On Second-Order Asymptotic Expansions at a Caustic

Abstract

This paper presents a detailed analysis of second-order asymptotic expansions for the description of the geometrical optics field in the vicinity of a caustic. It is shown that the stationary phase solution commonly found in textbooks and papers is valid only at the caustic, but not away from the caustic, as is usually claimed. The exact stationary phase expansion is derived and is compared to the steepest desenct solitions presented elsewhere in literature.