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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: Grover Swartzlander
  • Vol. 31, Iss. 3 — Mar. 1, 2014
  • pp: 526–533

Simplified bond-hyperpolarizability model of second harmonic generation, group theory, and Neumann’s principle

Adalberto Alejo-Molina, Hendradi Hardhienata, and Kurt Hingerl  »View Author Affiliations

JOSA B, Vol. 31, Issue 3, pp. 526-533 (2014)

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We discuss the susceptibility third-rank tensor for second harmonic and sum-frequency generation, associated with low index surfaces of silicon (Si(001), Si(011), and Si(111)), from two different approaches: the simplified bond-hyperpolarizability model (SBHM) and group theory (GT). We show that the SBHM agrees very well with the experimental results for simple surfaces because the definitions of the bond vectors implicitly include the geometry of the crystal and therefore the symmetry group. However, for more complex surfaces it is shown that one can derive from GT the SBHM tensor, if Kleinman symmetry is allowed.

© 2014 Optical Society of America

OCIS Codes
(190.4350) Nonlinear optics : Nonlinear optics at surfaces
(240.4350) Optics at surfaces : Nonlinear optics at surfaces
(240.6700) Optics at surfaces : Surfaces

ToC Category:
Optics at Surfaces

Original Manuscript: October 28, 2013
Revised Manuscript: January 10, 2014
Manuscript Accepted: January 10, 2014
Published: February 19, 2014

Adalberto Alejo-Molina, Hendradi Hardhienata, and Kurt Hingerl, "Simplified bond-hyperpolarizability model of second harmonic generation, group theory, and Neumann’s principle," J. Opt. Soc. Am. B 31, 526-533 (2014)

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  1. E. J. Adles and D. E. Aspnes, “Application of the anisotropic bond model to second-harmonic generation from amorphous media,” Phys. Rev. B 77, 165102 (2008). [CrossRef]
  2. J. Kwon, M. C. Downer, and B. S. Mendoza, “Second-harmonic and reflectance-anisotropy spectroscopy of vicinal Si(001)/SiO2 interfaces: experiment and simplified microscopic model,” Phys. Rev. B 73, 195330 (2006). [CrossRef]
  3. J. T. Madden, V. J. Hall, and G. J. Simpson, “Mining the polarization-dependence of nonlinear optical measurements,” Analyst 136, 652–662 (2011), and references therein. [CrossRef]
  4. C. J. Dehen, R. M. Everly, R. M. Plocinik, H. G. Hedderich, and G. J. Simpson, “Discrete retardance second harmonic generation ellipsometry,” Rev. Sci. Instrum. 78, 013106 (2007). [CrossRef]
  5. N. J. Begue, R. M. Everly, V. J. Hall, L. Haupert, and G. J. Simpson, “Nonlinear optical Stokes ellipsometry. 2. Experimental demonstration,” J. Phys. Chem. C 113, 10166–10175 (2009). [CrossRef]
  6. M. A. van der Veen, V. K. Valev, T. Verbiest, and D. E. De Vos, “In situ orientation-sensitive observation of molecular adsorption on a liquid/zeolite interface by second-harmonic generation,” Langmuir 25, 4256–4261 (2009). [CrossRef]
  7. B. S. Mendoza and W. L. Mochán, “Polarizable-bond model for second-harmonic generation,” Phys. Rev. B 55, 2489–2502 (1997). [CrossRef]
  8. N. Arzate and B. S. Mendoza, “Polarizable bond model for optical spectra of Si(100) reconstructed surfaces,” Phys. Rev. B 63, 113303 (2001). [CrossRef]
  9. G. D. Powell, J. F. Wang, and D. E. Aspnes, “Simplified bond-hyperpolarizability model of second harmonic generation,” Phys. Rev. B 65, 205320 (2002).
  10. J.-F. T. Wang, G. D. Powell, R. S. Johnson, G. Lucovsky, and D. E. Aspnes, “Simplified bond-hyperpolarizability model of second harmonic generation: application to Si-dielectric interfaces,” J. Vac. Sci. Technol. B 20, 1699–1705 (2002). [CrossRef]
  11. H. Hardhienata, A. Prylepa, D. Stifter, and K. Hingerl, “Simplified bond-hyperpolarizability model of second-harmonic-generation in Si(111): theory and experiment,” J. Phys. 423, 012046 (2013). [CrossRef]
  12. J. F. McGilp, “Using steps at the Si–SiO2 interface to test simple bond models of the optical second-harmonic response,” J. Phys. 19, 016006 (2007). [CrossRef]
  13. E. J. Adles and D. E. Aspnes, “The anisotropic bond model of nonlinear optics,” Phys. Stat. Sol. A 205, 728–731 (2008). [CrossRef]
  14. J. F. Nye, Physical Properties of Crystals, Their Representations by Tensors and Matrices (Clarendon, 1957).
  15. R. C. Powell, Symmetry, Group Theory, and the Physical Properties of Crystals, Lecture Notes in Physics (Springer, 2010).
  16. F. A. Cotton, Chemical Applications of Group Theory, 3rd ed. (Wiley, 1990).
  17. D. C. Harris and M. D. Bertolucci, Symmetry and Spectroscopy—An Introduction to Vibrational and Electronic Spectroscopy (Dover, 1989).
  18. R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic, 2003).
  19. Y. R. Shen, The Principles of Nonlinear Optics (Wiley, 1984).
  20. T. A. Driscoll and D. Guidotti, “Symmetry analysis of second-harmonic generation in silicon,” Phys. Rev. B 28, 1171–1173 (1983). [CrossRef]
  21. J. E. Sipe, D. J. Moss, and H. M. van Driel, “Phenomenological theory of optical second- and third-harmonic generation from cubic centrosymmetric crystals,” Phys. Rev. B 35, 1129–1141 (1987). [CrossRef]
  22. Factor 2 in all the tensors in Table 3.5 from Ref. [15] is a mistake. Prof. R. C. Powell, (private communication, September 2013).
  23. G. G. Malliaras, H. A. Wierenga, and T. Rasing, “Study of the step structure of vicinal Si(110) surfaces using optical second harmonic generation,” Surf. Sci. 287, 703–707 (1993). [CrossRef]
  24. G. Lüpke, D. J. Bottomley, and H. M. van Driel, “Second- and third-harmonic generation from cubic centrosymmetric crystals with vicinal faces: phenomenological theory and experiment,” J. Opt. Soc. Am. B 11, 33–44 (1994). [CrossRef]

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