Empirical modelling of the BLASTPol achromatic half-wave plate for precision submillimetre polarimetry

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 itworks in thewavelength range 200-600 μm, making it the broadestband HWP built to date at (sub)millimetre wavelengths. The frequency behaviour of the HWP has been fully characterized at room and cryogenic temperatures with incoherent radiation from a polarizing 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 4 K. 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 polarization angle on the sky at submillimetre wavelengths.