Beams with large depth of field

Abstract

Acoustic bullets, also known as limited diffraction beams, are solutions of the scalar wave equation with the property of maintaining their shape upon propagation, without spreading in space and in time. A necessary and sufficient condition for the generation of acoustic bullets is presented. In particular, it is proved that a necessary condition for acoustic bullets is that all the wave vectors characterizing the beam are disposed over a cone with a given vertex angle. Impulse responses for the case of axial symmetry, and for the situation in which axial symmetry is lacking, are then given. The results obtained for acoustic bullets are then contrasted with those of other types of beams with large depth of field recently presented in literature (an example is the so-called ‘‘sinc wave’’). Finally, the topic of the realization of practical approximation of these kind of beams, which, in principle, requires infinite apertures, is addressed. Numerical simulations are presented in order to analyze the departures from the ideal case when using a finite-dimension aperture.