Special types of elastic fields can be generated as beams defined by a given set of orthonormal scalar functions on a two-dimensional or three-dimensional beam manifold. The proposed method enables one to obtain sets of orthonormal beams and various families of localized fields in both isotropic and anisotropic solids. This can also be applied to sound beams in liquids and, by way of illustration, the fields defined by the spherical harmonics are considered. The families of orthonormal beams can be used as functional bases for complex elastic fields, and it is shown that they can induce chiral inhomogeneities in isotropic elastic mediums. The presented localized elastic fields include storms, whirls, and tornadoes, i.e., the localized fields for which the time-averaged energy flux is identically zero, azimuthal, and spiral, respectively. It is shown that the presented fields can be combined into a complex field structure such as an acoustic diffraction grating, which makes them promising tools to control laser radiation.
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