Assessing the validity of the localized approximation for discrete superpositions of Bessel beams

Abstract

This paper analyzes the validity of the integral localized approximation for discrete superpositions of arbitrary order Bessel beams—known as frozen waves. It is motivated by the fact that such an approximation has been adopted in previous works under the framework of the generalized Lorenz–Mie theory for electromagnetic scattering by microparticles when illuminated by paraxial frozen waves. The results presented here give support to those previous works, but they also serve as a warning for future research in the field in the sense that the localized approximation can be of limited validity for nonparaxial laser beams when the axicon angle is not small enough, or when a net topological charge exists.