On the validity of the integral localized approximation for Bessel beams and associated radiation pressure forces

Leonardo A. Ambrosio, Jiajie Wang, and Gérard Gouesbet

In this paper we investigate the integral version of the localized approximation (ILA)—a powerful technique for evaluating the beam shape coefficients in the framework of the generalized Lorenz–Mie theory—as applied to ideal scalar Bessel beams (BBs). Originally conceived for arbitrary shaped beams with a propagating factor exp(±𝑖𝑘𝑧)exp(±ikz), it has recently been shown that care must be taken when applying the ILA for the case of ideal scalar BBs, since they carry a propagating factor exp(±𝑖𝑘𝑧 cos 𝛼)exp(±ikz cos α), with 𝛼α being the axicon angle, which cannot be smoothly accommodated into its mathematical formalism. Comparisons are established between the beam shape coefficients calculated from both ILA and exact approaches, assuming paraxial approximation and both on- and off-axis beams. Particular simulations of radiation pressure forces are provided based on the existing data in the literature. This work helps us in elucidating that ILA provides adequate beam shape coefficients and descriptions of ideal scalar BBs up to certain limits and, even when it fails to do so, reliable information on the physical optical properties of interest can still be inferred, depending on specific geometric and electromagnetic aspects of the scatterer.

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