  Tightly-focused, ultrashort radially-polarized laser beams have a large
longitudinal field, which provides a strong motivation for direct particle
acceleration and manipulation in vacuum. The broadband nature of these beams
means that chromatic properties of propagation and focusing are important to
consider. We show via single particle simulations that using the correct
frequency-dependent beam parameters is imperative, especially as the pulse
duration decreases to the few-cycle regime. The results with different
spatio-spectral amplitude profiles show both a drastic increase or decrease of
the final accelerated electron energy depending on the shape, motivating both
proper characterization and potentially a route to optimization.
