemens, M.

M. Wagner, Z. Fei, A. S. McLeod, A. S. Rodin, W. Bao, E. G. Iwinski, Z. Zhao, M. Goldflam, M. Liu, G. Dominguez, M. Thiemens, M. M. Fogler, A. H. Castro Neto, C. N. Lau, S. Amarie, F. Keilmann, and D. N. Basov, “Ultrafast and nanoscale plasmonic phenomena in exfoliated graphene revealed by infrared pump-probe nanoscopy,” Nano Lett. 14(2), 894–900 (2014).
[Crossref] [PubMed]

Tuchscherer, P.

M. Aeschlimann, T. Brixner, A. Fischer, C. Kramer, P. Melchior, W. Pfeiffer, C. Schneider, C. Strüber, P. Tuchscherer, and D. V. Voronine, “Coherent two-dimensional nanoscopy,” Science 333(6050), 1723–1726 (2011).
[Crossref] [PubMed]

Ulin-Avila, E.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
[Crossref] [PubMed]

Valentine, J.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
[Crossref] [PubMed]

Van Dorpe, P.

J. Ye and P. Van Dorpe, “Improvement of figure of merit for gold nanobar array plasmonic sensors,” Plasmonics 6(4), 665–671 (2011).
[Crossref]

Voronine, D. V.

M. Aeschlimann, T. Brixner, A. Fischer, C. Kramer, P. Melchior, W. Pfeiffer, C. Schneider, C. Strüber, P. Tuchscherer, and D. V. Voronine, “Coherent two-dimensional nanoscopy,” Science 333(6050), 1723–1726 (2011).
[Crossref] [PubMed]

Wagner, M.

M. Wagner, Z. Fei, A. S. McLeod, A. S. Rodin, W. Bao, E. G. Iwinski, Z. Zhao, M. Goldflam, M. Liu, G. Dominguez, M. Thiemens, M. M. Fogler, A. H. Castro Neto, C. N. Lau, S. Amarie, F. Keilmann, and D. N. Basov, “Ultrafast and nanoscale plasmonic phenomena in exfoliated graphene revealed by infrared pump-probe nanoscopy,” Nano Lett. 14(2), 894–900 (2014).
[Crossref] [PubMed]

Wurtz, G. A.

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, and A. V. Zayats, “Plasmonic nanorod metamaterials for biosensing,” Nat. Mater. 8(11), 867–871 (2009).
[Crossref] [PubMed]

Xu, K.

K. Xu, L. Huang, Z. Zhang, J. Zhao, Z. Zhang, L. W. Snyman, and J. W. Swart, “Light emission from a poly-silicon device with carrier injection engineering,” Mater. Sci. Eng. B 231, 28–31 (2018).
[Crossref]

Yanik, A. A.

S. Aksu, A. A. Yanik, R. Adato, A. Artar, M. Huang, and H. Altug, “High-throughput nanofabrication of infrared plasmonic nanoantenna arrays for vibrational nanospectroscopy,” Nano Lett. 10(7), 2511–2518 (2010).
[Crossref] [PubMed]

Ye, J.

J. Ye and P. Van Dorpe, “Improvement of figure of merit for gold nanobar array plasmonic sensors,” Plasmonics 6(4), 665–671 (2011).
[Crossref]

Ye, Y.

X. Yin, Z. Ye, D. A. Chenet, Y. Ye, K. O’Brien, J. C. Hone, and X. Zhang, “Edge nonlinear optics on a MoS2 atomic monolayer,” Science 344(6183), 488–490 (2014).
[Crossref] [PubMed]

Ye, Z.

X. Yin, Z. Ye, D. A. Chenet, Y. Ye, K. O’Brien, J. C. Hone, and X. Zhang, “Edge nonlinear optics on a MoS2 atomic monolayer,” Science 344(6183), 488–490 (2014).
[Crossref] [PubMed]

Yin, X.

X. Yin, Z. Ye, D. A. Chenet, Y. Ye, K. O’Brien, J. C. Hone, and X. Zhang, “Edge nonlinear optics on a MoS2 atomic monolayer,” Science 344(6183), 488–490 (2014).
[Crossref] [PubMed]

Zayats, A. V.

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

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, and A. V. Zayats, “Plasmonic nanorod metamaterials for biosensing,” Nat. Mater. 8(11), 867–871 (2009).
[Crossref] [PubMed]

Zentgraf, T.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
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Supplementary Material (1)

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» Visualization 1       Visualization

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Figures (4)

Fig. 1
Fig. 1 Broadband VIS-NIR nano-FTIR characterization of a plasmonic nano-antenna. (a) Schematic of scattering-Scanning Near Field Microscope tip positioned over nanostructures. The nano-antennas are spaced 500 nm apart from eachother. Det: detector, PB: Parabolic Mirror. (b) AFM image of a gold nanoparticle on ITO covered glass. The nanoparticle’s dimensions are 140 × 60 × 40 nm3. Scale bar is 40 nm. (c) Near-field signal of the nanoparticle due to excitation with 660-1050 nm pulse. The double-arrow indicates the polarization of the exciting pulse. The image was acquired with white-light imaging, exhibiting the collective spectral response of the near-field. (d) Near-field spectra taken at two positions, a and b. Point a, shows an enhanced scattered optical signal at 726 ± 10 nm (left y-axis). Point b does not show any spectral feature, as expected. The far-field transmission spectrum, which exhibits a resonance at 702 ± 4 nm, can be seen at red (right y-axis). Spectra were normalized relatively to the background.
Fig. 2
Fig. 2 Spatio-spectral near-field mapping of plasmonic nanostructures. (a) SEM image of three different gold nano-antennas. Nano-antennas length, from left to right is 130nm, 150nm and 170nm. Scale bar is 120 nm. (b) Two-dimensional, 2×0.2 μ m 2 , nano-FTIR scan of the three nano-antennas. Images at different wavelengths were then constructed. A clear resonance red-shift is observed due to the lengthening of the nano-antenna. (Visualization 1) (c) Images at three selected wavelengths, in each a different nano-antenna is seen on resonance. White scale bar is 200 nm.
Fig. 3
Fig. 3 Hyperspectral near-field imaging of a nano-antenna. (a) Left: AFM image of a gold nanoparticle, with dimensions 60 × 40 × 380 nm3. Scale bar is 100 nm. Right: Near-field imaging of the nano-antenna, using 1580 nm CW excitation. (b) Left: FDTD simulation of a nanoparticle on glass, with light incident at 45°. Right: Simulated transmission. Shaded region is the spectrally-accessible region by our ultra broadband pulse. (c) Simulated (up) and experimental (bottom) near-field imaging of the amplitude and phase of the nanoparticle, at 890 nm. (d) Broadband experimental near-field imaging of the nano-antenna, due to the femtosecond pulse.
Fig. 4
Fig. 4 Experimental and simulated hyper-spectral near-field response of an elongated nano-antenna. (a) Experimental amplitude (a.u). (b) Experimental phase. (c) Simulated amplitude. (d) Simulated phase.

Equations (1)

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ω 0 NF = ω 0 FF 1 1 2 Q 2

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