OSA's Digital Library

Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics


  • Editor: Gregory W. Faris
  • Vol. 3, Iss. 9 — Sep. 8, 2008

Numerical simulations of global approach for photon scanning tunneling microscopy: coupling of finite-element and boundary integral methods

Peijun Li  »View Author Affiliations

JOSA A, Vol. 25, Issue 8, pp. 1929-1936 (2008)

View Full Text Article

Enhanced HTML    Acrobat PDF (718 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



An accurate global model is proposed for a two-dimensional probe–sample system of photon scanning tunneling microscopy in near-field optics. A coupling of a finite-element method in the inhomogeneous sample and a boundary integral method on the artificial boundary of the truncated domain is developed. Numerical experiments are included to demonstrate the effectiveness of the proposed method and to show the features of wave propagation in photon scanning tunneling microscopy.

© 2008 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(180.5810) Microscopy : Scanning microscopy
(290.2558) Scattering : Forward scattering
(180.4243) Microscopy : Near-field microscopy

ToC Category:

Original Manuscript: March 20, 2008
Revised Manuscript: May 28, 2008
Manuscript Accepted: June 8, 2008
Published: July 8, 2008

Virtual Issues
Vol. 3, Iss. 9 Virtual Journal for Biomedical Optics

Peijun Li, "Numerical simulations of global approach for photon scanning tunneling microscopy: coupling of finite-element and boundary integral methods," J. Opt. Soc. Am. A 25, 1929-1936 (2008)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, 2nd ed., Vol. 93of the Applied Mathematical Sciences Series (Springer-Verlag, 1998).
  2. D. Courjon, Near-Field Microscopy and Near-Field Optics (Imperial College Press, 2003).
  3. C. Girard and A. Dereux, “Near-field optics theories,” Rep. Prog. Phys. 59, 657-699 (1996). [CrossRef]
  4. E. Betzig and J. K. Trautman, “Near-field optics: Microscopy, spectroscopy, and surface modification beyond the diffraction limit,” Science 257, 189-195 (1992). [CrossRef] [PubMed]
  5. D. Courjon and C. Bainier, “Near field microscopy and near field optics,” Rep. Prog. Phys. 57, 989-1028 (1994). [CrossRef]
  6. P. Carney and J. Schotland, “Near-field tomography,” in Inside Out: Inverse Problems and Applications, G.Uhlmann, ed. (Cambridge U. Press, 2003), pp. 133-168.
  7. G. Binnig and H. Rohrer, “Scanning tunneling microscopy,” Helv. Phys. Acta 55, 726-735 (1982). [CrossRef]
  8. D. Courjon, K. Sarayeddine, and M. Spajer, “Scanning tunneling optical microscopy,” Opt. Commun. 71, 23-28 (1989). [CrossRef]
  9. P. Carney and J. Schotland, “Determination of three-dimensional structure in photon scanning tunneling mircoscopy,” J. Opt. A, Pure Appl. Opt. 4, S140-S144 (2002). [CrossRef]
  10. P. A. Temple, “Total internal reflection microscopy: A surface inspection technique,” Appl. Opt. 20, 2656-2664 (1981). [CrossRef] [PubMed]
  11. A. Cvitkovic, N. Ocelic, and R. Hillenbrand, “Analytical model for quantitative prediction of material contrasts in scattering-type near-field optical microscopy,” Opt. Express 15, 8550-8565. [CrossRef] [PubMed]
  12. C. Girard, “Theoretical atomic-force-microscopy study of a stepped surface: Nonlocal effects in the probe,” Phys. Rev. B 43, 8822-8828 (1991). [CrossRef]
  13. N. Gregersen, B. Tromborg, and S. Bozhevolnyi, “Vectorial modeling of near-field imaging with uncoated fiber probes: Transfer function and resolving power,” Appl. Opt. 45, 8739-8747 (2006). [CrossRef] [PubMed]
  14. S. Wang, “Analysis of probe-sample interaction in near-field optical image of dielectric structure,” Microsc. Microanal. 5, 290-295 (1999). [CrossRef] [PubMed]
  15. J.-C. Weeber, F. de Fornel, and J.-P. Goudonnet, “Numerical study of the tip-sample interaction in the photon scanning tunneling microscope,” Opt. Commun. 126, 285-292 (1996). [CrossRef]
  16. D. Van Labeke and D. Barchiesi, “Probes for scanning tunneling optical microscopy: A theoretical comparison,” J. Opt. Soc. Am. A 10, 2193-2201 (1993). [CrossRef]
  17. S. Bozhevolnyi, S. Berntsen, and E. Bozhevolnaya, “Extension of the macroscopic model for reflection near-field microscopy: Regularization and image formulation,” J. Opt. Soc. Am. A 11, 609-617 (1994). [CrossRef]
  18. J.-J. Greffet and R. Carminati, “Image formulation in near-field optics,” Prog. Surf. Sci. 56, 133-237 (1997). [CrossRef]
  19. A. Castiaux, H. Danzebrink, and X. Bouju, “Glass and silicon probes: A comparative theoretical study for near-field optical microscopy,” J. Appl. Phys. 84, 52-57 (1998). [CrossRef]
  20. J. Sun, P. Carney, and J. Schotland, “Strong tip effects in near-field scanning optical tomography,” J. Appl. Phys. 102, 103103 (2007). [CrossRef]
  21. L. Novotny, D. Pohl, and P. Regli, “Near-field, far-field and imaging properties of the 2D aperture SNOM,” Ultramicroscopy 57, 180-188 (1995). [CrossRef]
  22. H. Furukawa and S. Kawata, “Analysis of image formation in a near-field scanning optical microscope: Effects of multiple scattering,” Opt. Commun. 132, 170-178 (1996). [CrossRef]
  23. K. Tanaka, M. Tanaka, and T. Omoya, “Boundary integral equation for a two-dimensional simulator of a photon scanning tunneling microscopy,” J. Opt. Soc. Am. A 15, 1918-1931 (1998). [CrossRef]
  24. S. Goumri-Said, L. Salomon, J. Dufour, and F. de Fornel, “Two-dimensional numerical simulations of photon scanning tunneling microscopy: Fourier modal method and R-matrix algorithm,” Opt. Quantum Electron. 36, 787-806 (2004). [CrossRef]
  25. S. Goumri-Said, L. Salomon, J. Dufour, F. de Fornel, and A. Zayats, “Numerical simulations of photon scanning tunneling microscopy: Role of probe tip geometry in image formation,” Opt. Commun. 224, 245-258 (2005). [CrossRef]
  26. F. Brezzi and C. Johnson, “On the coupling of boundary integral and finite element methods,” Calcolo 16, 189-201 (1979). [CrossRef]
  27. G. N. Gatica and W. L. Wendland, “Coupling of mixed finite elements and boundary elements for linear and nonlinear elliptic problems,” Appl. Anal. 63, 39-75 (1996). [CrossRef]
  28. G.-C. Hsiao, “The coupling of BEM and FEM--a brief review,” in Boundary Element X, (Springer, 1988), Vol. 1, pp. 431-445.
  29. C. Johnson and J.-C. Nédélec, “On the coupling of boundary integral and finite element methods,” Math. Comput. 35, 1063-1079 (1980). [CrossRef]
  30. T. Tran, “The K-operator and the Galerkin method for strongly elliptic equations on smooth curves: Local estimates,” Math. Comput. 64, 501-513 (1995).
  31. P. Persson and G. Strang, “A simple mesh generator in Matlab,” SIAM Rev. 46, 329-345 (2004). [CrossRef]
  32. J. Jin, The Finite Element Method in Electromagnetics, (Wiley, 1993).
  33. J. Coyle, “Locating the support of objects contained in a two-layered background medium in two dimensions,” Inverse Probl. 16, 275-292 (2000). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited