  We study the impact of the spectral dependence of the linear polarization
rotation induced by an achromatic half-wave plate on measurements of cosmic
microwave background polarization in the presence of astrophysical foregrounds.
We focus on the systematic effects induced on the measurement of inflationary
gravitational waves by uncertainties in the polarization and spectral index of
Galactic dust. We find that for the experimental configuration and noise levels
of the balloon-borne EBEX experiment, which has three frequency bands centered
at 150, 250, and 410 GHz, a crude dust subtraction process mitigates systematic
effects to below detectable levels for 10% polarized dust and tensor to scalar
ratio of as low as r = 0.01. We also study the impact of uncertainties in the
spectral response of the instrument. With a top-hat model of the spectral
response for each band, characterized by band-center and band-width, and with
the same crude dust subtraction process, we find that these parameters need to
be determined to within 1 and 0.8 GHz at 150 GHz; 9 and 2.0 GHz at 250 GHz; and
20 and 14 GHz at 410 GHz, respectively. The approach presented in this paper is
applicable to other optical elements that exhibit polarization rotation as a
function of frequency.
