Abstract

Nanometer-scale mapping of complex optical constants by scattering-type near-field microscopy has been suffering from quantitative discrepancies between the theory and experiments. To resolve this problem, a novel analytical model is presented here. The comparison with experimental data demonstrates that the model quantitatively reproduces approach curves on a Au surface and yields an unprecedented agreement with amplitude and phase spectra recorded on a phonon-polariton resonant SiC sample. The simple closed-form solution derived here should enable the determination of the local complex dielectric function on an unknown sample, thereby identifying its nanoscale chemical composition, crystal structure and conductivity.

©2007 Optical Society of America

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  1. F. Zenhausern, M. Oboyle, and H. Wickramasinghe, “Apertureless near-field optical microscope,” Appl. Phys. Lett. 65, 1623–1625 (1994).
    [Crossref]
  2. Y. Inouye and S. Kawata, “Near-field scanning optical microscope with a metallic probe tip,” Opt. Lett. 19, 159–161 (1994).
    [Crossref] [PubMed]
  3. A. Lahrech, R. Bachelot, P. Gleyzes, and A. C. Boccara, “Infrared-reflection-mode near-field microscopy using an apertureless probe with a resolution of lambda/600,” Opt. Lett. 21, 1315–1317 (1996).
    [Crossref] [PubMed]
  4. F. Keilmann and R. Hillenbrand, “Near-field microscopy by elastic light scattering from a tip,” Philos. Trans. R. Soc. Lond. Ser. A-Math. Phys. Eng. Sci. 362, 787–805 (2004).
    [Crossref]
  5. B. Knoll and F. Keilmann, “Near-field probing of vibrational absorption for chemical microscopy,” Nature 399, 134–137 (1999).
    [Crossref]
  6. 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]
  7. R. Fikri, D. Barchiesi, F. H’Dhili, R. Bachelot, A. Vial, and P. Royer, “Modeling recent experiments of aperture-less near-field optical microscopy using 2D finite element method,” Opt. Commun. 221, 13–22 (2003).
    [Crossref]
  8. R. Esteban, R. Vogelgesang, and K. Kern, “Simulation of optical near and far fields of dielectric apertureless scanning probes,” Nanotechnology 17, 475–482 (2006).
    [Crossref]
  9. L. Novotny, E. J. Sanchez, and X. S. Xie, “Near-field optical imaging using metal tips illuminated by higher-order Hermite-Gaussian beams,” Ultramicroscopy 71, 21–29 (1998).
    [Crossref]
  10. T. Taubner, R. Hillenbrand, and F. Keilmann, “Performance of visible and mid-infrared scattering-type near-field optical microscopes,” J. Microsc.-Oxf. 210, 311–314 (2003).
    [Crossref]
  11. T. Taubner, R. Hillenbrand, and F. Keilmann, “Nanoscale polymer recognition by spectral signature in scattering infrared near-field microscopy,” Appl. Phys. Lett. 85, 5064–5066 (2004).
    [Crossref]
  12. M. B. Raschke, L. Molina, T. Elsaesser, D. H. Kim, W. Knoll, and K. Hinrichs, “Apertureless near-field vibra-tional imaging of block-copolymer nanostructures with ultrahigh spatial resolution,” ChemPhysChem 6, 2197–2203 (2005).
    [Crossref] [PubMed]
  13. M. Brehm, T. Taubner, R. Hillenbrand, and F. Keilmann, “Infrared spectroscopic mapping of single nanoparticles and viruses at nanoscale resolution,” Nano Lett. 6, 1307–1310 (2006).
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  14. N. Ocelic and R. Hillenbrand, “Subwavelength-scale tailoring of surface phonon polaritons by focused ion-beam implantation,” Nat. Mater. 3, 606–609 (2004).
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  15. A. Huber, N. Ocelic, T. Taubner, and R. Hillenbrand, “Nanoscale resolved infrared probing of crystal structure and of plasmon-phonon coupling,” Nano Lett. 6, 774–778 (2006).
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  16. B. Knoll and F. Keilmann, “Infrared conductivity mapping for nanoelectronics,” Appl. Phys. Lett. 77, 3980–3982 (2000).
    [Crossref]
  17. J. S. Samson, G. Wollny, E. Brundermann, A. Bergner, A. Hecker, G. Schwaab, A. D. Wieck, and M. Havenith, “Setup of a scanning near field infrared microscope (SNIM): Imaging of sub-surface nano-structures in gallium-doped silicon,” Phys. Chem. Chem. Phys. 8, 753 – 758 (2006).
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  18. A. Huber et al., “Simultaneous infrared material recognition and conductivity mapping by nanoscale near-field microscopy,” Adv. Mater. (in press).
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  20. A. Wokaun, J. P. Gordon, and P. F. Liao, “Radiation damping in surface-enhanced Raman-scattering,” Phys. Rev. Lett. 48, 957 – 960 (1982).
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  21. P. Aravind and H. Metiu, “The effects of the interaction between resonances in the electromagnetic response of a sphere-plane structure - applications to surface enhanced spectroscopy,” Surf. Sci. 124, 506–528 (1983).
    [Crossref]
  22. B. Knoll and F. Keilmann, “Enhanced dielectric contrast in scattering-type scanning near-field optical microscopy,” Opt. Commun. 182, 321–328 (2000).
    [Crossref]
  23. I. S. Averbukh, B. M. Chernobrod, O. A. Sedletsky, and Y. Prior, “Coherent near field optical microscopy,” Opt. Commun. 174, 33–41 (2000).
    [Crossref]
  24. F. Zenhausern, Y. Martin, and H. Wickramasinghe, “Scanning interferometric apertureless microscopy - optical imaging at 10 angstrom resolution,” Science 269, 1083–1085 (1995).
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  25. M. B. Raschke and C. Lienau, “Apertureless near-field optical microscopy: Tip-sample coupling in elastic light scattering,” Appl. Phys. Lett. 83, 5089–5091 (2003).
    [Crossref]
  26. Z. H. Kim, B. Liu, and S. R. Leone, “Nanometer-scale optical imaging of epitaxially grown GaN and InN islands using apertureless near-field microscopy,” J. Phys. Chem. B 109, 8503–8508 (2005).
    [Crossref]
  27. R. Hillenbrand and F. Keilmann, “Material-specific mapping of metal/semiconductor/dielectric nanosystems at 10 nm resolution by backscattering near-field optical microscopy,” Appl. Phys. Lett. 80, 25–27 (2002).
    [Crossref]
  28. R. Hillenbrand, T. Taubner, and F. Keilmann, “Phonon-enhanced light-matter interaction at the nanometre scale,” Nature 418, 159–162 (2002).
    [Crossref] [PubMed]
  29. T. Taubner, F. Keilmann, and R. Hillenbrand, “Nanomechanical resonance tuning and phase effects in optical near-field interaction,” Nano Lett. 4, 1669–1672 (2004).
    [Crossref]
  30. L. Stebounova, B. B. Akhremitchev, and G. C. Walker, “Enhancement of the weak scattered signal in apertureless near-field scanning infrared microscopy,” Rev. Sci. Instrum. 74, 3670–3674 (2003).
    [Crossref]
  31. A. Cvitkovic, N. Ocelic, J. Aizpurua, R. Guckenberger, and R. Hillenbrand, “Infrared imaging of single nanopar-ticles via strong field enhancement in a scanning nanogap,” Phys. Rev. Lett. 97, (2006).
    [Crossref] [PubMed]
  32. J. L. Bohn, D. J. Nesbitt, and A. Gallagher, “Field enhancement in apertureless near-field scanning optical microscopy,” J. Opt. Soc. Am. A-Opt. Image Sci. Vis. 18, 2998–3006 (2001).
    [Crossref]
  33. J. Renger, S. Grafstrom, L. M. Eng, and R. Hillenbrand, “Resonant light scattering by near-field-induced phonon polaritons,” Phys. Rev. B 71, (2005).
  34. S. V. Sukhov, “Role of multipole moment of the probe in apertureless near-field optical microscopy,” Ultrami-croscopy 101, 111–122 (2004).
    [Crossref]
  35. H. Hatano and S. Kawata, “Applicability of deconvolution and nonlinear optimization for reconstructing optical images from near-field optical microscope images,” J. Microsc.-Oxf. 194, 230 – 234 (1999).
    [Crossref]
  36. M. Labardi, S. Patane, and M. Allegrini, “Artifact-free near-field optical imaging by apertureless microscopy,” Appl. Phys. Lett. 77, 621–623 (2000).
    [Crossref]
  37. R. Hillenbrand and F. Keilmann, “Complex optical constants on a subwavelength scale,” Phys. Rev. Lett. 85, 3029–3032 (2000).
    [Crossref] [PubMed]
  38. J. N. Walford, J. A. Porto, R. Carminati, J. J. Greffet, P. M. Adam, S. Hudlet, J. L. Bijeon, A. Stashkevich, and P. Royer, “Influence of tip modulation on image formation in scanning near-field optical microscopy,” J. Appl. Phys. 89, 5159–5169 (2001).
    [Crossref]
  39. A. Wokaun, “Surface enhancement of optical-fields - mechanism and applications,” Mol. Phys. 56, 1 – 33 (1985).
    [Crossref]
  40. W. Denk and D. Pohl, “Near-field optics - microscopy with nanometer-size fields,” J. Vac. Sci. Technol. B 9, 510–513 (1991).
    [Crossref]
  41. N. Calander and M. Willander, “Theory of surface-plasmon resonance optical-field enhancement at prolate spheroids,” J. Appl. Phys. 92, 4878–4884 (2002).
    [Crossref]
  42. N. Ocelic, “Quantitative near-field phonon-polariton spectroscopy,” Ph.D. thesis, Technical University Munich (2007).
  43. Y. C. Martin, H. F. Hamann, and H. K. Wickramasinghe, “Strength of the electric field in apertureless near-field optical microscopy,” J. Appl. Phys. 89, 5774–5778 (2001).
    [Crossref]
  44. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons Inc, 1998).
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  45. J. D. Jackson, Classical Electrodynamics (Wiley & Sons, 1998).
  46. I. V. Lindell, G. Dassios, and K. I. Nikoskinen, “Electrostatic image theory for the conducting prolate spheroid,” J. Phys. D-Appl. Phys. 34, 2302–2307 (2001).
    [Crossref]
  47. D. V. Redzic, “An electrostatic problem - a point-charge outside a prolate dielectric spheroid,” Am. J. Phys. 62, 1118 – 1121 (1994).
    [Crossref]
  48. J. C. E. Sten and I. V. Lindell, “An electrostatic image solution for the conducting prolate spheroid,” J. Electro-magn. Waves Appl. 9, 599 – 609 (1995).
  49. D. V. Redzic, “Image of a moving spheroidal conductor,” Am. J. Phys. 60, 506–508 (1992).
    [Crossref]
  50. Z. H. Kim and S. R. Leone, “High-resolution apertureless near-field optical imaging using gold nanosphere probes,” J. Phys. Chem. B 110, 19,804–19,809 (2006).
  51. J. Aizpurua, personal communication (2005).
  52. N. Ocelic, A. Huber, and R. Hillenbrand, “Pseudoheterodyne detection for background-free near-field spec-troscopy,” Appl. Phys. Lett. 89, (2006).
    [Crossref]
  53. R. Bachelot, G. Wurtz, and P. Royer, “An application of the apertureless scanning near-field optical microscopy: imaging a GaAlAs laser diode in operation,” Appl. Phys. Lett. 73, 3333–3335 (1998).
    [Crossref]
  54. B. Knoll and F. Keilmann, “Electromagnetic fields in the cutoff regime of tapered metallic waveguides,” Opt. Commun. 162, 177–181 (1999).
    [Crossref]
  55. A. Huber, N. Ocelic, D. Kazantsev, and R. Hillenbrand, “Near-field imaging of mid-infrared surface phonon polariton propagation,” Appl. Phys. Lett. 87, (2005).
    [Crossref]
  56. F. Engelbrecht and R. Helbig, “Effect of crystal anisotropy on the infrared reflectivity of 6H-SiC,” Phys. Rev. B 48, 15,698 – 15,707 (1993).
    [Crossref]
  57. H. Mutschke, A. C. Andersen, D. Clement, T. Henning, and G. Peiter, “Infrared properties of SiC particles,” Astron. Astrophys. 345, 187–202 (1999).
  58. M. Hofmann, A. Zywietz, K. Karch, and F. Bechstedt, “Lattice-dynamics of SiC polytypes within the bond-charge model,” Phys. Rev. B 50, 13,401–13,411 (1994).
    [Crossref]
  59. H. Harima, S. Nakashima, and T. Uemura, “Raman-scattering from anisotropic LO-phonon-plasmon-coupled mode in n-type 4H-SiC and 6H-SiC,” J. Appl. Phys. 78, 1996–2005 (1995).
    [Crossref]
  60. I. V. Lindell, K. I. Nikoskinen, and M. J. Flykt, “Electrostatic image theory for an anisotropic half-space slightly deviating from transverse isotropy,” Radio Sci. 31, 1361 – 1368 (1996).
    [Crossref]
  61. I. V. Lindell, K. I. Nikoskinen, and A. Viljanen, “Electrostatic image method for the anisotropic half space,” IEE Proc.-Sci. Meas. Technol. 144, 156 – 162 (1997).
    [Crossref]
  62. S. C. Schneider, S. Grafstrom, and L. M. Eng, “Scattering near-field optical microscopy of optically anisotropicsystems,” Phys. Rev. B 71, (2005).
    [Crossref]
  63. M. A. Ordal et al., “Optical properties of the metals Al, Co,Cu,Au,Fe,Pb,Ni,Pd,Pt,Ag,Ti and W in the infrared and far infrared,” Appl. Opt. 22, (1983).
    [Crossref] [PubMed]

2006 (7)

R. Esteban, R. Vogelgesang, and K. Kern, “Simulation of optical near and far fields of dielectric apertureless scanning probes,” Nanotechnology 17, 475–482 (2006).
[Crossref]

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

A. Huber, N. Ocelic, T. Taubner, and R. Hillenbrand, “Nanoscale resolved infrared probing of crystal structure and of plasmon-phonon coupling,” Nano Lett. 6, 774–778 (2006).
[Crossref] [PubMed]

J. S. Samson, G. Wollny, E. Brundermann, A. Bergner, A. Hecker, G. Schwaab, A. D. Wieck, and M. Havenith, “Setup of a scanning near field infrared microscope (SNIM): Imaging of sub-surface nano-structures in gallium-doped silicon,” Phys. Chem. Chem. Phys. 8, 753 – 758 (2006).
[Crossref] [PubMed]

A. Cvitkovic, N. Ocelic, J. Aizpurua, R. Guckenberger, and R. Hillenbrand, “Infrared imaging of single nanopar-ticles via strong field enhancement in a scanning nanogap,” Phys. Rev. Lett. 97, (2006).
[Crossref] [PubMed]

Z. H. Kim and S. R. Leone, “High-resolution apertureless near-field optical imaging using gold nanosphere probes,” J. Phys. Chem. B 110, 19,804–19,809 (2006).

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

2005 (5)

A. Huber, N. Ocelic, D. Kazantsev, and R. Hillenbrand, “Near-field imaging of mid-infrared surface phonon polariton propagation,” Appl. Phys. Lett. 87, (2005).
[Crossref]

S. C. Schneider, S. Grafstrom, and L. M. Eng, “Scattering near-field optical microscopy of optically anisotropicsystems,” Phys. Rev. B 71, (2005).
[Crossref]

Z. H. Kim, B. Liu, and S. R. Leone, “Nanometer-scale optical imaging of epitaxially grown GaN and InN islands using apertureless near-field microscopy,” J. Phys. Chem. B 109, 8503–8508 (2005).
[Crossref]

J. Renger, S. Grafstrom, L. M. Eng, and R. Hillenbrand, “Resonant light scattering by near-field-induced phonon polaritons,” Phys. Rev. B 71, (2005).

M. B. Raschke, L. Molina, T. Elsaesser, D. H. Kim, W. Knoll, and K. Hinrichs, “Apertureless near-field vibra-tional imaging of block-copolymer nanostructures with ultrahigh spatial resolution,” ChemPhysChem 6, 2197–2203 (2005).
[Crossref] [PubMed]

2004 (5)

T. Taubner, R. Hillenbrand, and F. Keilmann, “Nanoscale polymer recognition by spectral signature in scattering infrared near-field microscopy,” Appl. Phys. Lett. 85, 5064–5066 (2004).
[Crossref]

F. Keilmann and R. Hillenbrand, “Near-field microscopy by elastic light scattering from a tip,” Philos. Trans. R. Soc. Lond. Ser. A-Math. Phys. Eng. Sci. 362, 787–805 (2004).
[Crossref]

N. Ocelic and R. Hillenbrand, “Subwavelength-scale tailoring of surface phonon polaritons by focused ion-beam implantation,” Nat. Mater. 3, 606–609 (2004).
[Crossref] [PubMed]

S. V. Sukhov, “Role of multipole moment of the probe in apertureless near-field optical microscopy,” Ultrami-croscopy 101, 111–122 (2004).
[Crossref]

T. Taubner, F. Keilmann, and R. Hillenbrand, “Nanomechanical resonance tuning and phase effects in optical near-field interaction,” Nano Lett. 4, 1669–1672 (2004).
[Crossref]

2003 (4)

L. Stebounova, B. B. Akhremitchev, and G. C. Walker, “Enhancement of the weak scattered signal in apertureless near-field scanning infrared microscopy,” Rev. Sci. Instrum. 74, 3670–3674 (2003).
[Crossref]

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

R. Fikri, D. Barchiesi, F. H’Dhili, R. Bachelot, A. Vial, and P. Royer, “Modeling recent experiments of aperture-less near-field optical microscopy using 2D finite element method,” Opt. Commun. 221, 13–22 (2003).
[Crossref]

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

2002 (3)

R. Hillenbrand and F. Keilmann, “Material-specific mapping of metal/semiconductor/dielectric nanosystems at 10 nm resolution by backscattering near-field optical microscopy,” Appl. Phys. Lett. 80, 25–27 (2002).
[Crossref]

R. Hillenbrand, T. Taubner, and F. Keilmann, “Phonon-enhanced light-matter interaction at the nanometre scale,” Nature 418, 159–162 (2002).
[Crossref] [PubMed]

N. Calander and M. Willander, “Theory of surface-plasmon resonance optical-field enhancement at prolate spheroids,” J. Appl. Phys. 92, 4878–4884 (2002).
[Crossref]

2001 (4)

Y. C. Martin, H. F. Hamann, and H. K. Wickramasinghe, “Strength of the electric field in apertureless near-field optical microscopy,” J. Appl. Phys. 89, 5774–5778 (2001).
[Crossref]

I. V. Lindell, G. Dassios, and K. I. Nikoskinen, “Electrostatic image theory for the conducting prolate spheroid,” J. Phys. D-Appl. Phys. 34, 2302–2307 (2001).
[Crossref]

J. L. Bohn, D. J. Nesbitt, and A. Gallagher, “Field enhancement in apertureless near-field scanning optical microscopy,” J. Opt. Soc. Am. A-Opt. Image Sci. Vis. 18, 2998–3006 (2001).
[Crossref]

J. N. Walford, J. A. Porto, R. Carminati, J. J. Greffet, P. M. Adam, S. Hudlet, J. L. Bijeon, A. Stashkevich, and P. Royer, “Influence of tip modulation on image formation in scanning near-field optical microscopy,” J. Appl. Phys. 89, 5159–5169 (2001).
[Crossref]

2000 (5)

M. Labardi, S. Patane, and M. Allegrini, “Artifact-free near-field optical imaging by apertureless microscopy,” Appl. Phys. Lett. 77, 621–623 (2000).
[Crossref]

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

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

I. S. Averbukh, B. M. Chernobrod, O. A. Sedletsky, and Y. Prior, “Coherent near field optical microscopy,” Opt. Commun. 174, 33–41 (2000).
[Crossref]

B. Knoll and F. Keilmann, “Infrared conductivity mapping for nanoelectronics,” Appl. Phys. Lett. 77, 3980–3982 (2000).
[Crossref]

1999 (4)

B. Knoll and F. Keilmann, “Near-field probing of vibrational absorption for chemical microscopy,” Nature 399, 134–137 (1999).
[Crossref]

H. Hatano and S. Kawata, “Applicability of deconvolution and nonlinear optimization for reconstructing optical images from near-field optical microscope images,” J. Microsc.-Oxf. 194, 230 – 234 (1999).
[Crossref]

H. Mutschke, A. C. Andersen, D. Clement, T. Henning, and G. Peiter, “Infrared properties of SiC particles,” Astron. Astrophys. 345, 187–202 (1999).

B. Knoll and F. Keilmann, “Electromagnetic fields in the cutoff regime of tapered metallic waveguides,” Opt. Commun. 162, 177–181 (1999).
[Crossref]

1998 (2)

R. Bachelot, G. Wurtz, and P. Royer, “An application of the apertureless scanning near-field optical microscopy: imaging a GaAlAs laser diode in operation,” Appl. Phys. Lett. 73, 3333–3335 (1998).
[Crossref]

L. Novotny, E. J. Sanchez, and X. S. Xie, “Near-field optical imaging using metal tips illuminated by higher-order Hermite-Gaussian beams,” Ultramicroscopy 71, 21–29 (1998).
[Crossref]

1997 (2)

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]

I. V. Lindell, K. I. Nikoskinen, and A. Viljanen, “Electrostatic image method for the anisotropic half space,” IEE Proc.-Sci. Meas. Technol. 144, 156 – 162 (1997).
[Crossref]

1996 (2)

I. V. Lindell, K. I. Nikoskinen, and M. J. Flykt, “Electrostatic image theory for an anisotropic half-space slightly deviating from transverse isotropy,” Radio Sci. 31, 1361 – 1368 (1996).
[Crossref]

A. Lahrech, R. Bachelot, P. Gleyzes, and A. C. Boccara, “Infrared-reflection-mode near-field microscopy using an apertureless probe with a resolution of lambda/600,” Opt. Lett. 21, 1315–1317 (1996).
[Crossref] [PubMed]

1995 (3)

H. Harima, S. Nakashima, and T. Uemura, “Raman-scattering from anisotropic LO-phonon-plasmon-coupled mode in n-type 4H-SiC and 6H-SiC,” J. Appl. Phys. 78, 1996–2005 (1995).
[Crossref]

J. C. E. Sten and I. V. Lindell, “An electrostatic image solution for the conducting prolate spheroid,” J. Electro-magn. Waves Appl. 9, 599 – 609 (1995).

F. Zenhausern, Y. Martin, and H. Wickramasinghe, “Scanning interferometric apertureless microscopy - optical imaging at 10 angstrom resolution,” Science 269, 1083–1085 (1995).
[Crossref] [PubMed]

1994 (4)

D. V. Redzic, “An electrostatic problem - a point-charge outside a prolate dielectric spheroid,” Am. J. Phys. 62, 1118 – 1121 (1994).
[Crossref]

M. Hofmann, A. Zywietz, K. Karch, and F. Bechstedt, “Lattice-dynamics of SiC polytypes within the bond-charge model,” Phys. Rev. B 50, 13,401–13,411 (1994).
[Crossref]

F. Zenhausern, M. Oboyle, and H. Wickramasinghe, “Apertureless near-field optical microscope,” Appl. Phys. Lett. 65, 1623–1625 (1994).
[Crossref]

Y. Inouye and S. Kawata, “Near-field scanning optical microscope with a metallic probe tip,” Opt. Lett. 19, 159–161 (1994).
[Crossref] [PubMed]

1993 (1)

F. Engelbrecht and R. Helbig, “Effect of crystal anisotropy on the infrared reflectivity of 6H-SiC,” Phys. Rev. B 48, 15,698 – 15,707 (1993).
[Crossref]

1992 (1)

D. V. Redzic, “Image of a moving spheroidal conductor,” Am. J. Phys. 60, 506–508 (1992).
[Crossref]

1991 (1)

W. Denk and D. Pohl, “Near-field optics - microscopy with nanometer-size fields,” J. Vac. Sci. Technol. B 9, 510–513 (1991).
[Crossref]

1985 (1)

A. Wokaun, “Surface enhancement of optical-fields - mechanism and applications,” Mol. Phys. 56, 1 – 33 (1985).
[Crossref]

1983 (2)

P. Aravind and H. Metiu, “The effects of the interaction between resonances in the electromagnetic response of a sphere-plane structure - applications to surface enhanced spectroscopy,” Surf. Sci. 124, 506–528 (1983).
[Crossref]

M. A. Ordal et al., “Optical properties of the metals Al, Co,Cu,Au,Fe,Pb,Ni,Pd,Pt,Ag,Ti and W in the infrared and far infrared,” Appl. Opt. 22, (1983).
[Crossref] [PubMed]

1982 (1)

A. Wokaun, J. P. Gordon, and P. F. Liao, “Radiation damping in surface-enhanced Raman-scattering,” Phys. Rev. Lett. 48, 957 – 960 (1982).
[Crossref]

1980 (1)

J. Gersten and A. Nitzan, “Electromagnetic theory of enhanced Raman-scattering by molecules adsorbed on rough surfaces,” J. Chem. Phys. 73, 3023–3037 (1980).
[Crossref]

Adam, P. M.

J. N. Walford, J. A. Porto, R. Carminati, J. J. Greffet, P. M. Adam, S. Hudlet, J. L. Bijeon, A. Stashkevich, and P. Royer, “Influence of tip modulation on image formation in scanning near-field optical microscopy,” J. Appl. Phys. 89, 5159–5169 (2001).
[Crossref]

Aizpurua, J.

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I. V. Lindell, K. I. Nikoskinen, and M. J. Flykt, “Electrostatic image theory for an anisotropic half-space slightly deviating from transverse isotropy,” Radio Sci. 31, 1361 – 1368 (1996).
[Crossref]

Nitzan, A.

J. Gersten and A. Nitzan, “Electromagnetic theory of enhanced Raman-scattering by molecules adsorbed on rough surfaces,” J. Chem. Phys. 73, 3023–3037 (1980).
[Crossref]

Novotny, L.

L. Novotny, E. J. Sanchez, and X. S. Xie, “Near-field optical imaging using metal tips illuminated by higher-order Hermite-Gaussian beams,” Ultramicroscopy 71, 21–29 (1998).
[Crossref]

Oboyle, M.

F. Zenhausern, M. Oboyle, and H. Wickramasinghe, “Apertureless near-field optical microscope,” Appl. Phys. Lett. 65, 1623–1625 (1994).
[Crossref]

Ocelic, N.

A. Huber, N. Ocelic, T. Taubner, and R. Hillenbrand, “Nanoscale resolved infrared probing of crystal structure and of plasmon-phonon coupling,” Nano Lett. 6, 774–778 (2006).
[Crossref] [PubMed]

A. Cvitkovic, N. Ocelic, J. Aizpurua, R. Guckenberger, and R. Hillenbrand, “Infrared imaging of single nanopar-ticles via strong field enhancement in a scanning nanogap,” Phys. Rev. Lett. 97, (2006).
[Crossref] [PubMed]

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

A. Huber, N. Ocelic, D. Kazantsev, and R. Hillenbrand, “Near-field imaging of mid-infrared surface phonon polariton propagation,” Appl. Phys. Lett. 87, (2005).
[Crossref]

N. Ocelic and R. Hillenbrand, “Subwavelength-scale tailoring of surface phonon polaritons by focused ion-beam implantation,” Nat. Mater. 3, 606–609 (2004).
[Crossref] [PubMed]

N. Ocelic, “Quantitative near-field phonon-polariton spectroscopy,” Ph.D. thesis, Technical University Munich (2007).

Ordal, M. A.

M. A. Ordal et al., “Optical properties of the metals Al, Co,Cu,Au,Fe,Pb,Ni,Pd,Pt,Ag,Ti and W in the infrared and far infrared,” Appl. Opt. 22, (1983).
[Crossref] [PubMed]

Patane, S.

M. Labardi, S. Patane, and M. Allegrini, “Artifact-free near-field optical imaging by apertureless microscopy,” Appl. Phys. Lett. 77, 621–623 (2000).
[Crossref]

Peiter, G.

H. Mutschke, A. C. Andersen, D. Clement, T. Henning, and G. Peiter, “Infrared properties of SiC particles,” Astron. Astrophys. 345, 187–202 (1999).

Pohl, D.

W. Denk and D. Pohl, “Near-field optics - microscopy with nanometer-size fields,” J. Vac. Sci. Technol. B 9, 510–513 (1991).
[Crossref]

Porto, J. A.

J. N. Walford, J. A. Porto, R. Carminati, J. J. Greffet, P. M. Adam, S. Hudlet, J. L. Bijeon, A. Stashkevich, and P. Royer, “Influence of tip modulation on image formation in scanning near-field optical microscopy,” J. Appl. Phys. 89, 5159–5169 (2001).
[Crossref]

Prior, Y.

I. S. Averbukh, B. M. Chernobrod, O. A. Sedletsky, and Y. Prior, “Coherent near field optical microscopy,” Opt. Commun. 174, 33–41 (2000).
[Crossref]

Raschke, M. B.

M. B. Raschke, L. Molina, T. Elsaesser, D. H. Kim, W. Knoll, and K. Hinrichs, “Apertureless near-field vibra-tional imaging of block-copolymer nanostructures with ultrahigh spatial resolution,” ChemPhysChem 6, 2197–2203 (2005).
[Crossref] [PubMed]

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

Redzic, D. V.

D. V. Redzic, “An electrostatic problem - a point-charge outside a prolate dielectric spheroid,” Am. J. Phys. 62, 1118 – 1121 (1994).
[Crossref]

D. V. Redzic, “Image of a moving spheroidal conductor,” Am. J. Phys. 60, 506–508 (1992).
[Crossref]

Renger, J.

J. Renger, S. Grafstrom, L. M. Eng, and R. Hillenbrand, “Resonant light scattering by near-field-induced phonon polaritons,” Phys. Rev. B 71, (2005).

Royer, P.

R. Fikri, D. Barchiesi, F. H’Dhili, R. Bachelot, A. Vial, and P. Royer, “Modeling recent experiments of aperture-less near-field optical microscopy using 2D finite element method,” Opt. Commun. 221, 13–22 (2003).
[Crossref]

J. N. Walford, J. A. Porto, R. Carminati, J. J. Greffet, P. M. Adam, S. Hudlet, J. L. Bijeon, A. Stashkevich, and P. Royer, “Influence of tip modulation on image formation in scanning near-field optical microscopy,” J. Appl. Phys. 89, 5159–5169 (2001).
[Crossref]

R. Bachelot, G. Wurtz, and P. Royer, “An application of the apertureless scanning near-field optical microscopy: imaging a GaAlAs laser diode in operation,” Appl. Phys. Lett. 73, 3333–3335 (1998).
[Crossref]

Samson, J. S.

J. S. Samson, G. Wollny, E. Brundermann, A. Bergner, A. Hecker, G. Schwaab, A. D. Wieck, and M. Havenith, “Setup of a scanning near field infrared microscope (SNIM): Imaging of sub-surface nano-structures in gallium-doped silicon,” Phys. Chem. Chem. Phys. 8, 753 – 758 (2006).
[Crossref] [PubMed]

Sanchez, E. J.

L. Novotny, E. J. Sanchez, and X. S. Xie, “Near-field optical imaging using metal tips illuminated by higher-order Hermite-Gaussian beams,” Ultramicroscopy 71, 21–29 (1998).
[Crossref]

Schneider, S. C.

S. C. Schneider, S. Grafstrom, and L. M. Eng, “Scattering near-field optical microscopy of optically anisotropicsystems,” Phys. Rev. B 71, (2005).
[Crossref]

Schwaab, G.

J. S. Samson, G. Wollny, E. Brundermann, A. Bergner, A. Hecker, G. Schwaab, A. D. Wieck, and M. Havenith, “Setup of a scanning near field infrared microscope (SNIM): Imaging of sub-surface nano-structures in gallium-doped silicon,” Phys. Chem. Chem. Phys. 8, 753 – 758 (2006).
[Crossref] [PubMed]

Sedletsky, O. A.

I. S. Averbukh, B. M. Chernobrod, O. A. Sedletsky, and Y. Prior, “Coherent near field optical microscopy,” Opt. Commun. 174, 33–41 (2000).
[Crossref]

Stashkevich, A.

J. N. Walford, J. A. Porto, R. Carminati, J. J. Greffet, P. M. Adam, S. Hudlet, J. L. Bijeon, A. Stashkevich, and P. Royer, “Influence of tip modulation on image formation in scanning near-field optical microscopy,” J. Appl. Phys. 89, 5159–5169 (2001).
[Crossref]

Stebounova, L.

L. Stebounova, B. B. Akhremitchev, and G. C. Walker, “Enhancement of the weak scattered signal in apertureless near-field scanning infrared microscopy,” Rev. Sci. Instrum. 74, 3670–3674 (2003).
[Crossref]

Sten, J. C. E.

J. C. E. Sten and I. V. Lindell, “An electrostatic image solution for the conducting prolate spheroid,” J. Electro-magn. Waves Appl. 9, 599 – 609 (1995).

Sukhov, S. V.

S. V. Sukhov, “Role of multipole moment of the probe in apertureless near-field optical microscopy,” Ultrami-croscopy 101, 111–122 (2004).
[Crossref]

Taubner, T.

A. Huber, N. Ocelic, T. Taubner, and R. Hillenbrand, “Nanoscale resolved infrared probing of crystal structure and of plasmon-phonon coupling,” Nano Lett. 6, 774–778 (2006).
[Crossref] [PubMed]

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

T. Taubner, R. Hillenbrand, and F. Keilmann, “Nanoscale polymer recognition by spectral signature in scattering infrared near-field microscopy,” Appl. Phys. Lett. 85, 5064–5066 (2004).
[Crossref]

T. Taubner, F. Keilmann, and R. Hillenbrand, “Nanomechanical resonance tuning and phase effects in optical near-field interaction,” Nano Lett. 4, 1669–1672 (2004).
[Crossref]

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

R. Hillenbrand, T. Taubner, and F. Keilmann, “Phonon-enhanced light-matter interaction at the nanometre scale,” Nature 418, 159–162 (2002).
[Crossref] [PubMed]

Uemura, T.

H. Harima, S. Nakashima, and T. Uemura, “Raman-scattering from anisotropic LO-phonon-plasmon-coupled mode in n-type 4H-SiC and 6H-SiC,” J. Appl. Phys. 78, 1996–2005 (1995).
[Crossref]

Vial, A.

R. Fikri, D. Barchiesi, F. H’Dhili, R. Bachelot, A. Vial, and P. Royer, “Modeling recent experiments of aperture-less near-field optical microscopy using 2D finite element method,” Opt. Commun. 221, 13–22 (2003).
[Crossref]

Viljanen, A.

I. V. Lindell, K. I. Nikoskinen, and A. Viljanen, “Electrostatic image method for the anisotropic half space,” IEE Proc.-Sci. Meas. Technol. 144, 156 – 162 (1997).
[Crossref]

Vogelgesang, R.

R. Esteban, R. Vogelgesang, and K. Kern, “Simulation of optical near and far fields of dielectric apertureless scanning probes,” Nanotechnology 17, 475–482 (2006).
[Crossref]

Walford, J. N.

J. N. Walford, J. A. Porto, R. Carminati, J. J. Greffet, P. M. Adam, S. Hudlet, J. L. Bijeon, A. Stashkevich, and P. Royer, “Influence of tip modulation on image formation in scanning near-field optical microscopy,” J. Appl. Phys. 89, 5159–5169 (2001).
[Crossref]

Walker, G. C.

L. Stebounova, B. B. Akhremitchev, and G. C. Walker, “Enhancement of the weak scattered signal in apertureless near-field scanning infrared microscopy,” Rev. Sci. Instrum. 74, 3670–3674 (2003).
[Crossref]

Wickramasinghe, H.

F. Zenhausern, Y. Martin, and H. Wickramasinghe, “Scanning interferometric apertureless microscopy - optical imaging at 10 angstrom resolution,” Science 269, 1083–1085 (1995).
[Crossref] [PubMed]

F. Zenhausern, M. Oboyle, and H. Wickramasinghe, “Apertureless near-field optical microscope,” Appl. Phys. Lett. 65, 1623–1625 (1994).
[Crossref]

Wickramasinghe, H. K.

Y. C. Martin, H. F. Hamann, and H. K. Wickramasinghe, “Strength of the electric field in apertureless near-field optical microscopy,” J. Appl. Phys. 89, 5774–5778 (2001).
[Crossref]

Wieck, A. D.

J. S. Samson, G. Wollny, E. Brundermann, A. Bergner, A. Hecker, G. Schwaab, A. D. Wieck, and M. Havenith, “Setup of a scanning near field infrared microscope (SNIM): Imaging of sub-surface nano-structures in gallium-doped silicon,” Phys. Chem. Chem. Phys. 8, 753 – 758 (2006).
[Crossref] [PubMed]

Willander, M.

N. Calander and M. Willander, “Theory of surface-plasmon resonance optical-field enhancement at prolate spheroids,” J. Appl. Phys. 92, 4878–4884 (2002).
[Crossref]

Wokaun, A.

A. Wokaun, “Surface enhancement of optical-fields - mechanism and applications,” Mol. Phys. 56, 1 – 33 (1985).
[Crossref]

A. Wokaun, J. P. Gordon, and P. F. Liao, “Radiation damping in surface-enhanced Raman-scattering,” Phys. Rev. Lett. 48, 957 – 960 (1982).
[Crossref]

Wollny, G.

J. S. Samson, G. Wollny, E. Brundermann, A. Bergner, A. Hecker, G. Schwaab, A. D. Wieck, and M. Havenith, “Setup of a scanning near field infrared microscope (SNIM): Imaging of sub-surface nano-structures in gallium-doped silicon,” Phys. Chem. Chem. Phys. 8, 753 – 758 (2006).
[Crossref] [PubMed]

Wurtz, G.

R. Bachelot, G. Wurtz, and P. Royer, “An application of the apertureless scanning near-field optical microscopy: imaging a GaAlAs laser diode in operation,” Appl. Phys. Lett. 73, 3333–3335 (1998).
[Crossref]

Xie, X. S.

L. Novotny, E. J. Sanchez, and X. S. Xie, “Near-field optical imaging using metal tips illuminated by higher-order Hermite-Gaussian beams,” Ultramicroscopy 71, 21–29 (1998).
[Crossref]

Zenhausern, F.

F. Zenhausern, Y. Martin, and H. Wickramasinghe, “Scanning interferometric apertureless microscopy - optical imaging at 10 angstrom resolution,” Science 269, 1083–1085 (1995).
[Crossref] [PubMed]

F. Zenhausern, M. Oboyle, and H. Wickramasinghe, “Apertureless near-field optical microscope,” Appl. Phys. Lett. 65, 1623–1625 (1994).
[Crossref]

Zywietz, A.

M. Hofmann, A. Zywietz, K. Karch, and F. Bechstedt, “Lattice-dynamics of SiC polytypes within the bond-charge model,” Phys. Rev. B 50, 13,401–13,411 (1994).
[Crossref]

Am. J. Phys. (2)

D. V. Redzic, “An electrostatic problem - a point-charge outside a prolate dielectric spheroid,” Am. J. Phys. 62, 1118 – 1121 (1994).
[Crossref]

D. V. Redzic, “Image of a moving spheroidal conductor,” Am. J. Phys. 60, 506–508 (1992).
[Crossref]

Appl. Opt. (1)

M. A. Ordal et al., “Optical properties of the metals Al, Co,Cu,Au,Fe,Pb,Ni,Pd,Pt,Ag,Ti and W in the infrared and far infrared,” Appl. Opt. 22, (1983).
[Crossref] [PubMed]

Appl. Phys. Lett. (10)

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

R. Bachelot, G. Wurtz, and P. Royer, “An application of the apertureless scanning near-field optical microscopy: imaging a GaAlAs laser diode in operation,” Appl. Phys. Lett. 73, 3333–3335 (1998).
[Crossref]

A. Huber, N. Ocelic, D. Kazantsev, and R. Hillenbrand, “Near-field imaging of mid-infrared surface phonon polariton propagation,” Appl. Phys. Lett. 87, (2005).
[Crossref]

F. Zenhausern, M. Oboyle, and H. Wickramasinghe, “Apertureless near-field optical microscope,” Appl. Phys. Lett. 65, 1623–1625 (1994).
[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]

T. Taubner, R. Hillenbrand, and F. Keilmann, “Nanoscale polymer recognition by spectral signature in scattering infrared near-field microscopy,” Appl. Phys. Lett. 85, 5064–5066 (2004).
[Crossref]

B. Knoll and F. Keilmann, “Infrared conductivity mapping for nanoelectronics,” Appl. Phys. Lett. 77, 3980–3982 (2000).
[Crossref]

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

R. Hillenbrand and F. Keilmann, “Material-specific mapping of metal/semiconductor/dielectric nanosystems at 10 nm resolution by backscattering near-field optical microscopy,” Appl. Phys. Lett. 80, 25–27 (2002).
[Crossref]

M. Labardi, S. Patane, and M. Allegrini, “Artifact-free near-field optical imaging by apertureless microscopy,” Appl. Phys. Lett. 77, 621–623 (2000).
[Crossref]

Astron. Astrophys. (1)

H. Mutschke, A. C. Andersen, D. Clement, T. Henning, and G. Peiter, “Infrared properties of SiC particles,” Astron. Astrophys. 345, 187–202 (1999).

ChemPhysChem (1)

M. B. Raschke, L. Molina, T. Elsaesser, D. H. Kim, W. Knoll, and K. Hinrichs, “Apertureless near-field vibra-tional imaging of block-copolymer nanostructures with ultrahigh spatial resolution,” ChemPhysChem 6, 2197–2203 (2005).
[Crossref] [PubMed]

IEE Proc.-Sci. Meas. Technol. (1)

I. V. Lindell, K. I. Nikoskinen, and A. Viljanen, “Electrostatic image method for the anisotropic half space,” IEE Proc.-Sci. Meas. Technol. 144, 156 – 162 (1997).
[Crossref]

J. Appl. Phys. (4)

H. Harima, S. Nakashima, and T. Uemura, “Raman-scattering from anisotropic LO-phonon-plasmon-coupled mode in n-type 4H-SiC and 6H-SiC,” J. Appl. Phys. 78, 1996–2005 (1995).
[Crossref]

J. N. Walford, J. A. Porto, R. Carminati, J. J. Greffet, P. M. Adam, S. Hudlet, J. L. Bijeon, A. Stashkevich, and P. Royer, “Influence of tip modulation on image formation in scanning near-field optical microscopy,” J. Appl. Phys. 89, 5159–5169 (2001).
[Crossref]

N. Calander and M. Willander, “Theory of surface-plasmon resonance optical-field enhancement at prolate spheroids,” J. Appl. Phys. 92, 4878–4884 (2002).
[Crossref]

Y. C. Martin, H. F. Hamann, and H. K. Wickramasinghe, “Strength of the electric field in apertureless near-field optical microscopy,” J. Appl. Phys. 89, 5774–5778 (2001).
[Crossref]

J. Chem. Phys. (1)

J. Gersten and A. Nitzan, “Electromagnetic theory of enhanced Raman-scattering by molecules adsorbed on rough surfaces,” J. Chem. Phys. 73, 3023–3037 (1980).
[Crossref]

J. Electro-magn. Waves Appl. (1)

J. C. E. Sten and I. V. Lindell, “An electrostatic image solution for the conducting prolate spheroid,” J. Electro-magn. Waves Appl. 9, 599 – 609 (1995).

J. Microsc.-Oxf. (2)

H. Hatano and S. Kawata, “Applicability of deconvolution and nonlinear optimization for reconstructing optical images from near-field optical microscope images,” J. Microsc.-Oxf. 194, 230 – 234 (1999).
[Crossref]

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

J. Opt. Soc. Am. A-Opt. Image Sci. Vis. (1)

J. L. Bohn, D. J. Nesbitt, and A. Gallagher, “Field enhancement in apertureless near-field scanning optical microscopy,” J. Opt. Soc. Am. A-Opt. Image Sci. Vis. 18, 2998–3006 (2001).
[Crossref]

J. Phys. Chem. B (2)

Z. H. Kim, B. Liu, and S. R. Leone, “Nanometer-scale optical imaging of epitaxially grown GaN and InN islands using apertureless near-field microscopy,” J. Phys. Chem. B 109, 8503–8508 (2005).
[Crossref]

Z. H. Kim and S. R. Leone, “High-resolution apertureless near-field optical imaging using gold nanosphere probes,” J. Phys. Chem. B 110, 19,804–19,809 (2006).

J. Phys. D-Appl. Phys. (1)

I. V. Lindell, G. Dassios, and K. I. Nikoskinen, “Electrostatic image theory for the conducting prolate spheroid,” J. Phys. D-Appl. Phys. 34, 2302–2307 (2001).
[Crossref]

J. Vac. Sci. Technol. B (1)

W. Denk and D. Pohl, “Near-field optics - microscopy with nanometer-size fields,” J. Vac. Sci. Technol. B 9, 510–513 (1991).
[Crossref]

Mol. Phys. (1)

A. Wokaun, “Surface enhancement of optical-fields - mechanism and applications,” Mol. Phys. 56, 1 – 33 (1985).
[Crossref]

Nano Lett. (3)

T. Taubner, F. Keilmann, and R. Hillenbrand, “Nanomechanical resonance tuning and phase effects in optical near-field interaction,” Nano Lett. 4, 1669–1672 (2004).
[Crossref]

A. Huber, N. Ocelic, T. Taubner, and R. Hillenbrand, “Nanoscale resolved infrared probing of crystal structure and of plasmon-phonon coupling,” Nano Lett. 6, 774–778 (2006).
[Crossref] [PubMed]

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

Nanotechnology (1)

R. Esteban, R. Vogelgesang, and K. Kern, “Simulation of optical near and far fields of dielectric apertureless scanning probes,” Nanotechnology 17, 475–482 (2006).
[Crossref]

Nat. Mater. (1)

N. Ocelic and R. Hillenbrand, “Subwavelength-scale tailoring of surface phonon polaritons by focused ion-beam implantation,” Nat. Mater. 3, 606–609 (2004).
[Crossref] [PubMed]

Nature (2)

B. Knoll and F. Keilmann, “Near-field probing of vibrational absorption for chemical microscopy,” Nature 399, 134–137 (1999).
[Crossref]

R. Hillenbrand, T. Taubner, and F. Keilmann, “Phonon-enhanced light-matter interaction at the nanometre scale,” Nature 418, 159–162 (2002).
[Crossref] [PubMed]

Opt. Commun. (4)

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

I. S. Averbukh, B. M. Chernobrod, O. A. Sedletsky, and Y. Prior, “Coherent near field optical microscopy,” Opt. Commun. 174, 33–41 (2000).
[Crossref]

R. Fikri, D. Barchiesi, F. H’Dhili, R. Bachelot, A. Vial, and P. Royer, “Modeling recent experiments of aperture-less near-field optical microscopy using 2D finite element method,” Opt. Commun. 221, 13–22 (2003).
[Crossref]

B. Knoll and F. Keilmann, “Electromagnetic fields in the cutoff regime of tapered metallic waveguides,” Opt. Commun. 162, 177–181 (1999).
[Crossref]

Opt. Lett. (2)

Philos. Trans. R. Soc. Lond. Ser. A-Math. Phys. Eng. Sci. (1)

F. Keilmann and R. Hillenbrand, “Near-field microscopy by elastic light scattering from a tip,” Philos. Trans. R. Soc. Lond. Ser. A-Math. Phys. Eng. Sci. 362, 787–805 (2004).
[Crossref]

Phys. Chem. Chem. Phys. (1)

J. S. Samson, G. Wollny, E. Brundermann, A. Bergner, A. Hecker, G. Schwaab, A. D. Wieck, and M. Havenith, “Setup of a scanning near field infrared microscope (SNIM): Imaging of sub-surface nano-structures in gallium-doped silicon,” Phys. Chem. Chem. Phys. 8, 753 – 758 (2006).
[Crossref] [PubMed]

Phys. Rev. B (4)

J. Renger, S. Grafstrom, L. M. Eng, and R. Hillenbrand, “Resonant light scattering by near-field-induced phonon polaritons,” Phys. Rev. B 71, (2005).

F. Engelbrecht and R. Helbig, “Effect of crystal anisotropy on the infrared reflectivity of 6H-SiC,” Phys. Rev. B 48, 15,698 – 15,707 (1993).
[Crossref]

S. C. Schneider, S. Grafstrom, and L. M. Eng, “Scattering near-field optical microscopy of optically anisotropicsystems,” Phys. Rev. B 71, (2005).
[Crossref]

M. Hofmann, A. Zywietz, K. Karch, and F. Bechstedt, “Lattice-dynamics of SiC polytypes within the bond-charge model,” Phys. Rev. B 50, 13,401–13,411 (1994).
[Crossref]

Phys. Rev. Lett. (3)

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

A. Cvitkovic, N. Ocelic, J. Aizpurua, R. Guckenberger, and R. Hillenbrand, “Infrared imaging of single nanopar-ticles via strong field enhancement in a scanning nanogap,” Phys. Rev. Lett. 97, (2006).
[Crossref] [PubMed]

A. Wokaun, J. P. Gordon, and P. F. Liao, “Radiation damping in surface-enhanced Raman-scattering,” Phys. Rev. Lett. 48, 957 – 960 (1982).
[Crossref]

Radio Sci. (1)

I. V. Lindell, K. I. Nikoskinen, and M. J. Flykt, “Electrostatic image theory for an anisotropic half-space slightly deviating from transverse isotropy,” Radio Sci. 31, 1361 – 1368 (1996).
[Crossref]

Rev. Sci. Instrum. (1)

L. Stebounova, B. B. Akhremitchev, and G. C. Walker, “Enhancement of the weak scattered signal in apertureless near-field scanning infrared microscopy,” Rev. Sci. Instrum. 74, 3670–3674 (2003).
[Crossref]

Science (1)

F. Zenhausern, Y. Martin, and H. Wickramasinghe, “Scanning interferometric apertureless microscopy - optical imaging at 10 angstrom resolution,” Science 269, 1083–1085 (1995).
[Crossref] [PubMed]

Surf. Sci. (1)

P. Aravind and H. Metiu, “The effects of the interaction between resonances in the electromagnetic response of a sphere-plane structure - applications to surface enhanced spectroscopy,” Surf. Sci. 124, 506–528 (1983).
[Crossref]

Ultrami-croscopy (1)

S. V. Sukhov, “Role of multipole moment of the probe in apertureless near-field optical microscopy,” Ultrami-croscopy 101, 111–122 (2004).
[Crossref]

Ultramicroscopy (1)

L. Novotny, E. J. Sanchez, and X. S. Xie, “Near-field optical imaging using metal tips illuminated by higher-order Hermite-Gaussian beams,” Ultramicroscopy 71, 21–29 (1998).
[Crossref]

Other (5)

A. Huber et al., “Simultaneous infrared material recognition and conductivity mapping by nanoscale near-field microscopy,” Adv. Mater. (in press).

J. Aizpurua, personal communication (2005).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons Inc, 1998).
[Crossref]

J. D. Jackson, Classical Electrodynamics (Wiley & Sons, 1998).

N. Ocelic, “Quantitative near-field phonon-polariton spectroscopy,” Ph.D. thesis, Technical University Munich (2007).

Cited By

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Figures (8)

Fig. 1.
Fig. 1.

Comparison of a typical s-SNOM probe-sample configuration with the finite-dipole and the point-dipole model. (a) The probing tip is typically an elongated structure illuminated by plain waves from the side. (b) In the finite-dipole model the tip is approximated by a spheroid in a uniform electric field E 0. (c) In the point dipole model the tip is first reduced to a small sphere in an uniform electric field E 0. The sphere is then further reduced to a point dipole located in its center. The scattered field is finally calculated from a dipolar near-field coupling with the sample.

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Fig. 2.
Fig. 2.

(a) Electric field Es around a perfectly conducting spheroid (ε→∞) with R = 0.1L located in a homogeneous external field E 0 oriented along the spheroid’s major axis. (b) Electric field of the spheroid as a function of the distance D from the spheroid apex along the z-axis. Shown are the exact result Es from Eq. 1 (dashed line), the monopole field Em (red line), point-dipole field Epd (blue line), and field of a point dipole at the center of the spheroid, Ecd (green line), all scaled to the exact value Es at the spheroid surface (D = 0).

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Fig. 3.
Fig. 3.

(a) The electric potential outside a grounded perfectly conducting spheroid in the presence of an external charge Qe is equivalent to the potential of a certain non-uniform line charge distribution qi . (b) Line charge distribution qi induced along the axis of R L = 0.1 spheroid as calculated from the first 10 terms in Eq. 4. The external point charge is located at D = 2R (dashed line) and D = 3R (full line).

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Fig. 4.
Fig. 4.

(a) Totally induced charge Qt , calculated for spheroids with R L = 0.2 (full line), R L = 0.1 (dashed) and R L = 0.05 (dotted). (b) Fraction g of the totally induced charge Qt found within the range R + D from the tip end. Three different shape factor are shown: R L = 0.2 (full line), R L = 0.1 (dashed), and R L = 0.05 (dotted). For D/R ≳ 1.5 the calculation was done according to Eq.4. As for D/R ≲ 1.5 the solution of Eq.4 exhibits convergence problems, an improved theory with better numerical behavior was used [46]. There the charge distribution is represented by a line charge plus a point charges located between the tip and the focus of each spheroid apex. Note that the shaded region between D = 0 and D = 0.5R represents distances which are not encountered in the model.

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Fig. 5.
Fig. 5.

Charges participating in the near-field interaction between the probe and the sample, together with their positions according to the finite-dipole model.

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Fig. 6.
Fig. 6.

Choosing the far-field reflection coefficient rp . (a) Probe close to the material boundary: rp ≈ r p,A, (b) Probe far from the material boundary: rp = r p,B.

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Fig. 7.
Fig. 7.

Approach curves on a gold surface demodulated at the second harmonic (n = 2) of the modulation frequency. (a) Predictions by the finite-dipole model (full line) and the point-dipole model (dashed line) compared to the experimentally obtained values (dots). All values are normalized to the signal at H = 0. (b) Experimental approach curve (red dots) fitted by a dipole model, with ratio between the spheroid’s semi-major and semi-minor axis being the fit parameter.

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Fig. 8.
Fig. 8.

Near-field spectra of a 4H-SiC crystal cut parallel to the c-axis. Signal demodulation was done at the second harmonic (n=2) of the tapping frequency. Shown are the experimental data (red dots) and the predictions by the finite-dipole model (solid line), the point-dipole model (dashed black line), and the point-dipole model employing the fit parameter as described in Section 3.2 (dashed blue line).

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Tables (1)

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Table 1. Literature data used for calculating the SiC dielectric function.

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Equations (26)

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E s ( D ) = 2 F ( L + D ) D 2 + L ( 2 D + R ) + ln L − F + D L + F + D 2 F ( L − ε t R ) LR ( ε t − 1 ) − ln L − F L + F E 0 ,
β = ε s − 1 ε s + 1
Q t = − Q e ln L + F + D L − F + D ln L + F L − F .
q i ( z ) = − Q e Θ ( F 2 − z 2 ) 2 F ∑ n = 0 ∞ ( 2 n + 1 ) Q n ( ( L + D ) F ) P n ( L F ) Q n ( L F ) P n ( z F )
Q i = gQ t = ∫ L − ( R + D ) L q i ( z ) dz
Q i = g ′ Q t = ( g − R + D 2 L ) Q t .
Q i = Q i , 0 + Q i , 1 .
D 0 = 2 H + R and
D 1 = 2 H + R 2 ,
Q i , 0 = f 0 Q ′ 0 = − ( g − R + H L ) ln 4 L 4 H + 3 R ln 4 L R Q ′ 0
Q i , 1 = f 1 Q ′ i = − ( g − 3 R + 4 H 4 L ) ln 2 L 2 H + R ln 4 L R Q ′ i .
Q ′ 0 = − β Q 0
Q ′ i = − β Q i .
Q i = − β f 0 1 + β f 1 Q 0 .
η = Q i Q 0 = β ( g − R + H L ) ln 4 L 4 H + 3 R ln 4 L R − β ( g − 3 R + 4 H 4 L ) ln 2 L 2 H + R .
α eff = p eff E 0 = R 2 L 2 L R + ln R 4 eL ln 4 L e 2 ( 2 + β ( g − R + H L ) ln 4 L 4 H + 3 R ln 4 L R − β ( g − 3 R + 4 H 4 L ) ln 2 L 2 H + R ) .
α effpd = α 1 − αβ 16 π ( R + H ) 3
E sca ∝ ( 1 + r p ) 2 α eff E inc ,
E sca ~ α ( 1 + β ) 1 − αβ 16 π ( R + H ) 3 E inc = ( 1 + β ) α effpd E inc
E n = s n e i ϕ n ~ ( 1 + r p ) 2 α eff , n E inc .
s n , A s n , B = ∣ ( 1 + r A ) 2 α eff , n , A ( 1 + r A ) 2 α eff , n , B ∣ = ∣ α eff , n , A α eff , n , B ∣
ϕ n , A ϕ n , B = arg ( ( 1 + r A ) 2 α eff , n , A ( 1 + r A ) 2 α eff , n , B ) = arg ( α eff , n , A α eff , n , B ) .
ε ( ω ) = ε ∞ + ε ∞ ( ω LO 2 − ω TO 2 ) ω TO 2 − ω 2 − iγω
β ⊥ = ε ⊥ − 1 ε ⊥ + 1 ,
β ∥ = ε ⊥ ε ∥ − 1 ε ⊥ ε ∥ + 1 .
β = β ⊥ + β ∥ 2 .

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