A study of nondiffracting Lommel beams propagating in a medium containing spherical scatterers

By means of the expansion of the nondiffracting beams on plane waves with help of the Whittaker integral, an exact analytical expression of the far-field form function of the scattering of the acoustic and optical nondiffracting Lommel beams propagating in a medium containing spherical particles, considered as rigid and single spheres, is investigated in this work. The form function of the scattering of the high order Bessel beam by a rigid and isolated sphere is deduced, from our finding, as a special case. The effects of the wave number-sphere radius product (ka), the polar angle (phi), the propagation half-cone angle (beta) and the scattering angle (theta) on the far-field form function of the scattered wave have been analyzed and discussed numerically. The numerical results show that the illumination of a rigid sphere by Lommel beams produces asymmetrical scattering. (C) 2016 Elsevier Ltd. All rights reserved.