Resumming divergent series in nonparaxial optics

Abstract

We show that the terms of a Lax series, commonly used to evaluate propagated optical fields in nonparaxial conditions, present a factorially divergent asymptotic behavior in the case of highly nonparaxial beams, under rather general conditions. This allows some resummation algorithms, such as the Weniger transformation, to be used in order for the evaluation of the propagated field to be successfully performed starting from the terms of the divergent Lax series. Examples are presented, concerning cases for which the terms of the Lax series can be evaluated explicitly.