Asymptotic high-frequency methods

TLDR

High‑frequency scattering is commonly addressed using asymptotic techniques such as the saddle‑point method, Watson transformation, residue series, geometrical optics, physical optics, and the geometrical theory of diffraction, and this review surveys their application and limitations. The paper examines how these asymptotic techniques arise from and solve Maxwell’s equations in the high‑frequency limit. The authors conclude that high‑frequency approximations are desirable for efficient analysis, but their usefulness depends on the problem context and the specific method’s strengths and weaknesses.

Abstract

A review is given of a wide variety of asymptotic methods used in high-frequency scattering. Following brief descriptions of the saddle point method, Watson transformation, and residue series, a survey of the literature is made in which these methods have been employed. The desirability of using high-frequency approximate methods is pointed out. A critical discussion of geometrical optics, physical optics, and the geometrical theory of diffraction is presented. The relationship of these methods to the asymptotic solution of Maxwell's equations is examined. Their applicability and limitations are discussed by referring to numerous examples in the literature.