Abstract
The rigorous calculation of Scanning Near-field Optical Microscope (SNOM) images is a difficult task which needs the resolution of a complicated problem of diffraction in unusual conditions: two diffracting objects are present, they contain details smaller than the wavelength and are very close. Various approaches have been proposed to attack this problem and the purpose of this paper is to present, classify and compare these theoretical works.
First we rapidly present the pioneer theoretical papers which give the principle of SNOM or calculate the near-field above various small apertures. After the various models of tip detection are discussed: energy flow or scattering theory.
Then we present the simpler model where the coupling between the sample and the tip is neglected but which give analytical solutions and thus can lead to a real discussion of the role of the various parameters. Finally we describe more rigorous models where the tip-sample coupling is taken into account.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Descouts, P. and Siegenthaler, H. (1991) ‘10 Years of STM’, Proceedings of the Sixth International Conference on Scanning Tunneling Microscopy Interlaken North Holland.
Pohl D. W., (1990) ‘Scanning near-field optical microscopy’, in C.J.R. Sheppard, and T. Mulvey (eds), Advances in optical and electron microscopy, Academic Press, London, pp. 243–312.
Synge E. A., (1928) ‘A suggested method for extending microscopic resolution into the ultramicroscopic region’, Phil. Mag. C, 356–362.
Mc Cutchen, C. W. (1967) ‘Superresolution in Microscopy and the Abbe resolution limit’, J. Opt. Soc. Amer. 57, 1190–1192.
Massey, G. A. (1984) ‘microscopy and pattern generation with scanned evanescent waves’, Appl. Opt. 23, 658–660.
Ch. Fischer, U., Düng, U. and Pohl, D. W. (1987) ‘Near-field optical scanning microscopy and enhanced spectroscopy with submicron aperture’, Scanning Microscopy Supplement 1, 47–52.
Leviatan, Y. (1988) ‘Electromagnetic coupling between two half-space regions separated by two slot-perforated parallel conducting screens’, IEEE trans. Microw. Theory Tech. MTT-36, 44–50.
Vigoureux, J. M., Girard, C. and Courjon, D. (1989) ‘General principle of scanning tunneling optical microscopy,’ Opt. Lett. 14, 1039–1041.
Vigoureux, J. M., Depasse, F. and Girard, C. (1992) ‘superresolution of near-field optical microscopy from properties of confined electromagnetic waves’, Appl. Opt. 16, 3036–3045.
Vigoureux, J. M. and Courjon, D. (1992) ‘Detection of nonradiative fields in light of the Heisenberg uncertainly principle and the Rayleigh criteriom’, Appl. Opt. 31 p 3170–3177
Bethe, H.A. (1944) ‘Theory of diffraction by small holes’, Phys. Rev. 66, 163–182.
Bouwkamp, C. J. (1954) ‘Diffraction theory’, Reports in Physics, 27, 35–100.
English, R. E. and George, N. (1988) ‘Diffraction from a small square aperture: approximate aperture fields’, J. Opt. Soc. Am. A5, 192–199.
Wirgin, M. (1970) ‘Influence de l’épaisseur de l’écran sur la diffraction par une fente’, C. R. Acad. Sci. Paris 270, 1457–1460.
Neerhoff, F. L. and Mur, G. (1973) ‘Diffraction of a plane electromagnetic wave by a slit in a thick screen placed between two different media’, Appl. Sci. Res. 28, 73–88.
Harrington, R. F. and Auckland, D. T. (1980) ‘Electromagnetic transmission through narrow slots in thick conducting screens’, IEEE Trans. Antennas Propagat. AP 28, 616–622.
Mata Mendez, O., Cadihac, O. and Petit, R. (1983) ‘Diffraction of a two-dimensional electromagnetic beam wave by a thick slit pierced in a perfectly conducting screen’, J. Opt. Soc. Am. 73, 328–331.
Betzig, E., Harootunian, A., Lewis, A. and Isaacson, M. (1986) ‘Near-field diffraction by a slit: implications for supperresolution microscopy’, Appl. Opt. 25, 1890–1900.
Roberts, A. (1987) ‘Electromagnetic theory of diffraction by a circular aperture in a thick, perfectly conducting screen,’ J. Opt. Soc. Am. A4, 1970–1983.
Roberts, A. (1992) ‘Small hole coupling of radiation into a near-field probe’, J. Appl. Phys. 70, 4045–4049.
Born, M., Wolf, E. (1970) ‘Principle of Optics’, Pergamon press, New York.
Van de Hulst, H.C. (1957) ‘Light scattering by small particles’, Wiley, New York.
Kerker, M. (1983) ‘The scattering of light and other electromagnetic radiation’, Academic Press, New York.
Tirosh, E. and Cohen, A. (1989) ‘Near-field scattering by passive and active small spherical particles’, J. Opt. Soc. Am. 6, 523–524.
Jones, D. S. (1986) ‘Acoustic and Electromagnetic waves’, Garendon Press, Oxford.
Au Kong, J. (1984) ‘Electromagnetic wave Theory’, John Wiley, New York.
Petit, R. (1980), ‘Electromagnetic Theory of gratings’ Vol. 22 of Topics in current Physics, Springer-Verlag, Berlin.
Maystre, D. (1984) ‘Rigorous vector theories of diffraction gratings’, in E. Wolf (ed) Progress in Optics XXI, Elsevier, Amsterdam, pp 1–66.
Soto-Crespo, J. M. and Nieto-Vesperinas, M. (1989) ‘Electromagnetic scattering from very rough random surfaces and deep reflection gratings’, J. Opt. Soc. Am. A 6, 367–384.
Toigo, F., Marvin, A., Celli, V. and Hill, N. R. (1977) ‘Optical properties of rough surfaces: General theory and the small roughness limit’, Phys. Rev. B13, 5618–5626.
Agarwal, G. S. (1977) ‘interaction of electromagnetic waves at rough dielectric surfaces’, Phys. Rev. B15, 2371–2383.
Maradudin, A. and Mills, D. (1975) ‘Scattering and absorption of electromagnetic radiation by a semi-infinite medium in the presence of surface roughness’, Phys. Rev. B 11, 1392–1415.
Labani, B., Girard, C., Courjon, D. and Van labeke, D. (1990) ‘Optical interaction between a dielectric tip and a nanometric lattice: implications for near-field microscopy’, J. Opt. Soc. Amer. A 7, 936–943.
Girard, C. and Courjon, D. (1990) ‘Model for scanning tunneling optical microscopy: A microscopic self-consistent approach’, Phys. Rev. B 42, 9340–9349.
Girard, C. and Spajer, M. (1990) ‘Model for reflection near-field optical microscopy’, Appl. Opt. 29, 3726–3733.
Girard, C. and Bouju, X. (1991) ‘Self-consistent study of dynamical and polarization effects in near-field optical microscopy’, J. Opt. Soc. Amer. B 9, 298–305.
Girard, C. and Bouju, X. (1991) ‘Coupled electromagnetic modes between a corrugated surface and a thin probe tip’, J. Chem. Phys. 95, 2056–2064.
Girard, C. (1992) ‘Multipolar propagators near a corrugated surface: Implication for local-probe microscopy’, Phys. Rev. B 45, 1800–1810.
Girard, C. (1993) ‘Near-field detection and local spectroscopy of a surface: a self consistent theoretical study,’ N.F.O. Besançon to be published in this review.
Salomon, L., De fornel, F. and Goudonnet, J.P. (1991) ‘Sample-tip coupling efficiencies of the photon scanning tunneling microscope’, J. Opt. Soc. Amer. 8, 2009–2015.
Cites, J., Sanghadasa, M. F. M., Sung, C. C., Reddick, R. C., Warmack, R. J. and Ferrell, T. L. (1992) ‘Analysis of photon scanning tunneling microscope images’, J. Appl. Phys. 71, 7–10.
Van Labeke, D and Barchiesi, D. (1992) ‘Scanning-tunneling optical microscopy: a theoretical macroscopic approach,’ J. Opt. Soc. Am. A 9, 732–739.
Jackson, J. D. (1975) ‘Classical electrodynamics’, John Wiley, New York.
Abramowitz, M. and Stegun, I. A. (1964) ‘Hanbook of mathematical functions,’ Dover, New-York.
Barchiesi, D. and Van Labeke, D. (1993) ‘Application of Mie scattering of evanescent waves to scanning optical tunneling microscopy theory’, to be published in Modern Optics.
Van Labeke, D. (1992) ‘Near-field optical microscopy: theoretical concepts and models’, in S. Gauthier and C. Joachim (eds.) ‘Scanning Probe microscopy: beyond the images’ Editions de Physique, les Hulis, France, pp. 228–275.
Betzig, E., Trautman, J. K., Harris, T. D., Weiner, J. S. and Kostelar, R. L (1991) ‘Breaking the diffraction barrier: optical microscopy on a nanometric scale’, Science 251, 1468–1470.
Barchiesi, D. and Van Labeke, D. (1993)’ scanning tunneling optical microscopy: theoretical study of polarization effects with two models of tip’, N.F.O. Besançon to be published in this review.
Goudonnet, J. P., Salomon, L., De Fornel, F., Bouillot, E., Adam, P. and Neviere, M. (1992) ‘Recent progress in photon scanning tunneling microscopy’, Conference SPIE, Los Angeles.
Denk, W. and Pohl, D. W. (1991) ‘Near-field optics: Microscopy with nanometer-size fields’, J. Vac. Sci. Technol. B 9, 510–513.
Bernt, R., Gimzewski, J. K. and Schlittler, R.R. (1992) ‘Enhanced photon emission from the STM: a general property of metal surfaces’, Ultramicroscopy 42-44, 355–359.
Dereux, A., Vigneron, J. P., Lambin, Ph. and Lucas, A. A. (1991) ‘Theory of near-field optics with applications to SNOM and optical binding’, Physica B 175, 65–67.
Dereux, A. (1991) ‘Théorie de l’optique du champ proche,’ thesis Namur, Belgium.
Greffet, J. J. and Ladan, F. R. (1992) ‘Comparison between theoretical and experimental scattering of an s-polarized electromagnetic wave by a two-dimensional obstacle on a surface’, J. Opt. Soc. Am. A 8, 1261–1269.
Santenac, A. and Greffet, J. J. (1992) ‘Scattering by deep inhomogeneous gratings’, J. Opt. Soc. Am. A 9, 996–1005.
Efrima, S. and Metiu, H. (1902) ‘Classical theory of light scattering by an adsorbed molecule. I. Theory’ J. Chem. Phys. 70, 1602–1613.
Fischer, U. Ch. and Pohl, D. W. (1989) ‘Observation of single-particle plasmon by near-field optical microscopy’, Phys. Rev. Lett. 62, 458–461.
Neviere, M. (1993) ‘Diffraction gratings as components for photon scanning tunneling microscope image interpretation’, N.F.O. Besançon to be published in this review.
Bernstsen, S., Bozhevolnaya, E. and Bozhevolnyi, S. (1993) ‘Macroscopic self consistent model for external reflection near-field microscopy,’ to be published in J. Opt. Soc. Am.
Singham, S. B. and Saltzman, G. C. (1986) ‘Evaluation of the scattering matrix of an arbitrary particle using the coupled dipole approximation,’ J. Chem. Phys. 84, 2658–2667.
Singham, S. B. and Bohren, C. F. (1992) ‘Light scattering by an arbitrary particle: the scattering-order formulation of the coupled-dipole method,’ J. Opt.Soc. Am. A 5, 1867–1872.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1993 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
van Labeke, D., Barchiesi, D. (1993). Theoretical Problems in Scanning Near-Field Optical Microscopy. In: Pohl, D.W., Courjon, D. (eds) Near Field Optics. NATO ASI Series, vol 242. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1978-8_19
Download citation
DOI: https://doi.org/10.1007/978-94-011-1978-8_19
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-4873-6
Online ISBN: 978-94-011-1978-8
eBook Packages: Springer Book Archive