Asymptotic Expansion of the Scattered Field by a Convex Grating at High Frequencies

Toufic  Abboud 
Centre de Mathematiques Appliquees, CNRS URA 756,
Ecole Polytechnique, 91128 Palaiseau Cedex, France.

Habib AMMARI 
Centre de Mathematiques Appliquees - CNRS URA 756,
Ecole Polytechnique, 91128 Palaiseau Cedex, France.

Gilles Lebeau 
Departement de Mathematiques, Bat 425, 
Universite de Paris-Sud, 91405 Orsay Cedex,France.


We consider a layer of dielectric material with period $\delta$
 covering a strictly convex perfectly conducting  cylinder
 lit up by a TE or TM polarized incident {\it plane} wave with
 a wave number $k$ of order $\delta^{-1}$. In this Note,
 we derive geometric-optics solution out side transition regions,
 satisfying Helmholtz equation to arbitrarily order in $\delta$.
 We show that the first order approximation is solution of the infinite
plane tangent grating diffraction problem.  



The whole paper is available as a compressed Postscript file by internet
procedure FTP anonymous on host barbes.polytechnique.fr ( 129.104.4.100)
in the directory pub/RI/1995 under the name

         abboud_ammari_lebeau_313.jan.ps.gz

or by Xmosaic or any other www client
via the CMAP www server "http://blanche.polytechnique.fr/"