  We study the interaction of dielectric rods and disks with the laser field of
a high finesse cavity. The quantum master equation for the coupled
particle-cavity dynamics, including Rayleigh scattering, is derived for
particle sizes comparable to the laser wavelength. We demonstrate that such
anisotropic nanoparticles can be captured from free flight at velocities higher
than those required to capture dielectric spheres of the same volume, and that
efficient ro-translational cavity cooling into the deep quantum regime is
achievable.
