A generalized modal impulse response and Fourier transform approach to investigate acoustic transient Bessel beams and Bessel bullets

Abstract

A generalized modal space–time impulse response and Fourier transform approach is developed to investigate the general properties of transient Bessel beam (TBB) fields which are generated using planar circular apertures. The approach is based on a modal decomposition of the aperture source distributions which are required to generate the space–time TBB fields. Numerical results are presented to illustrate the general space–time properties of the modal impulse responses and the modal source functions. The on-axis far field for the finite aperture is shown to be simply related to the lowest order term in the modal expansion. The space–time properties of the acoustic field for a particular type of band-limited TBB field which is designated as an acoustic Bessel bullet (BB) are then investigated. Some numerical results are presented to illustrate the space–time properties of acoustic BB fields generated from an infinite aperture. Analogous on-axis harmonic results from a finite aperture are presented. These latter results clearly indicate that the higher-order modes exhibit spatial rates of decay which are greater than the inverse range decay for the lowest order mode.