Abstract

The optical properties of the metallized tips used in tip-enhanced Raman spectroscopy (TERS) are vital to resonance enhancement. A white-light scattering-spectrum measuring setup based on total internal reflection microscopy is developed to characterize the optical responses of the metallized tips. The scattering spectra of the Ag-coated optical fiber tips are measured as a demonstration of the methodology and the performance of the setup. A prominent resonance band of 500550nm is observed experimentally, which can be interpreted as the result of the excitation of the localized surface plasmon resonance at the Ag-coated optical fiber tip. The optical responses of the Ag-coated optical fiber tips are simulated by a three- dimensional finite-difference time-domain method and the results are compared with the experiments. This method has great application potential in the selection and design of high-performance metallized tips for TERS and other apertureless near-field optical microscopy.

© 2010 Optical Society of America

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References

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  1. N. Anderson, A. Hartschuh, S. Cronin, and L. Novotny, “Nanoscale vibrational analysis of single-walled carbon nanotubes,” J. Am. Chem. Soc. 127, 2533–2537 (2005).
    [CrossRef] [PubMed]
  2. J. Steidtner and B. Pettinger, “Tip-enhanced Raman spectroscopy and microscopy on single dye molecules with 15nmresolution,” Phys. Rev. Lett. 100, 236101 (2008).
    [CrossRef] [PubMed]
  3. L. Novotny, “Nano-optics—optical antennas tuned to pitch,” Nature 455, 887–887 (2008).
    [CrossRef]
  4. C. Xudong, Z. Weihua, Y. Boon-Siang, R. Zenobi, C. Hafner, and D. Erni, “Tuning the resonance frequency of Ag-coated dielectric tips,” Opt. Express 15, 8309–8316 (2007).
    [CrossRef]
  5. C. Xudong, D. Erni, Z. Weihua, and R. Zenobi, “Highly efficient nano-tips with metal-dielectric coatings for tip-enhanced spectroscopy applications,” Chem. Phys. Lett. 453, 262–265 (2008).
    [CrossRef]
  6. A. L. Demming, F. Festy, and D. Richards, “Plasmon resonances on metal tips: understanding tip-enhanced Raman scattering,” J. Chem. Phys. 122, 184716–184723 (2005).
    [CrossRef] [PubMed]
  7. R. M. Roth, N. C. Panoiu, M. M. Adams, R. M. Osgood, C. C. Neacsu, and M. B. Raschke, “Resonant-plasmon field enhancement from asymmetrically illuminated conical metallic-probe tips,” Opt. Express 14, 2921–2931 (2006).
    [CrossRef] [PubMed]
  8. M. Sukharev and T. Seideman, “Optical properties of metal tips for tip-enhanced spectroscopies,” J. Phys. Chem. A 113, 7508–7513 (2009).
    [CrossRef] [PubMed]
  9. A. Downes, R. Mouras, M. Mari, and A. Elfick, “Optimising tip-enhanced optical microscopy,” J. Raman Spectrosc. 40, 1355–1360 (2009).
    [CrossRef]
  10. W. H. Zhang, X. D. Cui, and O. J. F. Martin, “Local field enhancement of an infinite conical metal tip illuminated by a focused beam,” J. Raman Spectrosc. 40, 1338–1342 (2009).
    [CrossRef]
  11. C. C. Neacsu, G. A. Steudle, and M. B. Raschko, “Plasmonic light scattering from nanoscopic metal tips,” Appl. Phys. B 80, 295–300 (2005).
    [CrossRef]
  12. D. Mehtani, N. Lee, R. D. Hartschuh, A. Kisliuk, M. D. Foster, A. P. Sokolov, F. Caiko, and I. Tsukerman, “Optical properties and enhancement factors of the tips for apertureless near-field optics,” J. Opt. A Pure Appl. Opt. 8, S183–S190 (2006).
    [CrossRef]
  13. A. Taguchi, N. Hayazawa, Y. Saito, H. Ishitobi, A. Tarun, and S. Kawata, “Controlling the plasmon resonance wavelength in metal-coated probe using refractive index modification,” Opt. Express 17, 6509–6518 (2009).
    [CrossRef] [PubMed]
  14. R. Wang, J. Wang, F. Hao, M. Zhang, and Q. Tian, “Tip-enhanced Raman spectroscopy with silver-coated optical fiber probe in reflection mode for investigating multiwall carbon nanotubes,” Appl. Opt. 49, 1845–1848 (2010).
    [CrossRef] [PubMed]
  15. K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107, 668–677 (2003).
    [CrossRef]
  16. C. Noguez, “Surface plasmons on metal nanoparticles: the influence of shape and physical environment,” J. Phys. Chem. C 111, 3806–3819 (2007).
    [CrossRef]
  17. L. Novotny and S. J. Stranick, “Near-field optical microscopy and spectroscopy with pointed probes,” Annu. Rev. Phys. Chem. 57, 303–331 (2006).
    [CrossRef] [PubMed]

2010 (1)

2009 (4)

A. Taguchi, N. Hayazawa, Y. Saito, H. Ishitobi, A. Tarun, and S. Kawata, “Controlling the plasmon resonance wavelength in metal-coated probe using refractive index modification,” Opt. Express 17, 6509–6518 (2009).
[CrossRef] [PubMed]

M. Sukharev and T. Seideman, “Optical properties of metal tips for tip-enhanced spectroscopies,” J. Phys. Chem. A 113, 7508–7513 (2009).
[CrossRef] [PubMed]

A. Downes, R. Mouras, M. Mari, and A. Elfick, “Optimising tip-enhanced optical microscopy,” J. Raman Spectrosc. 40, 1355–1360 (2009).
[CrossRef]

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

2008 (3)

J. Steidtner and B. Pettinger, “Tip-enhanced Raman spectroscopy and microscopy on single dye molecules with 15nmresolution,” Phys. Rev. Lett. 100, 236101 (2008).
[CrossRef] [PubMed]

L. Novotny, “Nano-optics—optical antennas tuned to pitch,” Nature 455, 887–887 (2008).
[CrossRef]

C. Xudong, D. Erni, Z. Weihua, and R. Zenobi, “Highly efficient nano-tips with metal-dielectric coatings for tip-enhanced spectroscopy applications,” Chem. Phys. Lett. 453, 262–265 (2008).
[CrossRef]

2007 (2)

C. Noguez, “Surface plasmons on metal nanoparticles: the influence of shape and physical environment,” J. Phys. Chem. C 111, 3806–3819 (2007).
[CrossRef]

C. Xudong, Z. Weihua, Y. Boon-Siang, R. Zenobi, C. Hafner, and D. Erni, “Tuning the resonance frequency of Ag-coated dielectric tips,” Opt. Express 15, 8309–8316 (2007).
[CrossRef]

2006 (3)

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

R. M. Roth, N. C. Panoiu, M. M. Adams, R. M. Osgood, C. C. Neacsu, and M. B. Raschke, “Resonant-plasmon field enhancement from asymmetrically illuminated conical metallic-probe tips,” Opt. Express 14, 2921–2931 (2006).
[CrossRef] [PubMed]

D. Mehtani, N. Lee, R. D. Hartschuh, A. Kisliuk, M. D. Foster, A. P. Sokolov, F. Caiko, and I. Tsukerman, “Optical properties and enhancement factors of the tips for apertureless near-field optics,” J. Opt. A Pure Appl. Opt. 8, S183–S190 (2006).
[CrossRef]

2005 (3)

N. Anderson, A. Hartschuh, S. Cronin, and L. Novotny, “Nanoscale vibrational analysis of single-walled carbon nanotubes,” J. Am. Chem. Soc. 127, 2533–2537 (2005).
[CrossRef] [PubMed]

C. C. Neacsu, G. A. Steudle, and M. B. Raschko, “Plasmonic light scattering from nanoscopic metal tips,” Appl. Phys. B 80, 295–300 (2005).
[CrossRef]

A. L. Demming, F. Festy, and D. Richards, “Plasmon resonances on metal tips: understanding tip-enhanced Raman scattering,” J. Chem. Phys. 122, 184716–184723 (2005).
[CrossRef] [PubMed]

2003 (1)

K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107, 668–677 (2003).
[CrossRef]

Adams, M. M.

Anderson, N.

N. Anderson, A. Hartschuh, S. Cronin, and L. Novotny, “Nanoscale vibrational analysis of single-walled carbon nanotubes,” J. Am. Chem. Soc. 127, 2533–2537 (2005).
[CrossRef] [PubMed]

Boon-Siang, Y.

Caiko, F.

D. Mehtani, N. Lee, R. D. Hartschuh, A. Kisliuk, M. D. Foster, A. P. Sokolov, F. Caiko, and I. Tsukerman, “Optical properties and enhancement factors of the tips for apertureless near-field optics,” J. Opt. A Pure Appl. Opt. 8, S183–S190 (2006).
[CrossRef]

Coronado, E.

K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107, 668–677 (2003).
[CrossRef]

Cronin, S.

N. Anderson, A. Hartschuh, S. Cronin, and L. Novotny, “Nanoscale vibrational analysis of single-walled carbon nanotubes,” J. Am. Chem. Soc. 127, 2533–2537 (2005).
[CrossRef] [PubMed]

Cui, X. D.

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

Demming, A. L.

A. L. Demming, F. Festy, and D. Richards, “Plasmon resonances on metal tips: understanding tip-enhanced Raman scattering,” J. Chem. Phys. 122, 184716–184723 (2005).
[CrossRef] [PubMed]

Downes, A.

A. Downes, R. Mouras, M. Mari, and A. Elfick, “Optimising tip-enhanced optical microscopy,” J. Raman Spectrosc. 40, 1355–1360 (2009).
[CrossRef]

Elfick, A.

A. Downes, R. Mouras, M. Mari, and A. Elfick, “Optimising tip-enhanced optical microscopy,” J. Raman Spectrosc. 40, 1355–1360 (2009).
[CrossRef]

Erni, D.

C. Xudong, D. Erni, Z. Weihua, and R. Zenobi, “Highly efficient nano-tips with metal-dielectric coatings for tip-enhanced spectroscopy applications,” Chem. Phys. Lett. 453, 262–265 (2008).
[CrossRef]

C. Xudong, Z. Weihua, Y. Boon-Siang, R. Zenobi, C. Hafner, and D. Erni, “Tuning the resonance frequency of Ag-coated dielectric tips,” Opt. Express 15, 8309–8316 (2007).
[CrossRef]

Festy, F.

A. L. Demming, F. Festy, and D. Richards, “Plasmon resonances on metal tips: understanding tip-enhanced Raman scattering,” J. Chem. Phys. 122, 184716–184723 (2005).
[CrossRef] [PubMed]

Foster, M. D.

D. Mehtani, N. Lee, R. D. Hartschuh, A. Kisliuk, M. D. Foster, A. P. Sokolov, F. Caiko, and I. Tsukerman, “Optical properties and enhancement factors of the tips for apertureless near-field optics,” J. Opt. A Pure Appl. Opt. 8, S183–S190 (2006).
[CrossRef]

Hafner, C.

Hao, F.

Hartschuh, A.

N. Anderson, A. Hartschuh, S. Cronin, and L. Novotny, “Nanoscale vibrational analysis of single-walled carbon nanotubes,” J. Am. Chem. Soc. 127, 2533–2537 (2005).
[CrossRef] [PubMed]

Hartschuh, R. D.

D. Mehtani, N. Lee, R. D. Hartschuh, A. Kisliuk, M. D. Foster, A. P. Sokolov, F. Caiko, and I. Tsukerman, “Optical properties and enhancement factors of the tips for apertureless near-field optics,” J. Opt. A Pure Appl. Opt. 8, S183–S190 (2006).
[CrossRef]

Hayazawa, N.

Ishitobi, H.

Kawata, S.

Kelly, K. L.

K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107, 668–677 (2003).
[CrossRef]

Kisliuk, A.

D. Mehtani, N. Lee, R. D. Hartschuh, A. Kisliuk, M. D. Foster, A. P. Sokolov, F. Caiko, and I. Tsukerman, “Optical properties and enhancement factors of the tips for apertureless near-field optics,” J. Opt. A Pure Appl. Opt. 8, S183–S190 (2006).
[CrossRef]

Lee, N.

D. Mehtani, N. Lee, R. D. Hartschuh, A. Kisliuk, M. D. Foster, A. P. Sokolov, F. Caiko, and I. Tsukerman, “Optical properties and enhancement factors of the tips for apertureless near-field optics,” J. Opt. A Pure Appl. Opt. 8, S183–S190 (2006).
[CrossRef]

Mari, M.

A. Downes, R. Mouras, M. Mari, and A. Elfick, “Optimising tip-enhanced optical microscopy,” J. Raman Spectrosc. 40, 1355–1360 (2009).
[CrossRef]

Martin, O. J. F.

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

Mehtani, D.

D. Mehtani, N. Lee, R. D. Hartschuh, A. Kisliuk, M. D. Foster, A. P. Sokolov, F. Caiko, and I. Tsukerman, “Optical properties and enhancement factors of the tips for apertureless near-field optics,” J. Opt. A Pure Appl. Opt. 8, S183–S190 (2006).
[CrossRef]

Mouras, R.

A. Downes, R. Mouras, M. Mari, and A. Elfick, “Optimising tip-enhanced optical microscopy,” J. Raman Spectrosc. 40, 1355–1360 (2009).
[CrossRef]

Neacsu, C. C.

Noguez, C.

C. Noguez, “Surface plasmons on metal nanoparticles: the influence of shape and physical environment,” J. Phys. Chem. C 111, 3806–3819 (2007).
[CrossRef]

Novotny, L.

L. Novotny, “Nano-optics—optical antennas tuned to pitch,” Nature 455, 887–887 (2008).
[CrossRef]

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

N. Anderson, A. Hartschuh, S. Cronin, and L. Novotny, “Nanoscale vibrational analysis of single-walled carbon nanotubes,” J. Am. Chem. Soc. 127, 2533–2537 (2005).
[CrossRef] [PubMed]

Osgood, R. M.

Panoiu, N. C.

Pettinger, B.

J. Steidtner and B. Pettinger, “Tip-enhanced Raman spectroscopy and microscopy on single dye molecules with 15nmresolution,” Phys. Rev. Lett. 100, 236101 (2008).
[CrossRef] [PubMed]

Raschke, M. B.

Raschko, M. B.

C. C. Neacsu, G. A. Steudle, and M. B. Raschko, “Plasmonic light scattering from nanoscopic metal tips,” Appl. Phys. B 80, 295–300 (2005).
[CrossRef]

Richards, D.

A. L. Demming, F. Festy, and D. Richards, “Plasmon resonances on metal tips: understanding tip-enhanced Raman scattering,” J. Chem. Phys. 122, 184716–184723 (2005).
[CrossRef] [PubMed]

Roth, R. M.

Saito, Y.

Schatz, G. C.

K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107, 668–677 (2003).
[CrossRef]

Seideman, T.

M. Sukharev and T. Seideman, “Optical properties of metal tips for tip-enhanced spectroscopies,” J. Phys. Chem. A 113, 7508–7513 (2009).
[CrossRef] [PubMed]

Sokolov, A. P.

D. Mehtani, N. Lee, R. D. Hartschuh, A. Kisliuk, M. D. Foster, A. P. Sokolov, F. Caiko, and I. Tsukerman, “Optical properties and enhancement factors of the tips for apertureless near-field optics,” J. Opt. A Pure Appl. Opt. 8, S183–S190 (2006).
[CrossRef]

Steidtner, J.

J. Steidtner and B. Pettinger, “Tip-enhanced Raman spectroscopy and microscopy on single dye molecules with 15nmresolution,” Phys. Rev. Lett. 100, 236101 (2008).
[CrossRef] [PubMed]

Steudle, G. A.

C. C. Neacsu, G. A. Steudle, and M. B. Raschko, “Plasmonic light scattering from nanoscopic metal tips,” Appl. Phys. B 80, 295–300 (2005).
[CrossRef]

Stranick, S. J.

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

Sukharev, M.

M. Sukharev and T. Seideman, “Optical properties of metal tips for tip-enhanced spectroscopies,” J. Phys. Chem. A 113, 7508–7513 (2009).
[CrossRef] [PubMed]

Taguchi, A.

Tarun, A.

Tian, Q.

Tsukerman, I.

D. Mehtani, N. Lee, R. D. Hartschuh, A. Kisliuk, M. D. Foster, A. P. Sokolov, F. Caiko, and I. Tsukerman, “Optical properties and enhancement factors of the tips for apertureless near-field optics,” J. Opt. A Pure Appl. Opt. 8, S183–S190 (2006).
[CrossRef]

Wang, J.

Wang, R.

Weihua, Z.

C. Xudong, D. Erni, Z. Weihua, and R. Zenobi, “Highly efficient nano-tips with metal-dielectric coatings for tip-enhanced spectroscopy applications,” Chem. Phys. Lett. 453, 262–265 (2008).
[CrossRef]

C. Xudong, Z. Weihua, Y. Boon-Siang, R. Zenobi, C. Hafner, and D. Erni, “Tuning the resonance frequency of Ag-coated dielectric tips,” Opt. Express 15, 8309–8316 (2007).
[CrossRef]

Xudong, C.

C. Xudong, D. Erni, Z. Weihua, and R. Zenobi, “Highly efficient nano-tips with metal-dielectric coatings for tip-enhanced spectroscopy applications,” Chem. Phys. Lett. 453, 262–265 (2008).
[CrossRef]

C. Xudong, Z. Weihua, Y. Boon-Siang, R. Zenobi, C. Hafner, and D. Erni, “Tuning the resonance frequency of Ag-coated dielectric tips,” Opt. Express 15, 8309–8316 (2007).
[CrossRef]

Zenobi, R.

C. Xudong, D. Erni, Z. Weihua, and R. Zenobi, “Highly efficient nano-tips with metal-dielectric coatings for tip-enhanced spectroscopy applications,” Chem. Phys. Lett. 453, 262–265 (2008).
[CrossRef]

C. Xudong, Z. Weihua, Y. Boon-Siang, R. Zenobi, C. Hafner, and D. Erni, “Tuning the resonance frequency of Ag-coated dielectric tips,” Opt. Express 15, 8309–8316 (2007).
[CrossRef]

Zhang, M.

Zhang, W. H.

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

Zhao, L. L.

K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107, 668–677 (2003).
[CrossRef]

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, 303–331 (2006).
[CrossRef] [PubMed]

Appl. Opt. (1)

Appl. Phys. B (1)

C. C. Neacsu, G. A. Steudle, and M. B. Raschko, “Plasmonic light scattering from nanoscopic metal tips,” Appl. Phys. B 80, 295–300 (2005).
[CrossRef]

Chem. Phys. Lett. (1)

C. Xudong, D. Erni, Z. Weihua, and R. Zenobi, “Highly efficient nano-tips with metal-dielectric coatings for tip-enhanced spectroscopy applications,” Chem. Phys. Lett. 453, 262–265 (2008).
[CrossRef]

J. Am. Chem. Soc. (1)

N. Anderson, A. Hartschuh, S. Cronin, and L. Novotny, “Nanoscale vibrational analysis of single-walled carbon nanotubes,” J. Am. Chem. Soc. 127, 2533–2537 (2005).
[CrossRef] [PubMed]

J. Chem. Phys. (1)

A. L. Demming, F. Festy, and D. Richards, “Plasmon resonances on metal tips: understanding tip-enhanced Raman scattering,” J. Chem. Phys. 122, 184716–184723 (2005).
[CrossRef] [PubMed]

J. Opt. A Pure Appl. Opt. (1)

D. Mehtani, N. Lee, R. D. Hartschuh, A. Kisliuk, M. D. Foster, A. P. Sokolov, F. Caiko, and I. Tsukerman, “Optical properties and enhancement factors of the tips for apertureless near-field optics,” J. Opt. A Pure Appl. Opt. 8, S183–S190 (2006).
[CrossRef]

J. Phys. Chem. A (1)

M. Sukharev and T. Seideman, “Optical properties of metal tips for tip-enhanced spectroscopies,” J. Phys. Chem. A 113, 7508–7513 (2009).
[CrossRef] [PubMed]

J. Phys. Chem. B (1)

K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107, 668–677 (2003).
[CrossRef]

J. Phys. Chem. C (1)

C. Noguez, “Surface plasmons on metal nanoparticles: the influence of shape and physical environment,” J. Phys. Chem. C 111, 3806–3819 (2007).
[CrossRef]

J. Raman Spectrosc. (2)

A. Downes, R. Mouras, M. Mari, and A. Elfick, “Optimising tip-enhanced optical microscopy,” J. Raman Spectrosc. 40, 1355–1360 (2009).
[CrossRef]

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

Nature (1)

L. Novotny, “Nano-optics—optical antennas tuned to pitch,” Nature 455, 887–887 (2008).
[CrossRef]

Opt. Express (3)

Phys. Rev. Lett. (1)

J. Steidtner and B. Pettinger, “Tip-enhanced Raman spectroscopy and microscopy on single dye molecules with 15nmresolution,” Phys. Rev. Lett. 100, 236101 (2008).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

Schematic diagram of white-light scattering microscopy based on TIR illumination mode.

Fig. 2
Fig. 2

SEM images of (a) the optical fiber tip and (b) the silver layer formed by a large number of 20 30 nm silver particles. (c) The silver coating is stripped away by ultrasonic.

Fig. 3
Fig. 3

(a) Simulation model of the Ag-coated silica tip close to the glass substrate. (b) Calculated spectral responses of the Ag-coated silica tip with a tip–substrate distance of 30 and 2 nm , respectively.

Fig. 4
Fig. 4

Experimentally measured scattering spectra of the Ag-coated optical fiber tip with a tip–substrate distance of 30 and 2 nm , respectively.

Equations (1)

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d P = λ 4 π [ n 1 2 sin 2 ( θ ) n 2 2 ] 1 / 2 ,

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