Abstract

We present and investigate a novel approach towards broad-bandwidth near-field scanning optical spectroscopy based on an in-line interferometer for homodyne mixing of the near field and a reference field. In scattering-type scanning near-field optical spectroscopy, the near-field signal is usually obscured by a large amount of unwanted background scattering from the probe shaft and the sample. Here we increase the light reflected from the sample by a semi-transparent gold layer and use it as a broad-bandwidth, phase-stable reference field to amplify the near-field signal in the visible and near-infrared spectral range. We experimentally demonstrate that this efficiently suppresses the unwanted background signal in monochromatic near-field measurements. For rapid acquisition of complete broad-bandwidth spectra we employ a monochromator and a fast line camera. Using this fast acquisition of spectra and the in-line interferometer we demonstrate the measurement of pure near-field spectra. The experimental observations are quantitatively explained by analytical expressions for the measured optical signals, based on Fourier decomposition of background and near field. The theoretical model and in-line interferometer together form an important step towards broad-bandwidth near-field scanning optical spectroscopy.

© 2017 Optical Society of America

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    [Crossref] [PubMed]
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  5. A. Anderson, K. S. Deryckx, X. G. Xu, G. Steinmeyer, and M. B. Raschke, “Few-femtosecond plasmon dephasing of a single metallic nanostructure from optical response function reconstruction by interferometric frequency resolved optical gating,” Nano Lett. 10(7), 2519–2524 (2010).
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  6. T. Guenther, C. Lienau, T. Elsaesser, M. Glanemann, V. M. Axt, T. Kuhn, S. Eshlaghi, and A. D. Wieck, “Coherent nonlinear optical response of single quantum dots studied by ultrafast near-field spectroscopy,” Phys. Rev. Lett. 89(5), 057401 (2002).
    [Crossref] [PubMed]
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  8. E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, and R. L. Kostelak, “Breaking the diffraction barrier: optical microscopy on a nanometric scale,” Science 251(5000), 1468–1470 (1991).
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  9. W. E. Moerner, T. Plakhotnik, T. Irngartinger, U. P. Wild, D. W. Pohl, and B. Hecht, “Near-field optical spectroscopy of individual molecules in solids,” Phys. Rev. Lett. 73(20), 2764–2767 (1994).
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  14. S. F. Becker, M. Esmann, K. Yoo, P. Groß, R. Vogelgesang, N. Park, and C. Lienau, “Gap-Plasmon-Enhanced Nanofocusing Near-Field Microscopy,” ACS Photonics 3(2), 223–232 (2016).
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    [Crossref] [PubMed]
  21. M. Esslinger, J. Dorfmüller, W. Khunsin, R. Vogelgesang, and K. Kern, “Background-free imaging of plasmonic structures with cross-polarized apertureless scanning near-field optical microscopy,” Rev. Sci. Instrum. 83(3), 033704 (2012).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]

2016 (3)

S. F. Becker, M. Esmann, K. Yoo, P. Groß, R. Vogelgesang, N. Park, and C. Lienau, “Gap-Plasmon-Enhanced Nanofocusing Near-Field Microscopy,” ACS Photonics 3(2), 223–232 (2016).
[Crossref]

V. Kravtsov, R. Ulbricht, J. M. Atkin, and M. B. Raschke, “Plasmonic nanofocused four-wave mixing for femtosecond near-field imaging,” Nat. Nanotechnol. 11(5), 459–464 (2016).
[Crossref] [PubMed]

R. Chikkaraddy, B. de Nijs, F. Benz, S. J. Barrow, O. A. Scherman, E. Rosta, A. Demetriadou, P. Fox, O. Hess, and J. J. Baumberg, “Single-molecule strong coupling at room temperature in plasmonic nanocavities,” Nature 535(7610), 127–130 (2016).
[Crossref] [PubMed]

2014 (1)

S. Yampolsky, D. A. Fishman, S. Dey, E. Hulkko, M. Banik, E. O. Potma, and V. A. Apkarian, “Seeing a single molecule vibrate through time-resolved coherent anti-Stokes Raman scattering,” Nat. Photonics 8(8), 650–656 (2014).
[Crossref]

2013 (4)

M. Esmann, S. F. Becker, B. B. da Cunha, J. H. Brauer, R. Vogelgesang, P. Groß, and C. Lienau, “k-space imaging of the eigenmodes of sharp gold tapers for scanning near-field optical microscopy,” Beilstein J. Nanotechnol. 4(1), 603–610 (2013).
[Crossref] [PubMed]

R. Hildner, D. Brinks, J. B. Nieder, R. J. Cogdell, and N. F. van Hulst, “Quantum coherent energy transfer over varying pathways in single light-harvesting complexes,” Science 340(6139), 1448–1451 (2013).
[Crossref] [PubMed]

W. Bao, M. Staffaroni, J. Bokor, M. B. Salmeron, E. Yablonovitch, S. Cabrini, A. Weber-Bargioni, and P. J. Schuck, “Plasmonic near-field probes: a comparison of the campanile geometry with other sharp tips,” Opt. Express 21(7), 8166–8176 (2013).
[Crossref] [PubMed]

R. Zhang, Y. Zhang, Z. C. Dong, S. Jiang, C. Zhang, L. G. Chen, L. Zhang, Y. Liao, J. Aizpurua, Y. Luo, J. L. Yang, and J. G. Hou, “Chemical mapping of a single molecule by plasmon-enhanced Raman scattering,” Nature 498(7452), 82–86 (2013).
[Crossref] [PubMed]

2012 (4)

S. Schmidt, B. Piglosiewicz, D. Sadiq, J. Shirdel, J. S. Lee, P. Vasa, N. Park, D.-S. Kim, and C. Lienau, “Adiabatic nanofocusing on ultrasmooth single-crystalline gold tapers creates a 10-nm-sized light source with few-cycle time resolution,” ACS Nano 6(7), 6040–6048 (2012).
[Crossref] [PubMed]

M. Esslinger, J. Dorfmüller, W. Khunsin, R. Vogelgesang, and K. Kern, “Background-free imaging of plasmonic structures with cross-polarized apertureless scanning near-field optical microscopy,” Rev. Sci. Instrum. 83(3), 033704 (2012).
[Crossref] [PubMed]

W. Bao, M. Melli, N. Caselli, F. Riboli, D. S. Wiersma, M. Staffaroni, H. Choo, D. F. Ogletree, S. Aloni, J. Bokor, S. Cabrini, F. Intonti, M. B. Salmeron, E. Yablonovitch, P. J. Schuck, and A. Weber-Bargioni, “Mapping local charge recombination heterogeneity by multidimensional nanospectroscopic imaging,” Science 338(6112), 1317–1321 (2012).
[Crossref] [PubMed]

S. Berweger, J. M. Atkin, R. L. Olmon, and M. B. Raschke, “Light on the tip of a needle: plasmonic nanofocusing for spectroscopy on the nanoscale,” J. Phys. Chem. Lett. 3(7), 945–952 (2012).
[Crossref] [PubMed]

2010 (1)

A. Anderson, K. S. Deryckx, X. G. Xu, G. Steinmeyer, and M. B. Raschke, “Few-femtosecond plasmon dephasing of a single metallic nanostructure from optical response function reconstruction by interferometric frequency resolved optical gating,” Nano Lett. 10(7), 2519–2524 (2010).
[Crossref] [PubMed]

2008 (1)

E. Bailo and V. Deckert, “Tip-enhanced Raman spectroscopy of single RNA strands: towards a novel direct-sequencing method,” Angew. Chem. Int. Ed. Engl. 47(9), 1658–1661 (2008).
[Crossref] [PubMed]

2006 (3)

N. Ocelic, A. Huber, and R. Hillenbrand, “Pseudoheterodyne detection for background-free near-field spectroscopy,” Appl. Phys. Lett. 89(10), 101124 (2006).
[Crossref]

L. Novotny and S. J. Stranick, “Near-field optical microscopy and spectroscopy with pointed probes,” Annu. Rev. Phys. Chem. 57(1), 303–331 (2006).
[Crossref] [PubMed]

P. Anger, P. Bharadwaj, and L. Novotny, “Enhancement and quenching of single-molecule fluorescence,” Phys. Rev. Lett. 96(11), 113002 (2006).
[Crossref] [PubMed]

2004 (2)

J. M. Gerton, L. A. Wade, G. A. Lessard, Z. Ma, and S. R. Quake, “Tip-enhanced fluorescence microscopy at 10 nanometer resolution,” Phys. Rev. Lett. 93(18), 180801 (2004).
[Crossref] [PubMed]

M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett. 93(13), 137404 (2004).
[Crossref] [PubMed]

2003 (2)

T. Taubner, R. Hillenbrand, and F. Keilmann, “Performance of visible and mid-infrared scattering-type near-field optical microscopes,” J. Microsc. 210(3), 311–314 (2003).
[Crossref] [PubMed]

M. B. Raschke and C. Lienau, “Apertureless near-field optical microscopy: Tip–sample coupling in elastic light scattering,” Appl. Phys. Lett. 83(24), 5089–5091 (2003).
[Crossref]

2002 (1)

T. Guenther, C. Lienau, T. Elsaesser, M. Glanemann, V. M. Axt, T. Kuhn, S. Eshlaghi, and A. D. Wieck, “Coherent nonlinear optical response of single quantum dots studied by ultrafast near-field spectroscopy,” Phys. Rev. Lett. 89(5), 057401 (2002).
[Crossref] [PubMed]

2001 (1)

R. Hillenbrand, B. Knoll, and F. Keilmann, “Pure optical contrast in scattering-type scanning near-field microscopy,” J. Microsc. 202(1), 77–83 (2001).
[Crossref] [PubMed]

2000 (5)

B. Knoll and F. Keilmann, “Enhanced dielectric contrast in scattering-type scanning near-field optical microscopy,” Opt. Commun. 182(4–6), 321–328 (2000).
[Crossref]

A. J. Babadjanyan, N. L. Margaryan, and K. V. Nerkararyan, “Superfocusing of surface polaritons in the conical structure,” J. Appl. Phys. 87(8), 3785–3788 (2000).
[Crossref]

R. Hillenbrand and F. Keilmann, “Complex optical constants on a subwavelength scale,” Phys. Rev. Lett. 85(14), 3029–3032 (2000).
[Crossref] [PubMed]

Y. Sasaki and H. Sasaki, “Heterodyne detection for the extraction of the probe-scattering signal in scattering-type scanning near-field optical microscope,” Jpn. J. Appl. Phys. 39(4A), L321–L323 (2000).
[Crossref]

A. V. Zayats and V. Sandoghdar, “Apertureless scanning near-field second-harmonic microscopy,” Opt. Commun. 178(1–3), 245–249 (2000).
[Crossref]

1995 (1)

1994 (1)

W. E. Moerner, T. Plakhotnik, T. Irngartinger, U. P. Wild, D. W. Pohl, and B. Hecht, “Near-field optical spectroscopy of individual molecules in solids,” Phys. Rev. Lett. 73(20), 2764–2767 (1994).
[Crossref] [PubMed]

1991 (1)

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, and R. L. Kostelak, “Breaking the diffraction barrier: optical microscopy on a nanometric scale,” Science 251(5000), 1468–1470 (1991).
[Crossref] [PubMed]

1972 (1)

E. A. Ash and G. Nicholls, “Super-resolution aperture scanning microscope,” Nature 237(5357), 510–512 (1972).
[Crossref] [PubMed]

Aizpurua, J.

R. Zhang, Y. Zhang, Z. C. Dong, S. Jiang, C. Zhang, L. G. Chen, L. Zhang, Y. Liao, J. Aizpurua, Y. Luo, J. L. Yang, and J. G. Hou, “Chemical mapping of a single molecule by plasmon-enhanced Raman scattering,” Nature 498(7452), 82–86 (2013).
[Crossref] [PubMed]

Aloni, S.

W. Bao, M. Melli, N. Caselli, F. Riboli, D. S. Wiersma, M. Staffaroni, H. Choo, D. F. Ogletree, S. Aloni, J. Bokor, S. Cabrini, F. Intonti, M. B. Salmeron, E. Yablonovitch, P. J. Schuck, and A. Weber-Bargioni, “Mapping local charge recombination heterogeneity by multidimensional nanospectroscopic imaging,” Science 338(6112), 1317–1321 (2012).
[Crossref] [PubMed]

Anderson, A.

A. Anderson, K. S. Deryckx, X. G. Xu, G. Steinmeyer, and M. B. Raschke, “Few-femtosecond plasmon dephasing of a single metallic nanostructure from optical response function reconstruction by interferometric frequency resolved optical gating,” Nano Lett. 10(7), 2519–2524 (2010).
[Crossref] [PubMed]

Anger, P.

P. Anger, P. Bharadwaj, and L. Novotny, “Enhancement and quenching of single-molecule fluorescence,” Phys. Rev. Lett. 96(11), 113002 (2006).
[Crossref] [PubMed]

Apkarian, V. A.

S. Yampolsky, D. A. Fishman, S. Dey, E. Hulkko, M. Banik, E. O. Potma, and V. A. Apkarian, “Seeing a single molecule vibrate through time-resolved coherent anti-Stokes Raman scattering,” Nat. Photonics 8(8), 650–656 (2014).
[Crossref]

Ash, E. A.

E. A. Ash and G. Nicholls, “Super-resolution aperture scanning microscope,” Nature 237(5357), 510–512 (1972).
[Crossref] [PubMed]

Atkin, J. M.

V. Kravtsov, R. Ulbricht, J. M. Atkin, and M. B. Raschke, “Plasmonic nanofocused four-wave mixing for femtosecond near-field imaging,” Nat. Nanotechnol. 11(5), 459–464 (2016).
[Crossref] [PubMed]

S. Berweger, J. M. Atkin, R. L. Olmon, and M. B. Raschke, “Light on the tip of a needle: plasmonic nanofocusing for spectroscopy on the nanoscale,” J. Phys. Chem. Lett. 3(7), 945–952 (2012).
[Crossref] [PubMed]

Axt, V. M.

T. Guenther, C. Lienau, T. Elsaesser, M. Glanemann, V. M. Axt, T. Kuhn, S. Eshlaghi, and A. D. Wieck, “Coherent nonlinear optical response of single quantum dots studied by ultrafast near-field spectroscopy,” Phys. Rev. Lett. 89(5), 057401 (2002).
[Crossref] [PubMed]

Babadjanyan, A. J.

A. J. Babadjanyan, N. L. Margaryan, and K. V. Nerkararyan, “Superfocusing of surface polaritons in the conical structure,” J. Appl. Phys. 87(8), 3785–3788 (2000).
[Crossref]

Bailo, E.

E. Bailo and V. Deckert, “Tip-enhanced Raman spectroscopy of single RNA strands: towards a novel direct-sequencing method,” Angew. Chem. Int. Ed. Engl. 47(9), 1658–1661 (2008).
[Crossref] [PubMed]

Banik, M.

S. Yampolsky, D. A. Fishman, S. Dey, E. Hulkko, M. Banik, E. O. Potma, and V. A. Apkarian, “Seeing a single molecule vibrate through time-resolved coherent anti-Stokes Raman scattering,” Nat. Photonics 8(8), 650–656 (2014).
[Crossref]

Bao, W.

W. Bao, M. Staffaroni, J. Bokor, M. B. Salmeron, E. Yablonovitch, S. Cabrini, A. Weber-Bargioni, and P. J. Schuck, “Plasmonic near-field probes: a comparison of the campanile geometry with other sharp tips,” Opt. Express 21(7), 8166–8176 (2013).
[Crossref] [PubMed]

W. Bao, M. Melli, N. Caselli, F. Riboli, D. S. Wiersma, M. Staffaroni, H. Choo, D. F. Ogletree, S. Aloni, J. Bokor, S. Cabrini, F. Intonti, M. B. Salmeron, E. Yablonovitch, P. J. Schuck, and A. Weber-Bargioni, “Mapping local charge recombination heterogeneity by multidimensional nanospectroscopic imaging,” Science 338(6112), 1317–1321 (2012).
[Crossref] [PubMed]

Barrow, S. J.

R. Chikkaraddy, B. de Nijs, F. Benz, S. J. Barrow, O. A. Scherman, E. Rosta, A. Demetriadou, P. Fox, O. Hess, and J. J. Baumberg, “Single-molecule strong coupling at room temperature in plasmonic nanocavities,” Nature 535(7610), 127–130 (2016).
[Crossref] [PubMed]

Baumberg, J. J.

R. Chikkaraddy, B. de Nijs, F. Benz, S. J. Barrow, O. A. Scherman, E. Rosta, A. Demetriadou, P. Fox, O. Hess, and J. J. Baumberg, “Single-molecule strong coupling at room temperature in plasmonic nanocavities,” Nature 535(7610), 127–130 (2016).
[Crossref] [PubMed]

Becker, S. F.

S. F. Becker, M. Esmann, K. Yoo, P. Groß, R. Vogelgesang, N. Park, and C. Lienau, “Gap-Plasmon-Enhanced Nanofocusing Near-Field Microscopy,” ACS Photonics 3(2), 223–232 (2016).
[Crossref]

M. Esmann, S. F. Becker, B. B. da Cunha, J. H. Brauer, R. Vogelgesang, P. Groß, and C. Lienau, “k-space imaging of the eigenmodes of sharp gold tapers for scanning near-field optical microscopy,” Beilstein J. Nanotechnol. 4(1), 603–610 (2013).
[Crossref] [PubMed]

Benz, F.

R. Chikkaraddy, B. de Nijs, F. Benz, S. J. Barrow, O. A. Scherman, E. Rosta, A. Demetriadou, P. Fox, O. Hess, and J. J. Baumberg, “Single-molecule strong coupling at room temperature in plasmonic nanocavities,” Nature 535(7610), 127–130 (2016).
[Crossref] [PubMed]

Berweger, S.

S. Berweger, J. M. Atkin, R. L. Olmon, and M. B. Raschke, “Light on the tip of a needle: plasmonic nanofocusing for spectroscopy on the nanoscale,” J. Phys. Chem. Lett. 3(7), 945–952 (2012).
[Crossref] [PubMed]

Betzig, E.

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, and R. L. Kostelak, “Breaking the diffraction barrier: optical microscopy on a nanometric scale,” Science 251(5000), 1468–1470 (1991).
[Crossref] [PubMed]

Bharadwaj, P.

P. Anger, P. Bharadwaj, and L. Novotny, “Enhancement and quenching of single-molecule fluorescence,” Phys. Rev. Lett. 96(11), 113002 (2006).
[Crossref] [PubMed]

Bokor, J.

W. Bao, M. Staffaroni, J. Bokor, M. B. Salmeron, E. Yablonovitch, S. Cabrini, A. Weber-Bargioni, and P. J. Schuck, “Plasmonic near-field probes: a comparison of the campanile geometry with other sharp tips,” Opt. Express 21(7), 8166–8176 (2013).
[Crossref] [PubMed]

W. Bao, M. Melli, N. Caselli, F. Riboli, D. S. Wiersma, M. Staffaroni, H. Choo, D. F. Ogletree, S. Aloni, J. Bokor, S. Cabrini, F. Intonti, M. B. Salmeron, E. Yablonovitch, P. J. Schuck, and A. Weber-Bargioni, “Mapping local charge recombination heterogeneity by multidimensional nanospectroscopic imaging,” Science 338(6112), 1317–1321 (2012).
[Crossref] [PubMed]

Brauer, J. H.

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S. Berweger, J. M. Atkin, R. L. Olmon, and M. B. Raschke, “Light on the tip of a needle: plasmonic nanofocusing for spectroscopy on the nanoscale,” J. Phys. Chem. Lett. 3(7), 945–952 (2012).
[Crossref] [PubMed]

A. Anderson, K. S. Deryckx, X. G. Xu, G. Steinmeyer, and M. B. Raschke, “Few-femtosecond plasmon dephasing of a single metallic nanostructure from optical response function reconstruction by interferometric frequency resolved optical gating,” Nano Lett. 10(7), 2519–2524 (2010).
[Crossref] [PubMed]

M. B. Raschke and C. Lienau, “Apertureless near-field optical microscopy: Tip–sample coupling in elastic light scattering,” Appl. Phys. Lett. 83(24), 5089–5091 (2003).
[Crossref]

Riboli, F.

W. Bao, M. Melli, N. Caselli, F. Riboli, D. S. Wiersma, M. Staffaroni, H. Choo, D. F. Ogletree, S. Aloni, J. Bokor, S. Cabrini, F. Intonti, M. B. Salmeron, E. Yablonovitch, P. J. Schuck, and A. Weber-Bargioni, “Mapping local charge recombination heterogeneity by multidimensional nanospectroscopic imaging,” Science 338(6112), 1317–1321 (2012).
[Crossref] [PubMed]

Rosta, E.

R. Chikkaraddy, B. de Nijs, F. Benz, S. J. Barrow, O. A. Scherman, E. Rosta, A. Demetriadou, P. Fox, O. Hess, and J. J. Baumberg, “Single-molecule strong coupling at room temperature in plasmonic nanocavities,” Nature 535(7610), 127–130 (2016).
[Crossref] [PubMed]

Sadiq, D.

S. Schmidt, B. Piglosiewicz, D. Sadiq, J. Shirdel, J. S. Lee, P. Vasa, N. Park, D.-S. Kim, and C. Lienau, “Adiabatic nanofocusing on ultrasmooth single-crystalline gold tapers creates a 10-nm-sized light source with few-cycle time resolution,” ACS Nano 6(7), 6040–6048 (2012).
[Crossref] [PubMed]

Salmeron, M. B.

W. Bao, M. Staffaroni, J. Bokor, M. B. Salmeron, E. Yablonovitch, S. Cabrini, A. Weber-Bargioni, and P. J. Schuck, “Plasmonic near-field probes: a comparison of the campanile geometry with other sharp tips,” Opt. Express 21(7), 8166–8176 (2013).
[Crossref] [PubMed]

W. Bao, M. Melli, N. Caselli, F. Riboli, D. S. Wiersma, M. Staffaroni, H. Choo, D. F. Ogletree, S. Aloni, J. Bokor, S. Cabrini, F. Intonti, M. B. Salmeron, E. Yablonovitch, P. J. Schuck, and A. Weber-Bargioni, “Mapping local charge recombination heterogeneity by multidimensional nanospectroscopic imaging,” Science 338(6112), 1317–1321 (2012).
[Crossref] [PubMed]

Sandoghdar, V.

A. V. Zayats and V. Sandoghdar, “Apertureless scanning near-field second-harmonic microscopy,” Opt. Commun. 178(1–3), 245–249 (2000).
[Crossref]

Sasaki, H.

Y. Sasaki and H. Sasaki, “Heterodyne detection for the extraction of the probe-scattering signal in scattering-type scanning near-field optical microscope,” Jpn. J. Appl. Phys. 39(4A), L321–L323 (2000).
[Crossref]

Sasaki, Y.

Y. Sasaki and H. Sasaki, “Heterodyne detection for the extraction of the probe-scattering signal in scattering-type scanning near-field optical microscope,” Jpn. J. Appl. Phys. 39(4A), L321–L323 (2000).
[Crossref]

Scherman, O. A.

R. Chikkaraddy, B. de Nijs, F. Benz, S. J. Barrow, O. A. Scherman, E. Rosta, A. Demetriadou, P. Fox, O. Hess, and J. J. Baumberg, “Single-molecule strong coupling at room temperature in plasmonic nanocavities,” Nature 535(7610), 127–130 (2016).
[Crossref] [PubMed]

Schmidt, S.

S. Schmidt, B. Piglosiewicz, D. Sadiq, J. Shirdel, J. S. Lee, P. Vasa, N. Park, D.-S. Kim, and C. Lienau, “Adiabatic nanofocusing on ultrasmooth single-crystalline gold tapers creates a 10-nm-sized light source with few-cycle time resolution,” ACS Nano 6(7), 6040–6048 (2012).
[Crossref] [PubMed]

Schuck, P. J.

W. Bao, M. Staffaroni, J. Bokor, M. B. Salmeron, E. Yablonovitch, S. Cabrini, A. Weber-Bargioni, and P. J. Schuck, “Plasmonic near-field probes: a comparison of the campanile geometry with other sharp tips,” Opt. Express 21(7), 8166–8176 (2013).
[Crossref] [PubMed]

W. Bao, M. Melli, N. Caselli, F. Riboli, D. S. Wiersma, M. Staffaroni, H. Choo, D. F. Ogletree, S. Aloni, J. Bokor, S. Cabrini, F. Intonti, M. B. Salmeron, E. Yablonovitch, P. J. Schuck, and A. Weber-Bargioni, “Mapping local charge recombination heterogeneity by multidimensional nanospectroscopic imaging,” Science 338(6112), 1317–1321 (2012).
[Crossref] [PubMed]

Shirdel, J.

S. Schmidt, B. Piglosiewicz, D. Sadiq, J. Shirdel, J. S. Lee, P. Vasa, N. Park, D.-S. Kim, and C. Lienau, “Adiabatic nanofocusing on ultrasmooth single-crystalline gold tapers creates a 10-nm-sized light source with few-cycle time resolution,” ACS Nano 6(7), 6040–6048 (2012).
[Crossref] [PubMed]

Staffaroni, M.

W. Bao, M. Staffaroni, J. Bokor, M. B. Salmeron, E. Yablonovitch, S. Cabrini, A. Weber-Bargioni, and P. J. Schuck, “Plasmonic near-field probes: a comparison of the campanile geometry with other sharp tips,” Opt. Express 21(7), 8166–8176 (2013).
[Crossref] [PubMed]

W. Bao, M. Melli, N. Caselli, F. Riboli, D. S. Wiersma, M. Staffaroni, H. Choo, D. F. Ogletree, S. Aloni, J. Bokor, S. Cabrini, F. Intonti, M. B. Salmeron, E. Yablonovitch, P. J. Schuck, and A. Weber-Bargioni, “Mapping local charge recombination heterogeneity by multidimensional nanospectroscopic imaging,” Science 338(6112), 1317–1321 (2012).
[Crossref] [PubMed]

Steinmeyer, G.

A. Anderson, K. S. Deryckx, X. G. Xu, G. Steinmeyer, and M. B. Raschke, “Few-femtosecond plasmon dephasing of a single metallic nanostructure from optical response function reconstruction by interferometric frequency resolved optical gating,” Nano Lett. 10(7), 2519–2524 (2010).
[Crossref] [PubMed]

Stockman, M. I.

M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett. 93(13), 137404 (2004).
[Crossref] [PubMed]

Stranick, S. J.

L. Novotny and S. J. Stranick, “Near-field optical microscopy and spectroscopy with pointed probes,” Annu. Rev. Phys. Chem. 57(1), 303–331 (2006).
[Crossref] [PubMed]

Taubner, T.

T. Taubner, R. Hillenbrand, and F. Keilmann, “Performance of visible and mid-infrared scattering-type near-field optical microscopes,” J. Microsc. 210(3), 311–314 (2003).
[Crossref] [PubMed]

Trautman, J. K.

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, and R. L. Kostelak, “Breaking the diffraction barrier: optical microscopy on a nanometric scale,” Science 251(5000), 1468–1470 (1991).
[Crossref] [PubMed]

Ulbricht, R.

V. Kravtsov, R. Ulbricht, J. M. Atkin, and M. B. Raschke, “Plasmonic nanofocused four-wave mixing for femtosecond near-field imaging,” Nat. Nanotechnol. 11(5), 459–464 (2016).
[Crossref] [PubMed]

van Hulst, N. F.

R. Hildner, D. Brinks, J. B. Nieder, R. J. Cogdell, and N. F. van Hulst, “Quantum coherent energy transfer over varying pathways in single light-harvesting complexes,” Science 340(6139), 1448–1451 (2013).
[Crossref] [PubMed]

Vasa, P.

S. Schmidt, B. Piglosiewicz, D. Sadiq, J. Shirdel, J. S. Lee, P. Vasa, N. Park, D.-S. Kim, and C. Lienau, “Adiabatic nanofocusing on ultrasmooth single-crystalline gold tapers creates a 10-nm-sized light source with few-cycle time resolution,” ACS Nano 6(7), 6040–6048 (2012).
[Crossref] [PubMed]

Vogelgesang, R.

S. F. Becker, M. Esmann, K. Yoo, P. Groß, R. Vogelgesang, N. Park, and C. Lienau, “Gap-Plasmon-Enhanced Nanofocusing Near-Field Microscopy,” ACS Photonics 3(2), 223–232 (2016).
[Crossref]

M. Esmann, S. F. Becker, B. B. da Cunha, J. H. Brauer, R. Vogelgesang, P. Groß, and C. Lienau, “k-space imaging of the eigenmodes of sharp gold tapers for scanning near-field optical microscopy,” Beilstein J. Nanotechnol. 4(1), 603–610 (2013).
[Crossref] [PubMed]

M. Esslinger, J. Dorfmüller, W. Khunsin, R. Vogelgesang, and K. Kern, “Background-free imaging of plasmonic structures with cross-polarized apertureless scanning near-field optical microscopy,” Rev. Sci. Instrum. 83(3), 033704 (2012).
[Crossref] [PubMed]

Wade, L. A.

J. M. Gerton, L. A. Wade, G. A. Lessard, Z. Ma, and S. R. Quake, “Tip-enhanced fluorescence microscopy at 10 nanometer resolution,” Phys. Rev. Lett. 93(18), 180801 (2004).
[Crossref] [PubMed]

Weber-Bargioni, A.

W. Bao, M. Staffaroni, J. Bokor, M. B. Salmeron, E. Yablonovitch, S. Cabrini, A. Weber-Bargioni, and P. J. Schuck, “Plasmonic near-field probes: a comparison of the campanile geometry with other sharp tips,” Opt. Express 21(7), 8166–8176 (2013).
[Crossref] [PubMed]

W. Bao, M. Melli, N. Caselli, F. Riboli, D. S. Wiersma, M. Staffaroni, H. Choo, D. F. Ogletree, S. Aloni, J. Bokor, S. Cabrini, F. Intonti, M. B. Salmeron, E. Yablonovitch, P. J. Schuck, and A. Weber-Bargioni, “Mapping local charge recombination heterogeneity by multidimensional nanospectroscopic imaging,” Science 338(6112), 1317–1321 (2012).
[Crossref] [PubMed]

Weiner, J. S.

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, and R. L. Kostelak, “Breaking the diffraction barrier: optical microscopy on a nanometric scale,” Science 251(5000), 1468–1470 (1991).
[Crossref] [PubMed]

Wieck, A. D.

T. Guenther, C. Lienau, T. Elsaesser, M. Glanemann, V. M. Axt, T. Kuhn, S. Eshlaghi, and A. D. Wieck, “Coherent nonlinear optical response of single quantum dots studied by ultrafast near-field spectroscopy,” Phys. Rev. Lett. 89(5), 057401 (2002).
[Crossref] [PubMed]

Wiersma, D. S.

W. Bao, M. Melli, N. Caselli, F. Riboli, D. S. Wiersma, M. Staffaroni, H. Choo, D. F. Ogletree, S. Aloni, J. Bokor, S. Cabrini, F. Intonti, M. B. Salmeron, E. Yablonovitch, P. J. Schuck, and A. Weber-Bargioni, “Mapping local charge recombination heterogeneity by multidimensional nanospectroscopic imaging,” Science 338(6112), 1317–1321 (2012).
[Crossref] [PubMed]

Wild, U. P.

W. E. Moerner, T. Plakhotnik, T. Irngartinger, U. P. Wild, D. W. Pohl, and B. Hecht, “Near-field optical spectroscopy of individual molecules in solids,” Phys. Rev. Lett. 73(20), 2764–2767 (1994).
[Crossref] [PubMed]

Xu, X. G.

A. Anderson, K. S. Deryckx, X. G. Xu, G. Steinmeyer, and M. B. Raschke, “Few-femtosecond plasmon dephasing of a single metallic nanostructure from optical response function reconstruction by interferometric frequency resolved optical gating,” Nano Lett. 10(7), 2519–2524 (2010).
[Crossref] [PubMed]

Yablonovitch, E.

W. Bao, M. Staffaroni, J. Bokor, M. B. Salmeron, E. Yablonovitch, S. Cabrini, A. Weber-Bargioni, and P. J. Schuck, “Plasmonic near-field probes: a comparison of the campanile geometry with other sharp tips,” Opt. Express 21(7), 8166–8176 (2013).
[Crossref] [PubMed]

W. Bao, M. Melli, N. Caselli, F. Riboli, D. S. Wiersma, M. Staffaroni, H. Choo, D. F. Ogletree, S. Aloni, J. Bokor, S. Cabrini, F. Intonti, M. B. Salmeron, E. Yablonovitch, P. J. Schuck, and A. Weber-Bargioni, “Mapping local charge recombination heterogeneity by multidimensional nanospectroscopic imaging,” Science 338(6112), 1317–1321 (2012).
[Crossref] [PubMed]

Yampolsky, S.

S. Yampolsky, D. A. Fishman, S. Dey, E. Hulkko, M. Banik, E. O. Potma, and V. A. Apkarian, “Seeing a single molecule vibrate through time-resolved coherent anti-Stokes Raman scattering,” Nat. Photonics 8(8), 650–656 (2014).
[Crossref]

Yang, J. L.

R. Zhang, Y. Zhang, Z. C. Dong, S. Jiang, C. Zhang, L. G. Chen, L. Zhang, Y. Liao, J. Aizpurua, Y. Luo, J. L. Yang, and J. G. Hou, “Chemical mapping of a single molecule by plasmon-enhanced Raman scattering,” Nature 498(7452), 82–86 (2013).
[Crossref] [PubMed]

Yoo, K.

S. F. Becker, M. Esmann, K. Yoo, P. Groß, R. Vogelgesang, N. Park, and C. Lienau, “Gap-Plasmon-Enhanced Nanofocusing Near-Field Microscopy,” ACS Photonics 3(2), 223–232 (2016).
[Crossref]

Zayats, A. V.

A. V. Zayats and V. Sandoghdar, “Apertureless scanning near-field second-harmonic microscopy,” Opt. Commun. 178(1–3), 245–249 (2000).
[Crossref]

Zhang, C.

R. Zhang, Y. Zhang, Z. C. Dong, S. Jiang, C. Zhang, L. G. Chen, L. Zhang, Y. Liao, J. Aizpurua, Y. Luo, J. L. Yang, and J. G. Hou, “Chemical mapping of a single molecule by plasmon-enhanced Raman scattering,” Nature 498(7452), 82–86 (2013).
[Crossref] [PubMed]

Zhang, L.

R. Zhang, Y. Zhang, Z. C. Dong, S. Jiang, C. Zhang, L. G. Chen, L. Zhang, Y. Liao, J. Aizpurua, Y. Luo, J. L. Yang, and J. G. Hou, “Chemical mapping of a single molecule by plasmon-enhanced Raman scattering,” Nature 498(7452), 82–86 (2013).
[Crossref] [PubMed]

Zhang, R.

R. Zhang, Y. Zhang, Z. C. Dong, S. Jiang, C. Zhang, L. G. Chen, L. Zhang, Y. Liao, J. Aizpurua, Y. Luo, J. L. Yang, and J. G. Hou, “Chemical mapping of a single molecule by plasmon-enhanced Raman scattering,” Nature 498(7452), 82–86 (2013).
[Crossref] [PubMed]

Zhang, Y.

R. Zhang, Y. Zhang, Z. C. Dong, S. Jiang, C. Zhang, L. G. Chen, L. Zhang, Y. Liao, J. Aizpurua, Y. Luo, J. L. Yang, and J. G. Hou, “Chemical mapping of a single molecule by plasmon-enhanced Raman scattering,” Nature 498(7452), 82–86 (2013).
[Crossref] [PubMed]

ACS Nano (1)

S. Schmidt, B. Piglosiewicz, D. Sadiq, J. Shirdel, J. S. Lee, P. Vasa, N. Park, D.-S. Kim, and C. Lienau, “Adiabatic nanofocusing on ultrasmooth single-crystalline gold tapers creates a 10-nm-sized light source with few-cycle time resolution,” ACS Nano 6(7), 6040–6048 (2012).
[Crossref] [PubMed]

ACS Photonics (1)

S. F. Becker, M. Esmann, K. Yoo, P. Groß, R. Vogelgesang, N. Park, and C. Lienau, “Gap-Plasmon-Enhanced Nanofocusing Near-Field Microscopy,” ACS Photonics 3(2), 223–232 (2016).
[Crossref]

Angew. Chem. Int. Ed. Engl. (1)

E. Bailo and V. Deckert, “Tip-enhanced Raman spectroscopy of single RNA strands: towards a novel direct-sequencing method,” Angew. Chem. Int. Ed. Engl. 47(9), 1658–1661 (2008).
[Crossref] [PubMed]

Annu. Rev. Phys. Chem. (1)

L. Novotny and S. J. Stranick, “Near-field optical microscopy and spectroscopy with pointed probes,” Annu. Rev. Phys. Chem. 57(1), 303–331 (2006).
[Crossref] [PubMed]

Appl. Phys. Lett. (2)

N. Ocelic, A. Huber, and R. Hillenbrand, “Pseudoheterodyne detection for background-free near-field spectroscopy,” Appl. Phys. Lett. 89(10), 101124 (2006).
[Crossref]

M. B. Raschke and C. Lienau, “Apertureless near-field optical microscopy: Tip–sample coupling in elastic light scattering,” Appl. Phys. Lett. 83(24), 5089–5091 (2003).
[Crossref]

Beilstein J. Nanotechnol. (1)

M. Esmann, S. F. Becker, B. B. da Cunha, J. H. Brauer, R. Vogelgesang, P. Groß, and C. Lienau, “k-space imaging of the eigenmodes of sharp gold tapers for scanning near-field optical microscopy,” Beilstein J. Nanotechnol. 4(1), 603–610 (2013).
[Crossref] [PubMed]

J. Appl. Phys. (1)

A. J. Babadjanyan, N. L. Margaryan, and K. V. Nerkararyan, “Superfocusing of surface polaritons in the conical structure,” J. Appl. Phys. 87(8), 3785–3788 (2000).
[Crossref]

J. Microsc. (2)

T. Taubner, R. Hillenbrand, and F. Keilmann, “Performance of visible and mid-infrared scattering-type near-field optical microscopes,” J. Microsc. 210(3), 311–314 (2003).
[Crossref] [PubMed]

R. Hillenbrand, B. Knoll, and F. Keilmann, “Pure optical contrast in scattering-type scanning near-field microscopy,” J. Microsc. 202(1), 77–83 (2001).
[Crossref] [PubMed]

J. Opt. Soc. Am. B (1)

J. Phys. Chem. Lett. (1)

S. Berweger, J. M. Atkin, R. L. Olmon, and M. B. Raschke, “Light on the tip of a needle: plasmonic nanofocusing for spectroscopy on the nanoscale,” J. Phys. Chem. Lett. 3(7), 945–952 (2012).
[Crossref] [PubMed]

Jpn. J. Appl. Phys. (1)

Y. Sasaki and H. Sasaki, “Heterodyne detection for the extraction of the probe-scattering signal in scattering-type scanning near-field optical microscope,” Jpn. J. Appl. Phys. 39(4A), L321–L323 (2000).
[Crossref]

Nano Lett. (1)

A. Anderson, K. S. Deryckx, X. G. Xu, G. Steinmeyer, and M. B. Raschke, “Few-femtosecond plasmon dephasing of a single metallic nanostructure from optical response function reconstruction by interferometric frequency resolved optical gating,” Nano Lett. 10(7), 2519–2524 (2010).
[Crossref] [PubMed]

Nat. Nanotechnol. (1)

V. Kravtsov, R. Ulbricht, J. M. Atkin, and M. B. Raschke, “Plasmonic nanofocused four-wave mixing for femtosecond near-field imaging,” Nat. Nanotechnol. 11(5), 459–464 (2016).
[Crossref] [PubMed]

Nat. Photonics (1)

S. Yampolsky, D. A. Fishman, S. Dey, E. Hulkko, M. Banik, E. O. Potma, and V. A. Apkarian, “Seeing a single molecule vibrate through time-resolved coherent anti-Stokes Raman scattering,” Nat. Photonics 8(8), 650–656 (2014).
[Crossref]

Nature (3)

R. Chikkaraddy, B. de Nijs, F. Benz, S. J. Barrow, O. A. Scherman, E. Rosta, A. Demetriadou, P. Fox, O. Hess, and J. J. Baumberg, “Single-molecule strong coupling at room temperature in plasmonic nanocavities,” Nature 535(7610), 127–130 (2016).
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E. A. Ash and G. Nicholls, “Super-resolution aperture scanning microscope,” Nature 237(5357), 510–512 (1972).
[Crossref] [PubMed]

R. Zhang, Y. Zhang, Z. C. Dong, S. Jiang, C. Zhang, L. G. Chen, L. Zhang, Y. Liao, J. Aizpurua, Y. Luo, J. L. Yang, and J. G. Hou, “Chemical mapping of a single molecule by plasmon-enhanced Raman scattering,” Nature 498(7452), 82–86 (2013).
[Crossref] [PubMed]

Opt. Commun. (2)

A. V. Zayats and V. Sandoghdar, “Apertureless scanning near-field second-harmonic microscopy,” Opt. Commun. 178(1–3), 245–249 (2000).
[Crossref]

B. Knoll and F. Keilmann, “Enhanced dielectric contrast in scattering-type scanning near-field optical microscopy,” Opt. Commun. 182(4–6), 321–328 (2000).
[Crossref]

Opt. Express (1)

Phys. Rev. Lett. (6)

P. Anger, P. Bharadwaj, and L. Novotny, “Enhancement and quenching of single-molecule fluorescence,” Phys. Rev. Lett. 96(11), 113002 (2006).
[Crossref] [PubMed]

W. E. Moerner, T. Plakhotnik, T. Irngartinger, U. P. Wild, D. W. Pohl, and B. Hecht, “Near-field optical spectroscopy of individual molecules in solids,” Phys. Rev. Lett. 73(20), 2764–2767 (1994).
[Crossref] [PubMed]

T. Guenther, C. Lienau, T. Elsaesser, M. Glanemann, V. M. Axt, T. Kuhn, S. Eshlaghi, and A. D. Wieck, “Coherent nonlinear optical response of single quantum dots studied by ultrafast near-field spectroscopy,” Phys. Rev. Lett. 89(5), 057401 (2002).
[Crossref] [PubMed]

R. Hillenbrand and F. Keilmann, “Complex optical constants on a subwavelength scale,” Phys. Rev. Lett. 85(14), 3029–3032 (2000).
[Crossref] [PubMed]

J. M. Gerton, L. A. Wade, G. A. Lessard, Z. Ma, and S. R. Quake, “Tip-enhanced fluorescence microscopy at 10 nanometer resolution,” Phys. Rev. Lett. 93(18), 180801 (2004).
[Crossref] [PubMed]

M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett. 93(13), 137404 (2004).
[Crossref] [PubMed]

Rev. Sci. Instrum. (1)

M. Esslinger, J. Dorfmüller, W. Khunsin, R. Vogelgesang, and K. Kern, “Background-free imaging of plasmonic structures with cross-polarized apertureless scanning near-field optical microscopy,” Rev. Sci. Instrum. 83(3), 033704 (2012).
[Crossref] [PubMed]

Science (3)

W. Bao, M. Melli, N. Caselli, F. Riboli, D. S. Wiersma, M. Staffaroni, H. Choo, D. F. Ogletree, S. Aloni, J. Bokor, S. Cabrini, F. Intonti, M. B. Salmeron, E. Yablonovitch, P. J. Schuck, and A. Weber-Bargioni, “Mapping local charge recombination heterogeneity by multidimensional nanospectroscopic imaging,” Science 338(6112), 1317–1321 (2012).
[Crossref] [PubMed]

R. Hildner, D. Brinks, J. B. Nieder, R. J. Cogdell, and N. F. van Hulst, “Quantum coherent energy transfer over varying pathways in single light-harvesting complexes,” Science 340(6139), 1448–1451 (2013).
[Crossref] [PubMed]

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, and R. L. Kostelak, “Breaking the diffraction barrier: optical microscopy on a nanometric scale,” Science 251(5000), 1468–1470 (1991).
[Crossref] [PubMed]

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Figures (6)

Fig. 1
Fig. 1

Experimental setup (left) and the fields that contribute to the measured signal (right). Left: Light from a Titanium:Sapphire laser is focused on a sample. The polarization is controlled by a half-wave plate (HWP), and the position of the focus is corrected by a steering mirror followed by a 4f-system (lenses L1 and L2), which image the beam tilt to the back focal plane (BFP) of the microscope objective (MO). A sharply etched gold tip is brought closely to the sample to scatter light from the near-field region to the far field. The scattered light is split off the incident beam path by a 50:50 beam splitter (BS), collected by a lens (L3) and detected by an avalanche photodiode (APD). Right: The sample is coated onto a thin glass-covered gold layer on top of a glass substrate. The signal detected by the APD comprises contributions of electric fields from the near field ( E NF ), of the field scattered from the tip shaft ( E B ), as well as the reference field that is reflected off the semi-transparent gold film ( E R ).

Fig. 2
Fig. 2

The measured optical signals S 0f plotted together with a sinusoidal fit (black and curves in the left hand graphs) and S 1f , S 3f , and S 4f (blue, green and red curves, respectively, in the right hand graphs) recorded during the approach of the three different substrates towards the gold nanotip. A, B: Approach of a gold-coated quartz microscope slide to the nanotip. A, The DC signal S 0f is weakly modulated and B, there is a strong near-field signal when the gold surface is in close proximity to the tip. The inset shows the tuning fork amplitude; the point of contact is defined as the position when the tuning fork amplitude is decreased by 5%. C, D: Approach of an uncoated quartz substrate to the nanotip. C, The DC signal is strongly modulated, and D, the near-field signal is very weak on the glass surface. E, F: Approach of the in-line interferometer to the gold tip, i. e., a quartz surface covered with a ~200-nm thick SiO2 film on top of the ~20-nm thick semitransparent gold film. E, The DC signal is moderately modulated, and F, when bringing the glass surface in close proximity to the tip, a near-field contribution is clearly visible. The in-line interferometer enables homodyne measurement of a weak near-field signal, such as on a glass surface in vicinity to a gold nanotip.

Fig. 3
Fig. 3

Graphical depiction of the sample, the origin of the interacting fields, and the tip-sample interaction region. The incident light field E in illuminates sample and tip in a diffraction-limited spot. A part E R is reflected off the semitransparent gold film, and a part E B is scattered back from the shaft of the gold tip, possibly after multiple reflections ( E ' B ). The inset on the right depicts the enhancement of the tip dipole with polarizability α tip by its image dipole. The electric field radiated from the tip dipole and propagating back towards the illuminating microscope objective is the origin of the near-field contribution E NF .

Fig. 4
Fig. 4

Relative amplitude of the Fourier coefficients b (0) to b (4) (red bars) and c (0) to c (4) (blue bars) normalized to b (0) and c (0) , respectively, as a function of demodulation order n. The amplitude of both decreases with demodulation order, but the background-field coefficients b (n) decreases much more rapidly than the near-field coefficients c (n) .

Fig. 5
Fig. 5

Disentangled background and near-field signals. The left hand side graphs show the measured optical signals S 2f (blue curves) and S 3f (green curves) as a function of the tip-sample distance together with calculated approach curves (dashed red curves) for A, the gold-coated quartz substrate, C, the uncoated quartz substrate, and E, the quartz substrate coated with a semitransparent gold film and ~200 nm quartz on top of the gold film. Adapting the theoretically derived expressions for S 0f to S 4f allows determination of the electric field strengths E R , E B,0 , and E NF , and, together with the Fourier coefficients b (n) and c (n) disentangling background and near-field contributions to the measured signals. Τhe right hand side graphs show the ratio of background and near-field contribution to the measured signals as red and blue bars, respectively, as function of the demodulation order for B, the gold-coated quartz substrate, D, the uncoated quartz substrate, and F, the quartz substrate coated with a semitransparent gold film and ~200 nm quartz on top of the gold film. The bars are normalized to Re{ E R E B,0 }| b (0) |=100% on the gold-coated quartz substrate. For the substrates with a gold film (B and F), the background signal decays much faster with increasing demodulation frequency than the near-field signal, such that when demodulating at f demod =4 f mod , basically only the near-field signal is measured. For the uncoated quartz substrate, even at fourth-order demodulation, the background signal surmounts the near-field signal.

Fig. 6
Fig. 6

Broad-bandwidth near-field spectroscopy. A, Input laser spectrum. B, Tuning fork amplitude as a function of tip-sample distance. The positions where spectra are measured are marked by colored circles. C, The measured spectra S 1f ( λ ), demodulated at the fundamental tip modulation frequency, do not resemble the input spectrum, but are prominently modulated by interference between reference and background fields. D, The calculated spectra S 1f ( λ ) model the main characteristics of the measured spectra very well. E, The measured as well as F, the calculated spectra S 2f also differ from the input laser, and due to different field components interfering they also strongly differ from S 1f . G, In contrast, the measured spectra S 4f ( λ ), demodulated at the fourth harmonic, mainly resemble the input laser spectrum and strongly decrease with increasing tip-sample distance. H, The calculated spectra S 4f show the same behavior.

Equations (25)

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E R ( z )= E R =const.
E B ( z )= E B,0 e 2ik( z+d )+i φ B
E ' B ( z )= E B,0 ( e 2ik( z+d )+i φ B1 +r e 4ik( z+d )+i φ B2 )
p tip = α tip ( E in + E ID )
E out ( r )= G out ( r , r ' ) p tip = G out ( r , r ' ) α tip ( E in + E ID )
E NF = E out ( r Det ) G out ( r Det , r ' ) α tip E in
E NF ( z )= E NF,0 e z z 0 e i φ NF
z( t )= z ¯ +Mcos( Ωt )
E B ( z )= E B ( z ¯ ,t )= E B,0 e i2k( z ¯ +d )+i φ B e i2kMcos( Ωt )
E NF ( z )= E NF ( z ¯ ,t )= E NF,0 e i φ NF e z ¯ z 0 e M z 0 cos( Ωt )
E B ( z ¯ ,t ) E B,0 e i2k( z ¯ +d )+i φ B n= b (n) e inΩt
E NF ( z ¯ ,t ) E NF,0 e i φ NF e z ¯ z 0 n= c (n) e inΩt
b (n) = 1 T 0 T e i2kMcos( Ωt ) e inΩt dt = ( i ) n J n ( 2kM )
c (n) = 1 T 0 T e M z 0 cos( Ωt ) e inΩt dt = ( 1 ) n I n ( M z 0 )
| E total ( z ¯ ,t ) | 2 = | E R + E B,0 e i2k( z ¯ +d )+i φ B n= b (n) e inΩt + E NF,0 e i φ NF e z ¯ z 0 n= c (n) e inΩt | 2
| E total ( z ¯ ) | 2 = | E R | 2 +( E R * E B,0 e i2k( z ¯ +d )+i φ B n= b (n) e inΩt +c.c. )+( E R * E NF,0 e i φ NF e z ¯ z 0 n= c (n) e inΩt +c.c. ) + | E B,0 | 2 n= m= b (n) b (m)* e i(nm)Ωt + | E NF,0 | 2 e 2 z ¯ z 0 n= m= c (n) c (m)* e i(nm)Ωt +( E B,0 E NF,0 * e i( 2k( z ¯ +d )+ φ B φ NF ) e z ¯ z 0 n= m= b (n) c (m)* e i( nm )Ωt +c.c. )
P( z,t )= 1 2 ε 0 cA | E total | 2
S 0f ( z ¯ )= U (0) ( z ¯ )=η P (0) ( z ¯ )
S nf ( z ¯ )=γ 1 T t'T t' cos[ nΩt+θ ]U( z ¯ ,t ) dt , | n |1 b 2 4ac
S 0f ( z ¯ ) 1 4 η ε 0 cA [ | E R | 2 + | E B,0 | 2 n=4 4 b (n) b (n)* + | E NF,0 | 2 e 2 z ¯ z 0 n=4 4 c (n) c (n)* +2Re{ E R E B,0 b (0) }cos( 2k( z ¯ +d )+ φ B )+2Re{ E R E NF,0 c (0) } e z ¯ z 0 cos( φ NF ) + ( E B,0 E NF,0 * e i( 2k( z ¯ +d )+ φ B φ NF ) e z ¯ z 0 n=4 4 b (n) c (n)* +c.c. ) ]
S 0f ( z ¯ ) 1 4 η ε 0 cA[ | E R | 2 + | E B,0 b (0) | 2 +2 E R E B,0 b (0) cos( 2k( z ¯ +d )+ φ B ) ]
S 1f ( z ¯ )γη ε 0 cA| Re{ E R E B,0 }| b (1) |sin( 2k( z ¯ +d )+ φ B )Re{ E R E NF,0 }| c (1) | e z ¯ z 0 cos φ NF Re{ E B,0 E NF,0 }| b (0) || c (1) | e z ¯ z 0 cos( 2k( z ¯ +d )+ φ B φ NF )|
S 2f ( z ¯ )γη ε 0 cA| Re{ E R E B,0 }| b (2) |cos( 2k( z ¯ +d )+ φ B )+Re{ E R E NF,0 }| c (2) | e z ¯ z 0 cos φ NF | E B,0 | 2 | b (0) || b (2) |+Re{ E B,0 E NF,0 }| b (0) || c (2) | e z ¯ z 0 cos( 2k( z ¯ +d )+ φ B φ NF )|
S 3f ( z ¯ )γη ε 0 cA| Re{ E R E B,0 }| b (3) |sin( 2k( z ¯ +d )+ φ B )Re{ E R E NF,0 }| c (3) | e z ¯ z 0 cos φ NF Re{ E B,0 E NF,0 }| b (0) || c (3) | e z ¯ z 0 cos( 2k( z ¯ +d )+ φ B φ NF )|
S 4f ( z ¯ )γη ε 0 cA| Re{ E R E B,0 }| b (4) |cos( 2k( z ¯ +d )+ φ B )+Re{ E R E NF,0 }| c (4) | e z ¯ z 0 cos φ NF + | E B,0 | 2 | b (2) | 2 +Re{ E B,0 E NF,0 }| b (0) || c (4) | e z ¯ z 0 cos( 2k( z ¯ +d )+ φ B φ NF )|

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