  We derive an analytic formula using the Mueller matrix formalism that
parameterizes the nonidealities of a half-wave plate (HWP) made from dielectric
antireflection-coated birefringent slabs. This model accounts for
frequency-dependent effects at normal incidence, including effects driven by
the reflections at dielectric boundaries. The model also may be used to guide
the characterization of an instrument that uses a HWP. We discuss the coupling
of a HWP to different source spectra, and the potential impact of that effect
on foreground removal for the SPIDER cosmic microwave background experiment. We
also describe a way to use this model in a mapmaking algorithm that fully
corrects for HWP nonidealities.
