Applied Physics A

, Volume 39, Issue 2, pp 115–121

Nonlinear polarisation inside metals: A mathematical study of the free-electron model

  • D. Maystre
  • M. Neviere
  • R. Reinisch
Contributed Papers

DOI: 10.1007/BF00616828

Cite this article as:
Maystre, D., Neviere, M. & Reinisch, R. Appl. Phys. A (1986) 39: 115. doi:10.1007/BF00616828

Abstract

A mathematical study of the free-electron model proposed by Bloembergen et al. to derive the nonlinear polarisation inside a metal is achieved. Using a local conformal mapping as a tool, we show that this model, which has been declared “ambiguous” by many authors, is in fact perfectly sound from a mathematical point of view. The values of the tangential and normal components of the surface nonlinear polarization are fully given and the boundary conditions at the metal-vacuum interface are rigorously established. Thus, we do not introduce phenomenological parameters such as the coefficients “a” and “b” which appear in the works of Rudnick and Stern, or Sipe and Stegeman. Moreover, we do not need the classical hypothesis which assumes that the nonlinear surface polarization is placed in vacuum.

PACS

42.65C 

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • D. Maystre
    • 1
  • M. Neviere
    • 1
  • R. Reinisch
    • 2
  1. 1.Laboratoire d'Optique Electromagnétique, U.A. au CNRS No. 843, Faculté des Sciences et TechniquesCentre de Saint-JérômeMarseille Céedex 13France
  2. 2.Laboratoire de Génie PhysiqueE.R.A. 836 CNRSSaint-Martin D'HeresFrance

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