  A cryogenic achromatic half-wave plate (HWP) for submillimetre astronomical
polarimetry has been designed, manufactured, tested, and deployed in the
Balloon-borne Large-Aperture Submillimeter Telescope for Polarimetry
(BLASTPol). The design is based on the five-slab Pancharatnam recipe and it
works in the wavelength range 200-600 micron, making it the broadest-band HWP
built to date at (sub)millimetre wavelengths. The frequency behaviour of the
HWP has been fully characterised at room and cryogenic temperatures with
incoherent radiation from a polarising Fourier transform spectrometer. We
develop a novel empirical model, complementary to the physical and analytical
ones available in the literature, that allows us to recover the HWP Mueller
matrix and phase shift as a function of frequency and extrapolated to 4K. We
show that most of the HWP non-idealities can be modelled by quantifying one
wavelength-dependent parameter, the position of the HWP equivalent axes, which
is then readily implemented in a map-making algorithm. We derive this parameter
for a range of spectral signatures of input astronomical sources relevant to
BLASTPol, and provide a benchmark example of how our method can yield improved
accuracy on measurements of the polarisation angle on the sky at submillimetre
wavelengths.
