Notice of Removal: A few twists regarding the momentum of shaped beams

In the acoustic tweezers literature, it is sometimes stated that there would be no radiation pressure in the absence of nonlinearity. In fact, such a circumstance would allow violation of the Second Law of Thermodynamics, an issue we discuss in this talk. In the limit where the Second Law applies, all radiant forms of energy must carry an associated momentum. Shaped beams offer (along with shaped targets) opportunity for discussion of the respective advantages of conservative and non-conservative forces. Commonly in acoustic trapping, conservative, gradient-induced mechanisms (e.g., standing waves) are used to manipulate matter. Such situations are reasonably described in terms of potential energy landscapes, an approach also applied to optics, for applications such as cell sorting [MacDonald et al, Nature 426 (2003)]. No such description is possible for radiation pressure, which is non-conservative, a distinction that is sometimes muddled in the literature, although it was made clear even in early landmark papers.