Electronic Journal of Differential Equations,
Vol. 1999(1999), No. 36, pp. 1-13.

Title: The effect of thin coatings on second harmonic generation 

Authors: Habib Ammari (Ecole Polytechnique, Palaiseau, France)
         Gang Bao (Michigan State Univ., East Lansing, MI, USA)
         Kamel Hamdache (Univ. de Paris, France)

Abstract: 
 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.