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

Abstract The LiteBIRD mission aims to measure the Cosmic Microwave Background (CMB) polarization with unprecedented precision to detect primordial B modes and constrain the tensor-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 a constant misalignment between the HWP's rotation axis and optical axis, in case of a reflective HWP, when the misalignment is small and thus not corrected for in the pointing reconstruction. While the HWP shape is assumed to be ideal (i.e., plane-parallel), this misalignment mimics the effect of a physical wedge. Throughout the paper, we refer to this as a wedge-like effect. This analysis also applies to the case of transmissive HWP with non-parallel surfaces, and is quantified by a wedge angle. This misalignment leads to HWP-synchronous pointing error. Using the LiteBIRD simulation framework, we implement the wedge-like effect in time-ordered data (TOD) and analyze its impact on reconstructed maps and angular power spectra. 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 Δ r wedge on the tensor-to-scalar ratio, we establish a constraint on the maximum allowable wedge angle ( α max ) to ensure systematic errors remain below mission requirements. Our analysis, based on CMB-only simulations with orthogonal detector pairs (ranging from two to six detectors in total), assuming perfectly matching detectors within each pair and neglecting noise and foregrounds, provides a constraint of α max = 22.7 arcmin from the point of view of spurious polarization. Beam reconstruction and pointing systematics are anyway dominant for values of α larger than 4 arcmin. Interestingly we find that the contamination mimics lensing B modes, and not primordial tensor modes and that it is reduced increasing the number of detectors. This study highlights the importance of precise optical alignment in future CMB polarization experiments. Throughout this work, we assume a constant wedge angle. However, the potential wobbling of the reflective HWP introduces a time-dependent variation of the wedge angle, which may have a non-negligible impact on the results of this paper. Future studies will address this effect by investigating the time-dependent variations in the wedge angle and their impact on the overall systematics, as well as exploring more realistic scenarios where detectors within each pair are not perfectly balanced.