One approach to describing the wave fields of focused acoustic beams is to use an angular spectrum representation. This has the advantage of facilitating a simple evaluation of the scattering by a sphere placed at the focal point of the beam in terms of the scattering by a superposition of Bessel beam components. This was recently demonstrated for a quasi-Gaussian beam [Marston, J. Acoust. Soc. Am. 129, 1773-1782 (2011)]. This approach also has the advantage of separating the propagating spectral components from the evanescent spectral components [Marston, J. Acoust. Soc. Am. (submitted)]. While, for most practical acoustic sources, the evanescent spectral components may be neglected, the spectral representation is helpful for explaining why in principle evanescent spectral components can be important in the production of extremely tightly focused beams. A tightly focused beam with a Gaussian profile at the focal plane is not as easily describable using the more widely investigated complex source point description of the focused wave field. In addition to a Gaussian beam, the propagating-component angular spectrum representation is easily applied to the lowest radial-order Laguerre-Gauss helicoidal acoustic beam in the usual case where the beam is not tightly focused. [Work supported by ONR.]