Systematic effect induced by misalignment in a reflective polarization modulator for CMB, and application to the LiteBIRD case

The LiteBIRD mission aims to measure the Cosmic Microwave Background (CMB)polarization with unprecedented precision to detect primordial B modes and constrain thetensor-to-scalar ratio r. A key component of LiteBIRD are the polarization modulators,based on Half-Wave Plates (HWP). In this work, we study the systematic effects caused by aconstant misalignment between the HWP's rotation axis and optical axis, in case of a reflectiveHWP, when the misalignment is small and thus not corrected for in the pointingreconstruction. While the HWP shape is assumed to be ideal (i.e., plane-parallel), thismisalignment mimics the effect of a physical wedge. Throughout the paper, we refer to this as awedge-like effect. This analysis also applies to the case of transmissive HWP with non-parallelsurfaces, and is quantified by a wedge angle. This misalignment leads to HWP-synchronouspointing error. Using the LiteBIRD simulation framework, we implement the wedge-likeeffect in time-ordered data (TOD) and analyze its impact on reconstructed maps and angular powerspectra. We find that the wedge systematically bias polarization measurements, leading to spurious B modes. By evaluating the total error induced by the wedge-like effect Δrwedgewedge​ on the tensor-to-scalar ratio, we establish a constraint on the maximumallowable wedge angle (αmaxmax​) to ensure systematic errors remain below missionrequirements. Our analysis, based on CMB-only simulations with orthogonal detector pairs (rangingfrom two to six detectors in total), assuming perfectly matching detectors within each pair andneglecting noise and foregrounds, provides a constraint of αmaxmax​ = 22.7 arcminfrom the point of view of spurious polarization. Beam reconstruction and pointing systematics areanyway dominant for values of α larger than 4 arcmin. Interestingly we find that thecontamination mimics lensing B modes, and not primordial tensor modes and that it is reducedincreasing the number of detectors. This study highlights the importance of precise opticalalignment in future CMB polarization experiments. Throughout this work, we assume a constant wedgeangle. However, the potential wobbling of the reflective HWP introduces a time-dependent variationof the wedge angle, which may have a non-negligible impact on the results of this paper. Futurestudies will address this effect by investigating the time-dependent variations in the wedge angleand their impact on the overall systematics, as well as exploring more realistic scenarios wheredetectors within each pair are not perfectly balanced.