Cross-polarization systematics due to Mizuguchi-Dragone condition breaking by a continuously rotating half-wave plate at prime focus in the Huan Tran telescope

Polarization modulation using a continuously rotating half-wave plate (HWP) is a promising technique to reduce both low-frequency noise and instrumental systematics for Cosmic Microwave Background (CMB) polarization measurements targeting in ationary B-modes. Although a HWP is best placed sky-side of the telescope optics in order to minimize systematics, >0.5 meter aperture class telescopes must put the HWP elsewhere in the optics chain due to current fabrication limitations in the available HWP size. Polarbear is a ground-based CMB experiment installed on the 2.5m aperture off-axis Gregorian-Dragone type Huan Tran Telescope (HTT) designed to satisfy the Mizuguchi-Dragone condition. Polarbear-2 is a receiver that will be installed on a second HTT in 2018. Polarbear-2 is designed to have a larger field-of-view (FOV) and vastly increased sensitivity to the polarized CMB compared to Polarbear. From the third season of observations, Polarbear has installed a continuously rotating HWP at the spatially localized focus plane between the HTT primary and secondary re ectors which is an optimal location for minimizing the HWP diameter. The HWP's polarization angle re ection with respect to its birefringent axis will theoretically break the Mizuguchi-Dragone condition when placed between the two reflectors and increase cross-polarization systematics. In this study, we analyze how the Mizuguchi-Dragone condition is violated due to a HWP at this location. We then estimate the crosspolarization systematics of the HTT using physical optics simulations. We model an ideal HWP at various angles to estimate the effects of demodulation. We evaluate the increased cross-polarization as the Stokes Q-U mixing term using the Mueller Matrix formalism. It is calculated that this term creates a varying dipole beam pattern whose amplitude ranges from 1% at the center to 10% at the edge FOV pixels for Polarbear and potentially up to 20% for Polarbear-2. We also estimate the leakage of the E-mode into the B-mode angular power spectrum measurements due to this cross-polarization. We show that the cross-polarization systematic error leakage is sufficiently lower than the Polarbear-2 statistical uncertainty thanks to mitigations such as focal plane averaging and sky rotation. Currently for Polarbear-2 we are planning to place the HWP at Gregorian focus, but keeping the HWP at prime focus as a back-up solution in case that there are unforeseen telescope spatial and HWP material size constraints. Through this study we find that even though a HWP between the two reflectors will violate the Mizuguchi-Dragone condition, this HWP at prime focus will still have sufficiently low cross-polarization for Polarbear-2. The prime focus HWP is a potential configuration that can be applied to similar off-axis Gregorian-Dragone telescopes in order to minimize the required HWP diameter.