Characterization of a half-wave plate for CMB circular polarization measurement with POLARBEAR

A half-wave plate (HWP) is often used as a modulator to suppress systematic error in the measurements of cosmic microwave background (CMB) polarization. An HWP can also be used to measure circular polarization (CP) through its optical leakage from CP to linear polarization. The CP of the CMB is predicted to be produced by interactions in the Universe, such as interactions with supernova remnants of population III stars. Thus, the observation of the CP of CMB is a new tool for searching for population III stars. In this paper, we demonstrate the improved measurement of the leakage coefficient using the transmission spectrum measurement of an actual HWP in the laboratory. We measured the transmittance of linearly polarized light through the HWP used in the \textsc{Polarbear} experiment in the frequency range of \SIrange{120}{160}{GHz}. We evaluate properties of the HWP by fitting the data with a physical model using the Markov Chain Monte Carlo method. We then estimate the band-averaged CP leakage coefficient using the physical model. We find that the leakage coefficient strongly depends on the spectra of CP sources. We thus calculate the maximum rate of leakage from CP to linear polarization as $0.133 \pm 0.009$ in the Rayleigh--Jeans spectrum. The nonzero value shows that \textsc{Polarbear} would have sensitivity to the CP. Additionally, because we use the bandpass of detectors installed in the telescope to calculate the band-averaged values, we also consider systematic effects in the experiment.