Optical asymptotics via Weniger transformation

TL;DR

This paper introduces the Weniger transformation as an effective method for asymptotic evaluation of integrals in physics and optics, demonstrating promising numerical performance compared to Hyperasymptotics.

Contribution

It proposes the Weniger transformation as a new, efficient computational scheme for optical asymptotics based on resurgence theory.

Findings

Numerical tests on Pearcey function show competitive performance.

Weniger transformation offers a straightforward implementation.

Potential for broad application in optical problems.

Abstract

Starting from the resurgence equation discovered by Berry and Howls [M. V. Berry and C. Howls "Hyperasymptotics for integrals with saddles," Proc. R. Soc. Lond. A 434, 657-675 (1991)], the Weniger transformation is here proposed as a natural, efficient, and straightforwardly implementable scheme for the efficient asymptotics evaluation of a class of integrals occurring in several areas of physics and, in particular, of optics. Preliminary numerical tests, carried out on the Pearcey function, provide a direct comparison between the performances of Weniger transformation and those of Hyperasymptotics, which seems to corroborate the theoretical predictions. We believe that Weniger transformation would be a very useful computational tool for the asymptotic treatment of several optical problems.