A localized approximation approach for the calculation of beam shape coefficients of acoustic and ultrasonic Bessel beams

Abstract

The description of acoustical waves can be achieved using an expansion over basic functions with weighting coefficients which may be called beam shape coefficients (BSCs). There is a strong analogy between the scalar formalism of acoustical waves and the vectorial electromagnetic formalism, known as generalized Lorenz–Mie theory (GLMT), describing the interaction between a homogeneous sphere and an arbitrary illuminating beam. In particular, BSCs have been introduced as well in GLMT and the mathematical arsenal to evaluate them, developed since several decades, can be used mutatis mutandis to evaluate BSCs in acoustics. In particular, the present paper introduces a method named localized approximation to the evaluation of the acoustical BSCs, similar to the localized approximation used to evaluate electromagnetic BSCs, in the case of Bessel beams. Such a formalism akin to the electromagnetic GLMT may be viewed as an acoustical GLMT and should allow a renewal of the calculation of various properties of acoustical wave scattering, in particular to the design of acoustical tweezers similar to optical tweezers.