Note on the asymptotic approximation of a double integral with an angular spectrum representation

TL;DR

This paper develops an asymptotic approximation method for a class of double integrals represented as angular spectrum superpositions, relevant to electromagnetic scattering, using steepest descent path techniques.

Contribution

It introduces a novel asymptotic approximation approach for double integrals in electromagnetic scattering using steepest descent path manipulation.

Findings

Derived approximate expressions for double integrals

Applicable to electromagnetic scattering problems

Enhanced understanding of asymptotic behavior

Abstract

In this note, we are concerned with the asymptotic approximation of a class of double integrals which can be represented as an angular spectrum superposition. These double integrals typically appear in electromagnetic scattering problems. Based on the synthetic manipulation of the method of steepest descent path, approximate expressions of the double integrals are derived in terms of the leading term of the contribution to the asymptotic expansions.