Current interest in focused vortex beams is motivated by the ability to trap particles axially and laterally using the resulting radiation force. A simple closed-form solution is obtained in the Fresnel approximation for a sound beam radiated by a Gaussian source with time dependence e−iωt , focal length d, amplitude distribution exp(− r 2/ a 2), and azimuthal phase dependence einθ , where θ is the angle in the plane perpendicular to the beam axis, and the integer n is the topological charge, referred to here as the vorticity. The solution is in good agreement with the pressure field predicted in the paraxial region by numerical evaluation of the Rayleigh integral. Of interest in optics as well as acoustics is the distance from the minimum along the beam axis to the first local maximum, referred to as the vortex ring. The present solution yields rn  =  ηn d/ ka for the vortex ring radius in the focal plane, where k is the wavenumber, and ηn  = 1.69 + 0.965( n−1) for vorticities in the range 1 ≤  n <  O(20). Within this range the radius rn thus increases linearly with the vorticity. Results are also presented for dependence of the focusing gain on the vorticity. [CAG was supported by the ARL:UT Chester M. McKinney Graduate Fellowship in Acoustics.]

“Study hard what interests you the most in the most undisciplined, irreverent and original manner possible” [ Perfectly Reasonable Deviations from the Beaten Track, Richard P. Feynman, Basic Books, 2005]. Writing original homework problems is a powerful way students of physical acoustics can practice Feynman’s advice. Three problems that involve a broad range of concepts covered in introductory graduate-level physical acoustics courses illustrate how the student-author unleashed his creativity in an undisciplined manner, injected his problems with an irreverent sense of humor, and derived a great sense of originality and ownership over physical acoustics. The problems synthesize David T. Blackstock’s problems 1D-2, 1E-3, 1G-1, 1G-3, 7-6, 10-10, and 10-11 [ Fundamentals of Physical Acoustics, David T. Blackstock, Wiley, 2000], addressing concepts including acoustic intensity, impedance, horns, enclosures, and radiation. [CAG was supported by the ARL:UT Chester M. McKinney Graduate Fellowship in Acoustics.]

The macroscopic response of acoustic metamaterials with sub-wavelength asymmetry may be described by the so-called Willis constitutive relations, which include coupling between the acoustic pressure and momentum density. One method to describe the behavior of acoustically-small, Willis material building-blocks is via a polarizability matrix relating the monopole and dipole scattering moments to the local pressure and velocity fields, providing a metric for the design of microscale structures leading to macroscopically observable Willis coupling. Additionally, heterogeneous, piezoelectric media with sub-wavelength asymmetry have been shown to exhibit coupling between momentum density and electric fields, a material response known as electro-momentum coupling. Recent studies have generalized the polarizability concept to include coupling between acoustic and electromagnetic fields for theoretical point scatterers in two and three dimensions, and derived analytical bounds based on conservation of energy. In this work, we computationally study the coupled, acousto-electromagnetic polarizability of heterogeneous, piezoelectric scatterers and assess the practicability of achieving electro-momentum coupling in physically realizable geometries. Numerical results are obtained using a custom finite element approach, which includes the fully electrodynamic nature of the system and accounts for large differences in the characteristic wavelengths of the acoustic and electromagnetic fields. [This work was supported by DARPA.]

No abstract