Electromagnetic reflection from a curved dielectric interface

The reflection of a high-frequency electromagnetic field from an arbitrarily curved dielectric interface is considered. The fields are expanded in asymptotic series of
k^{-1}
, known as Luneburg-Kline expansions. Based on a ray method the zero- and first-order terms of
k^{-1}
of the reflected and transmitted field are evaluated at the interface. Associated with the fields at the interface, effective surface current densities can be used to determine the reflected and transmitted field at points away from the interface, which is done analytically for the reflected far field in the case of plane wave incidence. The result consists of a frequency-independent term, which is related to geometrical optics solution, and a term of
k^{-1}
, which is a useful extension of geometrical optics solution in some cases.