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

- The scattering of the nondiffracting Lommel beams by a rigid sphere is studied.
- The scattered high order Bessel beam is deduced as a special case.
- The effects of some scattered wave parameters have been analyzed.

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 (φ), the propagation half-cone angle (β) and the scattering angle (θ) 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.