Abstract

We investigate numerically a Scanning Near field Optical Microscope (SNOM) that uses a Parabolic Mirror (PM) to focus a radially polarized beam on a metallic tip. In order to overcome problems - like overestimated near fields or resonances - that arise when only considering finite tips, we have introduced a semi-infinite continuation of the tip, which incorporates the analytic solution of surface waves. For a realistic modeling the right description of the incident field is essential and we have complied with this requirement by a Bessel expansion of the focal fields, which is also applicable to an aplanatic objective. The established numerical model is used for an extensive study of model parameters like tip geometry, illumination directions and tip materials (Ag, Au, Al and Cu). Compared with a simplified inverted microscope configuration, the PM setup shows an increased field enhancement (factor of 2–2.5), which can be ascribed to the efficient coupling of the exciting field to tip surface plasmons.

© 2013 OSA

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  1. B. Knoll and F. Keilmann, “Near-field probing of vibrational absorption for chemical microscopy,” Nature399, 134–137 (1999).
    [CrossRef]
  2. R. M. Stöckle, Y. D. Suh, V. Deckert, and R. Zenobi, “Nanoscale chemical analysis by tip-enhanced raman spectroscopy,” Chem. Phys. Lett.318, 131–136 (2000).
    [CrossRef]
  3. L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University Press, 2006).
    [CrossRef]
  4. 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]
  5. A. Hartschuh, “Tip-enhanced near-field optical microscopy,” Angew. Chem. Int. Ed.47, 8178–8191 (2008).
    [CrossRef]
  6. D. Zhang, X. Wang, K. Braun, H.-J. Egelhaaf, M. Fleischer, L. Hennemann, H. Hintz, C. Stanciu, C. J. Brabec, D. P. Kern, and A. J. Meixner, “Parabolic mirror-assisted tip-enhanced spectroscopic imaging for non-transparent materials,” J. Raman Spectrosc.40, 1371–1376 (2009).
    [CrossRef]
  7. M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett.93, 137404 (2004).
    [CrossRef] [PubMed]
  8. C. Ropers, C. C. Neacsu, T. Elsaesser, M. Albrecht, M. B. Raschke, and C. Lienau, “Grating-coupling of surface plasmons onto metallic tips: A nanoconfined light source,” Nano Lett.7, 2784–2788 (2007). PMID: .
    [CrossRef] [PubMed]
  9. F. Baida and A. Belkhir, “Superfocusing and light confinement by surface plasmon excitation through radially polarized beam,” Plasmonics4, 51–59 (2009).
    [CrossRef]
  10. X.-W. Chen, V. Sandoghdar, and M. Agio, “Highly efficient interfacing of guided plasmons and photons in nanowires,” Nano Lett.9, 3756–3761 (2009). PMID: .
    [CrossRef] [PubMed]
  11. J. S. Lee, S. Han, J. Shirdel, S. Koo, D. Sadiq, C. Lienau, and N. Park, “Superfocusing of electric or magnetic fields using conical metal tips: effect of mode symmetry on the plasmon excitation method,” Opt. Express19, 12342–12347 (2011).
    [CrossRef] [PubMed]
  12. H. G. Frey, C. Bolwien, A. Brandenburg, R. Ros, and D. Anselmetti, “Optimized apertureless optical near-field probes with 15 nm optical resolution,” Nanotechnology17, 3105 (2006).
    [CrossRef]
  13. W. Ding, S. R. Andrews, and S. A. Maier, “Internal excitation and superfocusing of surface plasmon polaritons on a silver-coated optical fiber tip,” Phys. Rev. A75, 063822 (2007).
    [CrossRef]
  14. J. Barthes, G. C. des Francs, A. Bouhelier, and A. Dereux, “A coupled lossy local-mode theory description of a plasmonic tip,” New J. Phys.14, 083041 (2012).
    [CrossRef]
  15. L. Novotny, R. X. Bian, and X. S. Xie, “Theory of nanometric optical tweezers,” Phys. Rev. Lett.79, 645–648 (1997).
    [CrossRef]
  16. M. Lieb and A. Meixner, “A high numerical aperture parabolic mirror as imaging device for confocal microscopy,” Opt. Express8, 458–474 (2001).
    [CrossRef] [PubMed]
  17. S. Quabis, R. Dorn, M. Eberler, O. Glckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt Commun179, 1–7 (2000).
    [CrossRef]
  18. J. Stadler, C. Stanciu, C. Stupperich, and A. J. Meixner, “Tighter focusing with a parabolic mirror,” Opt. Lett.33, 681–683 (2008).
    [CrossRef] [PubMed]
  19. O. J. F. Martin and C. Girard, “Controlling and tuning strong optical field gradients at a local probe microscope tip apex,” Appl. Phys. Lett.70, 705–707 (1997).
    [CrossRef]
  20. J. T. Krug, E. J. Sanchez, and X. S. Xie, “Design of near-field optical probes with optimal field enhancement by finite difference time domain electromagnetic simulation,” J. Chem. Phys.116, 10895–10901 (2002).
    [CrossRef]
  21. A. L. Demming, F. Festy, and D. Richards, “Plasmon resonances on metal tips: Understanding tip-enhanced raman scattering,” J. Chem. Phys.122, 184716 (2005).
    [CrossRef] [PubMed]
  22. R. Esteban, R. Vogelgesang, and K. Kern, “Simulation of optical near and far fields of dielectric apertureless scanning probes,” Nanotechnology17, 475 (2006).
    [CrossRef]
  23. D. Zhang, U. Heinemeyer, C. Stanciu, M. Sackrow, K. Braun, L. E. Hennemann, X. Wang, R. Scholz, F. Schreiber, and A. J. Meixner, “Nanoscale spectroscopic imaging of organic semiconductor films by plasmonpolariton coupling,” Phys. Rev. Lett.104, 056601 (2010).
    [CrossRef]
  24. J. Stadler, B. Oswald, T. Schmid, and R. Zenobi, “Characterizing unusual metal substrates for gap-mode tip-enhanced raman spectroscopy,” J. Raman Spectrosc.44, 227–233 (2013).
    [CrossRef]
  25. W. Zhang, X. Cui, and O. J. F. Martin, “Local field enhancement of an infinite conical metal tip illuminated by a focused beam,” J. Raman Spectrosc.40, 1338–1342 (2009).
    [CrossRef]
  26. N. A. Issa and R. Guckenberger, “Fluorescence near metal tips: The roles of energy transfer and surface plasmon polaritons,” Opt. Express15, 12131–12144 (2007).
    [CrossRef] [PubMed]
  27. C. Hafner, MaX-1: A Visual Electromagnetics Platform for PCs (Wiley, 1998).
  28. C. Hafner, Post-Modern Electromagnetics Using Intelligent MaXwell Solvers (Wiley, ChichesterUK, 1999).
  29. C. Hafner, “Openmax: Graphic platform for computational electromagnetics and computational optics,” http://openmax.ethz.ch/ , ETH Zürich (2013).
  30. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6, 4370–4379 (1972).
    [CrossRef]
  31. J. Weaver and H. Frederikse, “Optical Properties of Selected Elements” (CRC Handbook of Chemistry and Physics, CRC Press, Boca Raton, 2001), pp. 116–133.
  32. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York and London, 1941).
  33. A. Sommerfeld, “Ueber die fortpflanzung elektrodynamischer wellen längs eines drahtes,” Ann. Phys.303, 233–290 (1899).
    [CrossRef]
  34. D. Hondros, “über elektromagnetische drahtwellen,” Ann. Phys.335, 905–950 (1909).
    [CrossRef]
  35. J. Ashley and L. Emerson, “Dispersion relations for non-radiative surface plasmons on cylinders,” Surface Science41, 615–618 (1974).
    [CrossRef]
  36. C. A. Pfeiffer, E. N. Economou, and K. L. Ngai, “Surface polaritons in a circularly cylindrical interface: Surface plasmons,” Phys. Rev. B10, 3038–3051 (1974).
    [CrossRef]
  37. A. Boag and R. Mittra, “Complex multipole-beam approach to three-dimensional electromagnetic scattering problems,” J. Opt. Soc. Am. A11, 1505–1512 (1994).
    [CrossRef]
  38. J. S. Ch. Hafner and M. Agio, “Numerical methods for the electrodynamic analysis of nanostructures,” in “Nanoclusters and Nanostructured Surfaces,” A. K. Ray, ed. (American Scientific Publishers: Valencia, CA, 2010).
  39. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. ii. structure of the image field in an aplanatic system,” Proc. R. Soc. A253, 358–379 (1959).
    [CrossRef]
  40. C. J. R. Sheppard and P. Török, “Efficient calculation of electromagnetic diffraction in optical systems using a multipole expansion,” J. Mod. Opt.44, 803–818 (1997).
    [CrossRef]
  41. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1998).
  42. J. Stamnes, Waves in Focal Regions (Taylor & Francis, 1986).
  43. G. Arfken and H. J. Weber, “Mathematical methods for physicists,” (2005).
  44. C. Debus, M. A. Lieb, A. Drechsler, and A. J. Meixner, “Probing highly confined optical fields in the focal region of a high na parabolic mirror with subwavelength spatial resolution,” J. Microsc.210, 203–208(6) (June2003).
    [CrossRef] [PubMed]
  45. B. C. Brock, “Using vector spherical harmonics to compute antenna mutual impedance from measured or computed fields,” Sandia report, SAND2000-2217-Revised. Sandia National Laboratories, Albuquerque, NM (2001).
  46. J. J. Moré, B. S. Garbow, and K. E. Hillstrom, “The minpack project,” Sources and Development of Mathematical Software88–111 (1984).
  47. T. H. Taminiau, F. D. Stefani, and N. F. van Hulst, “Enhanced directional excitation and emission of single emitters by a nano-optical yagi-uda antenna,” Opt. Express16, 10858–10866 (2008).
    [CrossRef] [PubMed]
  48. A. Alparslan and C. Hafner, “Analysis of photonic structures by the multiple multipole program with complex origin layered geometry green’s functions,” J. Comput. Theor. Nanos.9, 479–485 (2012).
    [CrossRef]
  49. P. F. Liao and A. Wokaun, “Lightning rod effect in surface enhanced raman scattering,” J. Chem. Phys.76, 751–752 (1982).
    [CrossRef]
  50. P. Biagioni, J.-S. Huang, and B. Hecht, “Nanoantennas for visible and infrared radiation,” Rep. Prog. Phys.75, 024402 (2012).
    [CrossRef] [PubMed]

2013 (1)

J. Stadler, B. Oswald, T. Schmid, and R. Zenobi, “Characterizing unusual metal substrates for gap-mode tip-enhanced raman spectroscopy,” J. Raman Spectrosc.44, 227–233 (2013).
[CrossRef]

2012 (3)

J. Barthes, G. C. des Francs, A. Bouhelier, and A. Dereux, “A coupled lossy local-mode theory description of a plasmonic tip,” New J. Phys.14, 083041 (2012).
[CrossRef]

A. Alparslan and C. Hafner, “Analysis of photonic structures by the multiple multipole program with complex origin layered geometry green’s functions,” J. Comput. Theor. Nanos.9, 479–485 (2012).
[CrossRef]

P. Biagioni, J.-S. Huang, and B. Hecht, “Nanoantennas for visible and infrared radiation,” Rep. Prog. Phys.75, 024402 (2012).
[CrossRef] [PubMed]

2011 (1)

2010 (1)

D. Zhang, U. Heinemeyer, C. Stanciu, M. Sackrow, K. Braun, L. E. Hennemann, X. Wang, R. Scholz, F. Schreiber, and A. J. Meixner, “Nanoscale spectroscopic imaging of organic semiconductor films by plasmonpolariton coupling,” Phys. Rev. Lett.104, 056601 (2010).
[CrossRef]

2009 (4)

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

D. Zhang, X. Wang, K. Braun, H.-J. Egelhaaf, M. Fleischer, L. Hennemann, H. Hintz, C. Stanciu, C. J. Brabec, D. P. Kern, and A. J. Meixner, “Parabolic mirror-assisted tip-enhanced spectroscopic imaging for non-transparent materials,” J. Raman Spectrosc.40, 1371–1376 (2009).
[CrossRef]

F. Baida and A. Belkhir, “Superfocusing and light confinement by surface plasmon excitation through radially polarized beam,” Plasmonics4, 51–59 (2009).
[CrossRef]

X.-W. Chen, V. Sandoghdar, and M. Agio, “Highly efficient interfacing of guided plasmons and photons in nanowires,” Nano Lett.9, 3756–3761 (2009). PMID: .
[CrossRef] [PubMed]

2008 (3)

2007 (3)

N. A. Issa and R. Guckenberger, “Fluorescence near metal tips: The roles of energy transfer and surface plasmon polaritons,” Opt. Express15, 12131–12144 (2007).
[CrossRef] [PubMed]

C. Ropers, C. C. Neacsu, T. Elsaesser, M. Albrecht, M. B. Raschke, and C. Lienau, “Grating-coupling of surface plasmons onto metallic tips: A nanoconfined light source,” Nano Lett.7, 2784–2788 (2007). PMID: .
[CrossRef] [PubMed]

W. Ding, S. R. Andrews, and S. A. Maier, “Internal excitation and superfocusing of surface plasmon polaritons on a silver-coated optical fiber tip,” Phys. Rev. A75, 063822 (2007).
[CrossRef]

2006 (2)

H. G. Frey, C. Bolwien, A. Brandenburg, R. Ros, and D. Anselmetti, “Optimized apertureless optical near-field probes with 15 nm optical resolution,” Nanotechnology17, 3105 (2006).
[CrossRef]

R. Esteban, R. Vogelgesang, and K. Kern, “Simulation of optical near and far fields of dielectric apertureless scanning probes,” Nanotechnology17, 475 (2006).
[CrossRef]

2005 (2)

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

2004 (1)

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

2003 (1)

C. Debus, M. A. Lieb, A. Drechsler, and A. J. Meixner, “Probing highly confined optical fields in the focal region of a high na parabolic mirror with subwavelength spatial resolution,” J. Microsc.210, 203–208(6) (June2003).
[CrossRef] [PubMed]

2002 (1)

J. T. Krug, E. J. Sanchez, and X. S. Xie, “Design of near-field optical probes with optimal field enhancement by finite difference time domain electromagnetic simulation,” J. Chem. Phys.116, 10895–10901 (2002).
[CrossRef]

2001 (1)

2000 (2)

S. Quabis, R. Dorn, M. Eberler, O. Glckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt Commun179, 1–7 (2000).
[CrossRef]

R. M. Stöckle, Y. D. Suh, V. Deckert, and R. Zenobi, “Nanoscale chemical analysis by tip-enhanced raman spectroscopy,” Chem. Phys. Lett.318, 131–136 (2000).
[CrossRef]

1999 (1)

B. Knoll and F. Keilmann, “Near-field probing of vibrational absorption for chemical microscopy,” Nature399, 134–137 (1999).
[CrossRef]

1997 (3)

L. Novotny, R. X. Bian, and X. S. Xie, “Theory of nanometric optical tweezers,” Phys. Rev. Lett.79, 645–648 (1997).
[CrossRef]

O. J. F. Martin and C. Girard, “Controlling and tuning strong optical field gradients at a local probe microscope tip apex,” Appl. Phys. Lett.70, 705–707 (1997).
[CrossRef]

C. J. R. Sheppard and P. Török, “Efficient calculation of electromagnetic diffraction in optical systems using a multipole expansion,” J. Mod. Opt.44, 803–818 (1997).
[CrossRef]

1994 (1)

1984 (1)

J. J. Moré, B. S. Garbow, and K. E. Hillstrom, “The minpack project,” Sources and Development of Mathematical Software88–111 (1984).

1982 (1)

P. F. Liao and A. Wokaun, “Lightning rod effect in surface enhanced raman scattering,” J. Chem. Phys.76, 751–752 (1982).
[CrossRef]

1974 (2)

J. Ashley and L. Emerson, “Dispersion relations for non-radiative surface plasmons on cylinders,” Surface Science41, 615–618 (1974).
[CrossRef]

C. A. Pfeiffer, E. N. Economou, and K. L. Ngai, “Surface polaritons in a circularly cylindrical interface: Surface plasmons,” Phys. Rev. B10, 3038–3051 (1974).
[CrossRef]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6, 4370–4379 (1972).
[CrossRef]

1959 (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. ii. structure of the image field in an aplanatic system,” Proc. R. Soc. A253, 358–379 (1959).
[CrossRef]

1909 (1)

D. Hondros, “über elektromagnetische drahtwellen,” Ann. Phys.335, 905–950 (1909).
[CrossRef]

1899 (1)

A. Sommerfeld, “Ueber die fortpflanzung elektrodynamischer wellen längs eines drahtes,” Ann. Phys.303, 233–290 (1899).
[CrossRef]

Agio, M.

X.-W. Chen, V. Sandoghdar, and M. Agio, “Highly efficient interfacing of guided plasmons and photons in nanowires,” Nano Lett.9, 3756–3761 (2009). PMID: .
[CrossRef] [PubMed]

J. S. Ch. Hafner and M. Agio, “Numerical methods for the electrodynamic analysis of nanostructures,” in “Nanoclusters and Nanostructured Surfaces,” A. K. Ray, ed. (American Scientific Publishers: Valencia, CA, 2010).

Albrecht, M.

C. Ropers, C. C. Neacsu, T. Elsaesser, M. Albrecht, M. B. Raschke, and C. Lienau, “Grating-coupling of surface plasmons onto metallic tips: A nanoconfined light source,” Nano Lett.7, 2784–2788 (2007). PMID: .
[CrossRef] [PubMed]

Alparslan, A.

A. Alparslan and C. Hafner, “Analysis of photonic structures by the multiple multipole program with complex origin layered geometry green’s functions,” J. Comput. Theor. Nanos.9, 479–485 (2012).
[CrossRef]

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]

Andrews, S. R.

W. Ding, S. R. Andrews, and S. A. Maier, “Internal excitation and superfocusing of surface plasmon polaritons on a silver-coated optical fiber tip,” Phys. Rev. A75, 063822 (2007).
[CrossRef]

Anselmetti, D.

H. G. Frey, C. Bolwien, A. Brandenburg, R. Ros, and D. Anselmetti, “Optimized apertureless optical near-field probes with 15 nm optical resolution,” Nanotechnology17, 3105 (2006).
[CrossRef]

Arfken, G.

G. Arfken and H. J. Weber, “Mathematical methods for physicists,” (2005).

Ashley, J.

J. Ashley and L. Emerson, “Dispersion relations for non-radiative surface plasmons on cylinders,” Surface Science41, 615–618 (1974).
[CrossRef]

Baida, F.

F. Baida and A. Belkhir, “Superfocusing and light confinement by surface plasmon excitation through radially polarized beam,” Plasmonics4, 51–59 (2009).
[CrossRef]

Barthes, J.

J. Barthes, G. C. des Francs, A. Bouhelier, and A. Dereux, “A coupled lossy local-mode theory description of a plasmonic tip,” New J. Phys.14, 083041 (2012).
[CrossRef]

Belkhir, A.

F. Baida and A. Belkhir, “Superfocusing and light confinement by surface plasmon excitation through radially polarized beam,” Plasmonics4, 51–59 (2009).
[CrossRef]

Biagioni, P.

P. Biagioni, J.-S. Huang, and B. Hecht, “Nanoantennas for visible and infrared radiation,” Rep. Prog. Phys.75, 024402 (2012).
[CrossRef] [PubMed]

Bian, R. X.

L. Novotny, R. X. Bian, and X. S. Xie, “Theory of nanometric optical tweezers,” Phys. Rev. Lett.79, 645–648 (1997).
[CrossRef]

Boag, A.

Bolwien, C.

H. G. Frey, C. Bolwien, A. Brandenburg, R. Ros, and D. Anselmetti, “Optimized apertureless optical near-field probes with 15 nm optical resolution,” Nanotechnology17, 3105 (2006).
[CrossRef]

Bouhelier, A.

J. Barthes, G. C. des Francs, A. Bouhelier, and A. Dereux, “A coupled lossy local-mode theory description of a plasmonic tip,” New J. Phys.14, 083041 (2012).
[CrossRef]

Brabec, C. J.

D. Zhang, X. Wang, K. Braun, H.-J. Egelhaaf, M. Fleischer, L. Hennemann, H. Hintz, C. Stanciu, C. J. Brabec, D. P. Kern, and A. J. Meixner, “Parabolic mirror-assisted tip-enhanced spectroscopic imaging for non-transparent materials,” J. Raman Spectrosc.40, 1371–1376 (2009).
[CrossRef]

Brandenburg, A.

H. G. Frey, C. Bolwien, A. Brandenburg, R. Ros, and D. Anselmetti, “Optimized apertureless optical near-field probes with 15 nm optical resolution,” Nanotechnology17, 3105 (2006).
[CrossRef]

Braun, K.

D. Zhang, U. Heinemeyer, C. Stanciu, M. Sackrow, K. Braun, L. E. Hennemann, X. Wang, R. Scholz, F. Schreiber, and A. J. Meixner, “Nanoscale spectroscopic imaging of organic semiconductor films by plasmonpolariton coupling,” Phys. Rev. Lett.104, 056601 (2010).
[CrossRef]

D. Zhang, X. Wang, K. Braun, H.-J. Egelhaaf, M. Fleischer, L. Hennemann, H. Hintz, C. Stanciu, C. J. Brabec, D. P. Kern, and A. J. Meixner, “Parabolic mirror-assisted tip-enhanced spectroscopic imaging for non-transparent materials,” J. Raman Spectrosc.40, 1371–1376 (2009).
[CrossRef]

Brock, B. C.

B. C. Brock, “Using vector spherical harmonics to compute antenna mutual impedance from measured or computed fields,” Sandia report, SAND2000-2217-Revised. Sandia National Laboratories, Albuquerque, NM (2001).

Chen, X.-W.

X.-W. Chen, V. Sandoghdar, and M. Agio, “Highly efficient interfacing of guided plasmons and photons in nanowires,” Nano Lett.9, 3756–3761 (2009). PMID: .
[CrossRef] [PubMed]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6, 4370–4379 (1972).
[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.

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

Debus, C.

C. Debus, M. A. Lieb, A. Drechsler, and A. J. Meixner, “Probing highly confined optical fields in the focal region of a high na parabolic mirror with subwavelength spatial resolution,” J. Microsc.210, 203–208(6) (June2003).
[CrossRef] [PubMed]

Deckert, V.

R. M. Stöckle, Y. D. Suh, V. Deckert, and R. Zenobi, “Nanoscale chemical analysis by tip-enhanced raman spectroscopy,” Chem. Phys. Lett.318, 131–136 (2000).
[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 (2005).
[CrossRef] [PubMed]

Dereux, A.

J. Barthes, G. C. des Francs, A. Bouhelier, and A. Dereux, “A coupled lossy local-mode theory description of a plasmonic tip,” New J. Phys.14, 083041 (2012).
[CrossRef]

des Francs, G. C.

J. Barthes, G. C. des Francs, A. Bouhelier, and A. Dereux, “A coupled lossy local-mode theory description of a plasmonic tip,” New J. Phys.14, 083041 (2012).
[CrossRef]

Ding, W.

W. Ding, S. R. Andrews, and S. A. Maier, “Internal excitation and superfocusing of surface plasmon polaritons on a silver-coated optical fiber tip,” Phys. Rev. A75, 063822 (2007).
[CrossRef]

Dorn, R.

S. Quabis, R. Dorn, M. Eberler, O. Glckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt Commun179, 1–7 (2000).
[CrossRef]

Drechsler, A.

C. Debus, M. A. Lieb, A. Drechsler, and A. J. Meixner, “Probing highly confined optical fields in the focal region of a high na parabolic mirror with subwavelength spatial resolution,” J. Microsc.210, 203–208(6) (June2003).
[CrossRef] [PubMed]

Eberler, M.

S. Quabis, R. Dorn, M. Eberler, O. Glckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt Commun179, 1–7 (2000).
[CrossRef]

Economou, E. N.

C. A. Pfeiffer, E. N. Economou, and K. L. Ngai, “Surface polaritons in a circularly cylindrical interface: Surface plasmons,” Phys. Rev. B10, 3038–3051 (1974).
[CrossRef]

Egelhaaf, H.-J.

D. Zhang, X. Wang, K. Braun, H.-J. Egelhaaf, M. Fleischer, L. Hennemann, H. Hintz, C. Stanciu, C. J. Brabec, D. P. Kern, and A. J. Meixner, “Parabolic mirror-assisted tip-enhanced spectroscopic imaging for non-transparent materials,” J. Raman Spectrosc.40, 1371–1376 (2009).
[CrossRef]

Elsaesser, T.

C. Ropers, C. C. Neacsu, T. Elsaesser, M. Albrecht, M. B. Raschke, and C. Lienau, “Grating-coupling of surface plasmons onto metallic tips: A nanoconfined light source,” Nano Lett.7, 2784–2788 (2007). PMID: .
[CrossRef] [PubMed]

Emerson, L.

J. Ashley and L. Emerson, “Dispersion relations for non-radiative surface plasmons on cylinders,” Surface Science41, 615–618 (1974).
[CrossRef]

Esteban, R.

R. Esteban, R. Vogelgesang, and K. Kern, “Simulation of optical near and far fields of dielectric apertureless scanning probes,” Nanotechnology17, 475 (2006).
[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 (2005).
[CrossRef] [PubMed]

Fleischer, M.

D. Zhang, X. Wang, K. Braun, H.-J. Egelhaaf, M. Fleischer, L. Hennemann, H. Hintz, C. Stanciu, C. J. Brabec, D. P. Kern, and A. J. Meixner, “Parabolic mirror-assisted tip-enhanced spectroscopic imaging for non-transparent materials,” J. Raman Spectrosc.40, 1371–1376 (2009).
[CrossRef]

Frederikse, H.

J. Weaver and H. Frederikse, “Optical Properties of Selected Elements” (CRC Handbook of Chemistry and Physics, CRC Press, Boca Raton, 2001), pp. 116–133.

Frey, H. G.

H. G. Frey, C. Bolwien, A. Brandenburg, R. Ros, and D. Anselmetti, “Optimized apertureless optical near-field probes with 15 nm optical resolution,” Nanotechnology17, 3105 (2006).
[CrossRef]

Garbow, B. S.

J. J. Moré, B. S. Garbow, and K. E. Hillstrom, “The minpack project,” Sources and Development of Mathematical Software88–111 (1984).

Girard, C.

O. J. F. Martin and C. Girard, “Controlling and tuning strong optical field gradients at a local probe microscope tip apex,” Appl. Phys. Lett.70, 705–707 (1997).
[CrossRef]

Glckl, O.

S. Quabis, R. Dorn, M. Eberler, O. Glckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt Commun179, 1–7 (2000).
[CrossRef]

Guckenberger, R.

Hafner, C.

A. Alparslan and C. Hafner, “Analysis of photonic structures by the multiple multipole program with complex origin layered geometry green’s functions,” J. Comput. Theor. Nanos.9, 479–485 (2012).
[CrossRef]

C. Hafner, MaX-1: A Visual Electromagnetics Platform for PCs (Wiley, 1998).

C. Hafner, Post-Modern Electromagnetics Using Intelligent MaXwell Solvers (Wiley, ChichesterUK, 1999).

Hafner, J. S. Ch.

J. S. Ch. Hafner and M. Agio, “Numerical methods for the electrodynamic analysis of nanostructures,” in “Nanoclusters and Nanostructured Surfaces,” A. K. Ray, ed. (American Scientific Publishers: Valencia, CA, 2010).

Han, S.

Hartschuh, A.

A. Hartschuh, “Tip-enhanced near-field optical microscopy,” Angew. Chem. Int. Ed.47, 8178–8191 (2008).
[CrossRef]

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]

Hecht, B.

P. Biagioni, J.-S. Huang, and B. Hecht, “Nanoantennas for visible and infrared radiation,” Rep. Prog. Phys.75, 024402 (2012).
[CrossRef] [PubMed]

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University Press, 2006).
[CrossRef]

Heinemeyer, U.

D. Zhang, U. Heinemeyer, C. Stanciu, M. Sackrow, K. Braun, L. E. Hennemann, X. Wang, R. Scholz, F. Schreiber, and A. J. Meixner, “Nanoscale spectroscopic imaging of organic semiconductor films by plasmonpolariton coupling,” Phys. Rev. Lett.104, 056601 (2010).
[CrossRef]

Hennemann, L.

D. Zhang, X. Wang, K. Braun, H.-J. Egelhaaf, M. Fleischer, L. Hennemann, H. Hintz, C. Stanciu, C. J. Brabec, D. P. Kern, and A. J. Meixner, “Parabolic mirror-assisted tip-enhanced spectroscopic imaging for non-transparent materials,” J. Raman Spectrosc.40, 1371–1376 (2009).
[CrossRef]

Hennemann, L. E.

D. Zhang, U. Heinemeyer, C. Stanciu, M. Sackrow, K. Braun, L. E. Hennemann, X. Wang, R. Scholz, F. Schreiber, and A. J. Meixner, “Nanoscale spectroscopic imaging of organic semiconductor films by plasmonpolariton coupling,” Phys. Rev. Lett.104, 056601 (2010).
[CrossRef]

Hillstrom, K. E.

J. J. Moré, B. S. Garbow, and K. E. Hillstrom, “The minpack project,” Sources and Development of Mathematical Software88–111 (1984).

Hintz, H.

D. Zhang, X. Wang, K. Braun, H.-J. Egelhaaf, M. Fleischer, L. Hennemann, H. Hintz, C. Stanciu, C. J. Brabec, D. P. Kern, and A. J. Meixner, “Parabolic mirror-assisted tip-enhanced spectroscopic imaging for non-transparent materials,” J. Raman Spectrosc.40, 1371–1376 (2009).
[CrossRef]

Hondros, D.

D. Hondros, “über elektromagnetische drahtwellen,” Ann. Phys.335, 905–950 (1909).
[CrossRef]

Huang, J.-S.

P. Biagioni, J.-S. Huang, and B. Hecht, “Nanoantennas for visible and infrared radiation,” Rep. Prog. Phys.75, 024402 (2012).
[CrossRef] [PubMed]

Issa, N. A.

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1998).

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6, 4370–4379 (1972).
[CrossRef]

Keilmann, F.

B. Knoll and F. Keilmann, “Near-field probing of vibrational absorption for chemical microscopy,” Nature399, 134–137 (1999).
[CrossRef]

Kern, D. P.

D. Zhang, X. Wang, K. Braun, H.-J. Egelhaaf, M. Fleischer, L. Hennemann, H. Hintz, C. Stanciu, C. J. Brabec, D. P. Kern, and A. J. Meixner, “Parabolic mirror-assisted tip-enhanced spectroscopic imaging for non-transparent materials,” J. Raman Spectrosc.40, 1371–1376 (2009).
[CrossRef]

Kern, K.

R. Esteban, R. Vogelgesang, and K. Kern, “Simulation of optical near and far fields of dielectric apertureless scanning probes,” Nanotechnology17, 475 (2006).
[CrossRef]

Knoll, B.

B. Knoll and F. Keilmann, “Near-field probing of vibrational absorption for chemical microscopy,” Nature399, 134–137 (1999).
[CrossRef]

Koo, S.

Krug, J. T.

J. T. Krug, E. J. Sanchez, and X. S. Xie, “Design of near-field optical probes with optimal field enhancement by finite difference time domain electromagnetic simulation,” J. Chem. Phys.116, 10895–10901 (2002).
[CrossRef]

Lee, J. S.

Leuchs, G.

S. Quabis, R. Dorn, M. Eberler, O. Glckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt Commun179, 1–7 (2000).
[CrossRef]

Liao, P. F.

P. F. Liao and A. Wokaun, “Lightning rod effect in surface enhanced raman scattering,” J. Chem. Phys.76, 751–752 (1982).
[CrossRef]

Lieb, M.

Lieb, M. A.

C. Debus, M. A. Lieb, A. Drechsler, and A. J. Meixner, “Probing highly confined optical fields in the focal region of a high na parabolic mirror with subwavelength spatial resolution,” J. Microsc.210, 203–208(6) (June2003).
[CrossRef] [PubMed]

Lienau, C.

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

C. Ropers, C. C. Neacsu, T. Elsaesser, M. Albrecht, M. B. Raschke, and C. Lienau, “Grating-coupling of surface plasmons onto metallic tips: A nanoconfined light source,” Nano Lett.7, 2784–2788 (2007). PMID: .
[CrossRef] [PubMed]

Maier, S. A.

W. Ding, S. R. Andrews, and S. A. Maier, “Internal excitation and superfocusing of surface plasmon polaritons on a silver-coated optical fiber tip,” Phys. Rev. A75, 063822 (2007).
[CrossRef]

Martin, O. J. F.

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

O. J. F. Martin and C. Girard, “Controlling and tuning strong optical field gradients at a local probe microscope tip apex,” Appl. Phys. Lett.70, 705–707 (1997).
[CrossRef]

Meixner, A.

Meixner, A. J.

D. Zhang, U. Heinemeyer, C. Stanciu, M. Sackrow, K. Braun, L. E. Hennemann, X. Wang, R. Scholz, F. Schreiber, and A. J. Meixner, “Nanoscale spectroscopic imaging of organic semiconductor films by plasmonpolariton coupling,” Phys. Rev. Lett.104, 056601 (2010).
[CrossRef]

D. Zhang, X. Wang, K. Braun, H.-J. Egelhaaf, M. Fleischer, L. Hennemann, H. Hintz, C. Stanciu, C. J. Brabec, D. P. Kern, and A. J. Meixner, “Parabolic mirror-assisted tip-enhanced spectroscopic imaging for non-transparent materials,” J. Raman Spectrosc.40, 1371–1376 (2009).
[CrossRef]

J. Stadler, C. Stanciu, C. Stupperich, and A. J. Meixner, “Tighter focusing with a parabolic mirror,” Opt. Lett.33, 681–683 (2008).
[CrossRef] [PubMed]

C. Debus, M. A. Lieb, A. Drechsler, and A. J. Meixner, “Probing highly confined optical fields in the focal region of a high na parabolic mirror with subwavelength spatial resolution,” J. Microsc.210, 203–208(6) (June2003).
[CrossRef] [PubMed]

Mittra, R.

Moré, J. J.

J. J. Moré, B. S. Garbow, and K. E. Hillstrom, “The minpack project,” Sources and Development of Mathematical Software88–111 (1984).

Neacsu, C. C.

C. Ropers, C. C. Neacsu, T. Elsaesser, M. Albrecht, M. B. Raschke, and C. Lienau, “Grating-coupling of surface plasmons onto metallic tips: A nanoconfined light source,” Nano Lett.7, 2784–2788 (2007). PMID: .
[CrossRef] [PubMed]

Ngai, K. L.

C. A. Pfeiffer, E. N. Economou, and K. L. Ngai, “Surface polaritons in a circularly cylindrical interface: Surface plasmons,” Phys. Rev. B10, 3038–3051 (1974).
[CrossRef]

Novotny, L.

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]

L. Novotny, R. X. Bian, and X. S. Xie, “Theory of nanometric optical tweezers,” Phys. Rev. Lett.79, 645–648 (1997).
[CrossRef]

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University Press, 2006).
[CrossRef]

Oswald, B.

J. Stadler, B. Oswald, T. Schmid, and R. Zenobi, “Characterizing unusual metal substrates for gap-mode tip-enhanced raman spectroscopy,” J. Raman Spectrosc.44, 227–233 (2013).
[CrossRef]

Park, N.

Pfeiffer, C. A.

C. A. Pfeiffer, E. N. Economou, and K. L. Ngai, “Surface polaritons in a circularly cylindrical interface: Surface plasmons,” Phys. Rev. B10, 3038–3051 (1974).
[CrossRef]

Quabis, S.

S. Quabis, R. Dorn, M. Eberler, O. Glckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt Commun179, 1–7 (2000).
[CrossRef]

Raschke, M. B.

C. Ropers, C. C. Neacsu, T. Elsaesser, M. Albrecht, M. B. Raschke, and C. Lienau, “Grating-coupling of surface plasmons onto metallic tips: A nanoconfined light source,” Nano Lett.7, 2784–2788 (2007). PMID: .
[CrossRef] [PubMed]

Richards, B.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. ii. structure of the image field in an aplanatic system,” Proc. R. Soc. A253, 358–379 (1959).
[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 (2005).
[CrossRef] [PubMed]

Ropers, C.

C. Ropers, C. C. Neacsu, T. Elsaesser, M. Albrecht, M. B. Raschke, and C. Lienau, “Grating-coupling of surface plasmons onto metallic tips: A nanoconfined light source,” Nano Lett.7, 2784–2788 (2007). PMID: .
[CrossRef] [PubMed]

Ros, R.

H. G. Frey, C. Bolwien, A. Brandenburg, R. Ros, and D. Anselmetti, “Optimized apertureless optical near-field probes with 15 nm optical resolution,” Nanotechnology17, 3105 (2006).
[CrossRef]

Sackrow, M.

D. Zhang, U. Heinemeyer, C. Stanciu, M. Sackrow, K. Braun, L. E. Hennemann, X. Wang, R. Scholz, F. Schreiber, and A. J. Meixner, “Nanoscale spectroscopic imaging of organic semiconductor films by plasmonpolariton coupling,” Phys. Rev. Lett.104, 056601 (2010).
[CrossRef]

Sadiq, D.

Sanchez, E. J.

J. T. Krug, E. J. Sanchez, and X. S. Xie, “Design of near-field optical probes with optimal field enhancement by finite difference time domain electromagnetic simulation,” J. Chem. Phys.116, 10895–10901 (2002).
[CrossRef]

Sandoghdar, V.

X.-W. Chen, V. Sandoghdar, and M. Agio, “Highly efficient interfacing of guided plasmons and photons in nanowires,” Nano Lett.9, 3756–3761 (2009). PMID: .
[CrossRef] [PubMed]

Schmid, T.

J. Stadler, B. Oswald, T. Schmid, and R. Zenobi, “Characterizing unusual metal substrates for gap-mode tip-enhanced raman spectroscopy,” J. Raman Spectrosc.44, 227–233 (2013).
[CrossRef]

Scholz, R.

D. Zhang, U. Heinemeyer, C. Stanciu, M. Sackrow, K. Braun, L. E. Hennemann, X. Wang, R. Scholz, F. Schreiber, and A. J. Meixner, “Nanoscale spectroscopic imaging of organic semiconductor films by plasmonpolariton coupling,” Phys. Rev. Lett.104, 056601 (2010).
[CrossRef]

Schreiber, F.

D. Zhang, U. Heinemeyer, C. Stanciu, M. Sackrow, K. Braun, L. E. Hennemann, X. Wang, R. Scholz, F. Schreiber, and A. J. Meixner, “Nanoscale spectroscopic imaging of organic semiconductor films by plasmonpolariton coupling,” Phys. Rev. Lett.104, 056601 (2010).
[CrossRef]

Sheppard, C. J. R.

C. J. R. Sheppard and P. Török, “Efficient calculation of electromagnetic diffraction in optical systems using a multipole expansion,” J. Mod. Opt.44, 803–818 (1997).
[CrossRef]

Shirdel, J.

Sommerfeld, A.

A. Sommerfeld, “Ueber die fortpflanzung elektrodynamischer wellen längs eines drahtes,” Ann. Phys.303, 233–290 (1899).
[CrossRef]

Stadler, J.

J. Stadler, B. Oswald, T. Schmid, and R. Zenobi, “Characterizing unusual metal substrates for gap-mode tip-enhanced raman spectroscopy,” J. Raman Spectrosc.44, 227–233 (2013).
[CrossRef]

J. Stadler, C. Stanciu, C. Stupperich, and A. J. Meixner, “Tighter focusing with a parabolic mirror,” Opt. Lett.33, 681–683 (2008).
[CrossRef] [PubMed]

Stamnes, J.

J. Stamnes, Waves in Focal Regions (Taylor & Francis, 1986).

Stanciu, C.

D. Zhang, U. Heinemeyer, C. Stanciu, M. Sackrow, K. Braun, L. E. Hennemann, X. Wang, R. Scholz, F. Schreiber, and A. J. Meixner, “Nanoscale spectroscopic imaging of organic semiconductor films by plasmonpolariton coupling,” Phys. Rev. Lett.104, 056601 (2010).
[CrossRef]

D. Zhang, X. Wang, K. Braun, H.-J. Egelhaaf, M. Fleischer, L. Hennemann, H. Hintz, C. Stanciu, C. J. Brabec, D. P. Kern, and A. J. Meixner, “Parabolic mirror-assisted tip-enhanced spectroscopic imaging for non-transparent materials,” J. Raman Spectrosc.40, 1371–1376 (2009).
[CrossRef]

J. Stadler, C. Stanciu, C. Stupperich, and A. J. Meixner, “Tighter focusing with a parabolic mirror,” Opt. Lett.33, 681–683 (2008).
[CrossRef] [PubMed]

Stefani, F. D.

Stöckle, R. M.

R. M. Stöckle, Y. D. Suh, V. Deckert, and R. Zenobi, “Nanoscale chemical analysis by tip-enhanced raman spectroscopy,” Chem. Phys. Lett.318, 131–136 (2000).
[CrossRef]

Stockman, M. I.

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

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York and London, 1941).

Stupperich, C.

Suh, Y. D.

R. M. Stöckle, Y. D. Suh, V. Deckert, and R. Zenobi, “Nanoscale chemical analysis by tip-enhanced raman spectroscopy,” Chem. Phys. Lett.318, 131–136 (2000).
[CrossRef]

Taminiau, T. H.

Török, P.

C. J. R. Sheppard and P. Török, “Efficient calculation of electromagnetic diffraction in optical systems using a multipole expansion,” J. Mod. Opt.44, 803–818 (1997).
[CrossRef]

van Hulst, N. F.

Vogelgesang, R.

R. Esteban, R. Vogelgesang, and K. Kern, “Simulation of optical near and far fields of dielectric apertureless scanning probes,” Nanotechnology17, 475 (2006).
[CrossRef]

Wang, X.

D. Zhang, U. Heinemeyer, C. Stanciu, M. Sackrow, K. Braun, L. E. Hennemann, X. Wang, R. Scholz, F. Schreiber, and A. J. Meixner, “Nanoscale spectroscopic imaging of organic semiconductor films by plasmonpolariton coupling,” Phys. Rev. Lett.104, 056601 (2010).
[CrossRef]

D. Zhang, X. Wang, K. Braun, H.-J. Egelhaaf, M. Fleischer, L. Hennemann, H. Hintz, C. Stanciu, C. J. Brabec, D. P. Kern, and A. J. Meixner, “Parabolic mirror-assisted tip-enhanced spectroscopic imaging for non-transparent materials,” J. Raman Spectrosc.40, 1371–1376 (2009).
[CrossRef]

Weaver, J.

J. Weaver and H. Frederikse, “Optical Properties of Selected Elements” (CRC Handbook of Chemistry and Physics, CRC Press, Boca Raton, 2001), pp. 116–133.

Weber, H. J.

G. Arfken and H. J. Weber, “Mathematical methods for physicists,” (2005).

Wokaun, A.

P. F. Liao and A. Wokaun, “Lightning rod effect in surface enhanced raman scattering,” J. Chem. Phys.76, 751–752 (1982).
[CrossRef]

Wolf, E.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. ii. structure of the image field in an aplanatic system,” Proc. R. Soc. A253, 358–379 (1959).
[CrossRef]

Xie, X. S.

J. T. Krug, E. J. Sanchez, and X. S. Xie, “Design of near-field optical probes with optimal field enhancement by finite difference time domain electromagnetic simulation,” J. Chem. Phys.116, 10895–10901 (2002).
[CrossRef]

L. Novotny, R. X. Bian, and X. S. Xie, “Theory of nanometric optical tweezers,” Phys. Rev. Lett.79, 645–648 (1997).
[CrossRef]

Zenobi, R.

J. Stadler, B. Oswald, T. Schmid, and R. Zenobi, “Characterizing unusual metal substrates for gap-mode tip-enhanced raman spectroscopy,” J. Raman Spectrosc.44, 227–233 (2013).
[CrossRef]

R. M. Stöckle, Y. D. Suh, V. Deckert, and R. Zenobi, “Nanoscale chemical analysis by tip-enhanced raman spectroscopy,” Chem. Phys. Lett.318, 131–136 (2000).
[CrossRef]

Zhang, D.

D. Zhang, U. Heinemeyer, C. Stanciu, M. Sackrow, K. Braun, L. E. Hennemann, X. Wang, R. Scholz, F. Schreiber, and A. J. Meixner, “Nanoscale spectroscopic imaging of organic semiconductor films by plasmonpolariton coupling,” Phys. Rev. Lett.104, 056601 (2010).
[CrossRef]

D. Zhang, X. Wang, K. Braun, H.-J. Egelhaaf, M. Fleischer, L. Hennemann, H. Hintz, C. Stanciu, C. J. Brabec, D. P. Kern, and A. J. Meixner, “Parabolic mirror-assisted tip-enhanced spectroscopic imaging for non-transparent materials,” J. Raman Spectrosc.40, 1371–1376 (2009).
[CrossRef]

Zhang, W.

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

Angew. Chem. Int. Ed. (1)

A. Hartschuh, “Tip-enhanced near-field optical microscopy,” Angew. Chem. Int. Ed.47, 8178–8191 (2008).
[CrossRef]

Ann. Phys. (2)

A. Sommerfeld, “Ueber die fortpflanzung elektrodynamischer wellen längs eines drahtes,” Ann. Phys.303, 233–290 (1899).
[CrossRef]

D. Hondros, “über elektromagnetische drahtwellen,” Ann. Phys.335, 905–950 (1909).
[CrossRef]

Appl. Phys. Lett. (1)

O. J. F. Martin and C. Girard, “Controlling and tuning strong optical field gradients at a local probe microscope tip apex,” Appl. Phys. Lett.70, 705–707 (1997).
[CrossRef]

Chem. Phys. Lett. (1)

R. M. Stöckle, Y. D. Suh, V. Deckert, and R. Zenobi, “Nanoscale chemical analysis by tip-enhanced raman spectroscopy,” Chem. Phys. Lett.318, 131–136 (2000).
[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. (3)

J. T. Krug, E. J. Sanchez, and X. S. Xie, “Design of near-field optical probes with optimal field enhancement by finite difference time domain electromagnetic simulation,” J. Chem. Phys.116, 10895–10901 (2002).
[CrossRef]

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

P. F. Liao and A. Wokaun, “Lightning rod effect in surface enhanced raman scattering,” J. Chem. Phys.76, 751–752 (1982).
[CrossRef]

J. Comput. Theor. Nanos. (1)

A. Alparslan and C. Hafner, “Analysis of photonic structures by the multiple multipole program with complex origin layered geometry green’s functions,” J. Comput. Theor. Nanos.9, 479–485 (2012).
[CrossRef]

J. Microsc. (1)

C. Debus, M. A. Lieb, A. Drechsler, and A. J. Meixner, “Probing highly confined optical fields in the focal region of a high na parabolic mirror with subwavelength spatial resolution,” J. Microsc.210, 203–208(6) (June2003).
[CrossRef] [PubMed]

J. Mod. Opt. (1)

C. J. R. Sheppard and P. Török, “Efficient calculation of electromagnetic diffraction in optical systems using a multipole expansion,” J. Mod. Opt.44, 803–818 (1997).
[CrossRef]

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

J. Raman Spectrosc. (3)

J. Stadler, B. Oswald, T. Schmid, and R. Zenobi, “Characterizing unusual metal substrates for gap-mode tip-enhanced raman spectroscopy,” J. Raman Spectrosc.44, 227–233 (2013).
[CrossRef]

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

D. Zhang, X. Wang, K. Braun, H.-J. Egelhaaf, M. Fleischer, L. Hennemann, H. Hintz, C. Stanciu, C. J. Brabec, D. P. Kern, and A. J. Meixner, “Parabolic mirror-assisted tip-enhanced spectroscopic imaging for non-transparent materials,” J. Raman Spectrosc.40, 1371–1376 (2009).
[CrossRef]

Nano Lett. (2)

C. Ropers, C. C. Neacsu, T. Elsaesser, M. Albrecht, M. B. Raschke, and C. Lienau, “Grating-coupling of surface plasmons onto metallic tips: A nanoconfined light source,” Nano Lett.7, 2784–2788 (2007). PMID: .
[CrossRef] [PubMed]

X.-W. Chen, V. Sandoghdar, and M. Agio, “Highly efficient interfacing of guided plasmons and photons in nanowires,” Nano Lett.9, 3756–3761 (2009). PMID: .
[CrossRef] [PubMed]

Nanotechnology (2)

H. G. Frey, C. Bolwien, A. Brandenburg, R. Ros, and D. Anselmetti, “Optimized apertureless optical near-field probes with 15 nm optical resolution,” Nanotechnology17, 3105 (2006).
[CrossRef]

R. Esteban, R. Vogelgesang, and K. Kern, “Simulation of optical near and far fields of dielectric apertureless scanning probes,” Nanotechnology17, 475 (2006).
[CrossRef]

Nature (1)

B. Knoll and F. Keilmann, “Near-field probing of vibrational absorption for chemical microscopy,” Nature399, 134–137 (1999).
[CrossRef]

New J. Phys. (1)

J. Barthes, G. C. des Francs, A. Bouhelier, and A. Dereux, “A coupled lossy local-mode theory description of a plasmonic tip,” New J. Phys.14, 083041 (2012).
[CrossRef]

Opt Commun (1)

S. Quabis, R. Dorn, M. Eberler, O. Glckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt Commun179, 1–7 (2000).
[CrossRef]

Opt. Express (4)

Opt. Lett. (1)

Phys. Rev. A (1)

W. Ding, S. R. Andrews, and S. A. Maier, “Internal excitation and superfocusing of surface plasmon polaritons on a silver-coated optical fiber tip,” Phys. Rev. A75, 063822 (2007).
[CrossRef]

Phys. Rev. B (2)

C. A. Pfeiffer, E. N. Economou, and K. L. Ngai, “Surface polaritons in a circularly cylindrical interface: Surface plasmons,” Phys. Rev. B10, 3038–3051 (1974).
[CrossRef]

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6, 4370–4379 (1972).
[CrossRef]

Phys. Rev. Lett. (3)

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

D. Zhang, U. Heinemeyer, C. Stanciu, M. Sackrow, K. Braun, L. E. Hennemann, X. Wang, R. Scholz, F. Schreiber, and A. J. Meixner, “Nanoscale spectroscopic imaging of organic semiconductor films by plasmonpolariton coupling,” Phys. Rev. Lett.104, 056601 (2010).
[CrossRef]

L. Novotny, R. X. Bian, and X. S. Xie, “Theory of nanometric optical tweezers,” Phys. Rev. Lett.79, 645–648 (1997).
[CrossRef]

Plasmonics (1)

F. Baida and A. Belkhir, “Superfocusing and light confinement by surface plasmon excitation through radially polarized beam,” Plasmonics4, 51–59 (2009).
[CrossRef]

Proc. R. Soc. A (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. ii. structure of the image field in an aplanatic system,” Proc. R. Soc. A253, 358–379 (1959).
[CrossRef]

Rep. Prog. Phys. (1)

P. Biagioni, J.-S. Huang, and B. Hecht, “Nanoantennas for visible and infrared radiation,” Rep. Prog. Phys.75, 024402 (2012).
[CrossRef] [PubMed]

Sources and Development of Mathematical Software (1)

J. J. Moré, B. S. Garbow, and K. E. Hillstrom, “The minpack project,” Sources and Development of Mathematical Software88–111 (1984).

Surface Science (1)

J. Ashley and L. Emerson, “Dispersion relations for non-radiative surface plasmons on cylinders,” Surface Science41, 615–618 (1974).
[CrossRef]

Other (11)

J. Weaver and H. Frederikse, “Optical Properties of Selected Elements” (CRC Handbook of Chemistry and Physics, CRC Press, Boca Raton, 2001), pp. 116–133.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York and London, 1941).

J. S. Ch. Hafner and M. Agio, “Numerical methods for the electrodynamic analysis of nanostructures,” in “Nanoclusters and Nanostructured Surfaces,” A. K. Ray, ed. (American Scientific Publishers: Valencia, CA, 2010).

B. C. Brock, “Using vector spherical harmonics to compute antenna mutual impedance from measured or computed fields,” Sandia report, SAND2000-2217-Revised. Sandia National Laboratories, Albuquerque, NM (2001).

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1998).

J. Stamnes, Waves in Focal Regions (Taylor & Francis, 1986).

G. Arfken and H. J. Weber, “Mathematical methods for physicists,” (2005).

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University Press, 2006).
[CrossRef]

C. Hafner, MaX-1: A Visual Electromagnetics Platform for PCs (Wiley, 1998).

C. Hafner, Post-Modern Electromagnetics Using Intelligent MaXwell Solvers (Wiley, ChichesterUK, 1999).

C. Hafner, “Openmax: Graphic platform for computational electromagnetics and computational optics,” http://openmax.ethz.ch/ , ETH Zürich (2013).

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Figures (9)

Fig. 1
Fig. 1

(a) The studied SNOM setup. A radially polarized beam is focused by parabolic mirror on a metal tip and leads to a high field enhancement at the tip apex. (b) Domains (Di), boundaries (Γi,j) and geometrical parameters of the tip in the numerical model.

Fig. 2
Fig. 2

Essential parameters for the calculation of the focal fields in a PM. The radially polarized incident beam with amplitude l0(ρ(θ)) is reflected by the PM onto the Gaussian reference sphere (GRS).

Fig. 3
Fig. 3

(a,b) Polar field component Eθ on the GRS calculated by Eq. (10) for t0 and t1, and the corresponding Bessel expansion with an order of 30. (c) Field intensity near the focus in a logarithmic scale (factor of 2 between adjacent contour levels). (d) Modulus of the vertical and lateral field component in the focal plane (z=0).

Fig. 4
Fig. 4

(a) Logarithmic contour of the modulus of equation (23) in the complex γ0 plane (Au, ϱ = 300nm, λ = 410nm). The red star marks the point of the asymptotic solution of the principal wave, which is located close to the root for the present wire radius. The hollow circles mark the approximate solutions of the complementary waves that start close to k2/k1 (black cross). Note that some of the complementary wave solutions are very fine and not properly visible in this plot. (b) Normalized wave propagation number for the considered materials for λ = 300 – 1000nm, corresponding to the measured data [30, 31].

Fig. 5
Fig. 5

(a)–(g) normalized propagation constant (γ0) of the principal wave. ϱ marks the solution for the asymptotic large wire limit. Furthermore wire radii of 1.5, 0.5 and 0.15μm are considered (black labels). Note that the wavelength (in nanometre) is labelled without units.

Fig. 6
Fig. 6

Field enhancement for bottom and top illumination for several wire radii ϱ = 0.5, 1. and 1.5μm (R1 = 5nm, α = 25°).

Fig. 7
Fig. 7

Al tip with R1 = 5nm, α = 25°, λ = 500nm, ϱ = 1.5μm. Contour of the time averaged electric scattered field for a tip illuminated from top (a) and bottom (b) (log scale with a factor of 2 between adjacent contour levels). (a) shows a standing wave pattern, which indicates the presence of counterpropagating SPPs. Time averaged poynting vector of the scattered field for top (c) and bottom (d) illumination (log scale with factor of 2).

Fig. 8
Fig. 8

Field enhancement for bottom and top illumination for several tip angles. (R1 = 5nm, α = 15, 20, 25°, ϱ = 1.5μm).

Fig. 9
Fig. 9

Field enhancement for bottom and top illumination for several tip radii (R1 = 5, 10, 20, 30 and 50nm, α = 25°, ϱ = 1.5μm). The field enhancement increases with decreasing radius.

Equations (30)

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E inc = n = 1 m = n n a n m M n m ( k r ) + b n m N n m ( k r ) .
M n m ( k r ) = 1 n ( n + 1 ) j n ( k r ) { im sin θ Y n m ( θ , ϕ ) e ^ θ θ Y n m ( θ , ϕ ) e ^ ϕ }
N n m ( k r ) = n ( n + 1 ) k r j n ( k r ) Y n m ( θ , ϕ ) e ^ r + 1 n ( n + 1 ) × { j n 1 ( k r ) n j n ( k r ) k r } { θ Y n m ( θ , ϕ ) e ^ θ + im sin θ Y n m ( θ , ϕ ) e ^ ϕ }
a n m = 1 M n m , M n m M n m , E inc b n m = 1 N n m , N n m N n m , E inc
Ψ , Ψ = 0 2 π 0 π Ψ * ( r , θ , ϕ ) Ψ ( r , θ , ϕ ) sin θ d θ d ϕ
l 0 ( θ ) = E 0 2 ρ ( θ ) w 0 e ρ ( θ ) 2 w 0 2 = E 0 2 ( 2 f tan θ 2 ) w 0 e ( 2 f tan θ 2 ) 2 w 0 2 .
E ( R , θ , ϕ ) = E r e ^ r + E ϕ e ^ ϕ + E θ e ^ θ = { 2 l 0 ( θ ) 1 + cos θ e ^ θ for θ 0 θ θ m 0 else
E ρ ( ρ , ϕ , z ) = E ρ * ( ρ , ϕ , z )
E z ( ρ , ϕ , z ) = E z * ( ρ , ϕ , z )
E θ ( θ , { t 0 , [ t 1 ] } ) = [ i ] { 2 l 0 ( θ ) 1 + cos θ for θ 0 θ θ m [ ] 2 l 0 ( π θ ) 1 + cos ( π θ ) for π θ m θ π θ 0 0 else
N n , N n = 2 n + 1 n ( n + 1 ) 4 π { j n 1 ( k r ) n j n ( k r ) k r } 2 0 2 π d ϕ 0 π P n 1 ( cos θ ) 2 sin θ d θ 2 n ( n + 1 ) 2 n + 1 = { j n 1 ( k r ) n j n ( k r ) k r } 2
Y n 0 ( θ , ϕ ) = 2 n + 1 4 π P n ( cos θ ) θ Y n 0 ( θ , ϕ ) = 2 n + 1 4 π P n 1 ( cos θ ) .
b n = 1 { j n 1 ( k r ) n j n ( k r ) k r } 2 n + 1 4 π n ( n + 1 ) 0 2 π 0 π P n 1 ( cos θ ) ( E θ ( θ , t 0 ) + E θ ( θ , t 1 ) ) sin θ d θ d ϕ .
k R = π ( 2 N + 1 / 4 )
j n ( k r ) cos ( k r n + 1 2 π ) k r valid for k r n ( n + 1 ) / 2
1 j n 1 ( k R ) 2 ( 1 ) [ n 2 ] k R where [ n / 2 ] = { n / 2 for n even ( n 1 ) / 2 for n odd .
b n = ( 1 ) [ n 2 ] π ( 2 n + 1 ) n ( n + 1 ) k R 0 π P n 1 ( cos θ ) { E θ ( θ , t 0 ) + E θ ( θ , t 1 ) } sin θ d θ .
E ρ = A l i γ κ l Z 1 ( κ l ρ ) e i γ z E z = A l κ l 2 Z 0 ( κ l ρ ) e i γ z H ϕ = A l i ω ε l κ l Z 1 ( κ l ρ ) e i γ z }
κ l = k l 2 γ 2 with k l = ω ε l μ l ,
E z : A 1 κ 1 2 H 0 1 ( κ 1 ϱ ) = A 2 κ 2 2 J 0 ( κ 2 ϱ ) H ϕ : A 1 k 1 2 μ 1 κ 1 H 0 1 ( κ 1 ϱ ) = A 2 k 2 2 μ 2 κ 2 J 0 ( κ 2 ϱ )
d d x H 0 1 ( x ) = H 1 1 ( x ) d d x J 0 ( x ) = J 1 ( x )
x l = k l 2 γ 2 ϱ = κ l ϱ
| x 1 H 0 1 ( x 1 ) x 2 J 0 ( x 2 ) k 1 2 μ 1 H 1 1 ( x 1 ) k 2 2 μ 2 J 1 ( x 2 ) | = 0 x 1 H 0 1 ( x 1 ) H 1 1 ( x 1 ) k 1 2 k 2 2 μ 2 μ 1 x 2 J 0 ( x 2 ) J 1 ( x 2 ) = 0 .
A 1 = β γ 2 k 1 2 1 H 0 1 ( x 1 ) A 2 = β γ 2 k 2 2 1 J 0 ( x 2 ) .
J 0 ( x ) J 1 ( x ) i H 0 1 ( x ) H 1 1 ( x ) i
γ 0 = γ k 1 = k 2 ( k 2 2 k 1 2 k 2 4 k 1 4 ) 1 2 = ( ε 2 ε 1 ε 2 + ε 1 ) 1 2 ,
x 1 i = ( k 1 k 2 ) 2 x 2 J 0 ( x 2 ) J 1 ( x 2 ) J 1 ( x 2 ) J 0 ( x 2 ) x 2 = ( k 1 k 2 ) 2 ( 1 k 2 2 k 1 2 x 2 2 ) 1 2 .
γ 0 , m ( k 2 2 k 1 2 j 1 , m 2 ϱ 2 k 1 2 ) 1 2 .
E tip = ( 1 A a ) ( ε 1 ) 1 + ( ε 1 ) A a E L + E L
γ = 3 2 ( a b ) 2 ( 1 A a ) .

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