Electron. J. Diff. Eqns., Vol. 1999(1999), No. 36, pp. 1-13.

The effect of thin coatings on second harmonic generation

Habib Ammari, Gang Bao, & Kamel Hamdache

The effect of thin coatings of nonlinear material on second harmonic generation is studied in this paper. Asymptotic expansions of the fields inside a thin nonlinear coating are performed. The convergence of these formal expansions is established. Our asymptotic analysis reveals the physical nature of this nonlinear problem. It also provides an effective method for overcoming the computational difficulties that arise in thin nonlinear coatings.

Submitted May 30, 1999. Published September 20, 1999.
Math Subject Classifications: 35C20, 78A45, 78A60.
Key Words: Thin coatings, second harmonic generation, asymptotic analysis.

Show me the PDF file (142K), TEX file, and other files for this article.

Habib Ammari
Centre de Mathematiques Appliquees, UMR CNRS 7641
Ecole Polytechnique
91128 Palaiseau, France
e-mail address: ammari@cmapx.polytechnique.fr

Gang Bao
Department of Mathematics, Michigan State University
East Lansing, MI 48824-1027
e-mail address: bao@math.msu.edu

Kamel Hamdache
Institut Galilee, UMR CNRS 7539, Universite de Paris XIII
93430 Villetaneuse, France
e-mail address: hamdache@cmapx.polytechnique.fr

Return to the EJDE web page