Elastic Orbital Angular Momentum

Abstract

We identify that flexural guided elastic waves in elastic pipes carry a well-defined orbital angular momentum associated with the compressional dilatational potential. This enables the transfer of elastic orbital angular momentum, that we numerically demonstrate, through the coupling of the compressional potential in a pipe to the acoustic pressure field in a surrounding fluid in contact with the pipe.

Observation of Elastic Orbital Angular Momentum Transfer

“…Specifically in acoustics, the generation of these modes conventionally relies on discrete phased arrays. By considering the elastic orbital angular momentum associated with compressional motion we have demonstrated the first experimental observation of elastic orbital angular momentum transfer from guided flexural modes in a pipe to acoustic waves in a fluid, verifying the experiment proposed in [32], and thus providing a new avenue to generate acoustic OAM beams.…”

“…In the case of elastic OAM carried by flexural modes in pipes there is no such singularity as the pipe is hollow -a direct analogy cannot be drawn in this case as there is no elastic medium to suspend particles with at the pipe centre, along its axis. However, as fluids do not support shear waves it has been proposed that the transfer of elastic OAM can be observed via the coupling of the OAM associated with dilatation to the compressional waves that are supported by fluids [32]. Here for the first time we experimentally validate this OAM transfer, thereby developing a new continuous-phased acoustic source in the form of flexural modes in pipes; Bessel-like beams are generated following from the radial distribution of the compressional potential.…”

“…In a similar vain to LG beams, it has been shown that the scalar dilatational potential carries a well-defined OAM about the pipe axis, in the sense that it is purely proportional to m. The corresponding OAM flux density is given by [32]…”

“…Recently the consideration of OAM has been extended further, into the realm of elasticity [32], where it was proved that the compressional component of elastic vibrations also carry a well-defined OAM. In this paper we extend this theoretical work and experimentally show that the elastic OAM associated with dilatation can be coupled to a fluid, thereby observing its transfer through the excitation of acoustic pressure fields that carry OAM.…”

“…The displacement comprises both shear and compressional motion, described by an equivoluminal vector potential Ψ i and scalar dilatational potential Φ respectively such that, by Helmholtz decomposition, ξ i = ∂ i Φ + ǫ ijk ∂ j Ψ k . Elastic waves with inclined phase-fronts naturally occur as flexural modes in pipe walls [32]. Choosing cylindrical coordinates oriented with z along the pipe axis the potentials take the form…”