Acoustic beam interaction with a rigid sphere: The case of a first-order non-diffracting Bessel trigonometric beam

Mathematical expressions for the acoustic scattering, instantaneous (linear), and time-averaged (nonlinear) forces resulting from the interaction of a new type of Bessel beam, termed here a first-order non-diffracting Bessel trigonometric beam (FOBTB) with a sphere, are derived. The beam is termed “trigonometric” because of the dependence of its phase on the cosine function. The FOBTB is regarded as a superposition of two equi-amplitude first-order Bessel vortex (helicoidal) beams having a unit positive and negative order (known also as topological charge), respectively. The FOBTB is non-diffracting, possesses an axial null, a geometric phase, and has an azimuthal phase that depends on cos(ϕ±ϕ0), where ϕ0 is an initial arbitrary phase angle. Beam rotation around its wave propagation axis can be achieved by varying ϕ0. The 3D directivity patterns are computed, and the resulting modifications of the scattering are illustrated for a rigid sphere centered on the beamʹs axis and immersed in water. Moreover, the backward and forward acoustic scattering by a sphere vanish for all frequencies. The present paper will shed light on the novel scattering properties of an acoustical FOBTB by a sphere that may be useful in particle manipulation and entrapment, non-destructive/medical imaging, and may be extended to other potentially useful applications in optics and electromagnetism.