Resumming divergent series in nonparaxial optics

Riccardo Borghi; Franco Gori; Giorgio Guattari; Massimo Santarsiero

doi:10.1117/12.903364

2 November 2011 Resumming divergent series in nonparaxial optics

Riccardo Borghi, Franco Gori, Giorgio Guattari, Massimo Santarsiero

Proceedings Volume 8011, 22nd Congress of the International Commission for Optics: Light for the Development of the World; 80116G (2011) https://doi.org/10.1117/12.903364
Event: International Commission for Optics (ICO 22), 2011, Puebla, Mexico

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.

Citation Download Citation

Riccardo Borghi, Franco Gori, Giorgio Guattari, and Massimo Santarsiero "Resumming divergent series in nonparaxial optics", Proc. SPIE 8011, 22nd Congress of the International Commission for Optics: Light for the Development of the World, 80116G (2 November 2011); https://doi.org/10.1117/12.903364

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