A continuously rotating half-wave plate (CRHWP) is a promising tool to improve the sensitivity to large angular scales in cosmic microwave background (CMB) polarization measurements. With a CRHWP, single detectors can measure three of the Stokes parameters, $I$, $Q$ and $U$, thereby avoiding the set of systematic errors that can be introduced by mismatches in the properties of orthogonal detector pairs. We focus on the implementation of CRHWPs in large aperture telescopes (i.e. the primary mirror is larger than the current maximum half-wave plate diameter of $sim$0.5 m), where the CRHWP can be placed between the primary mirror and focal plane. In this configuration, one needs to address the intensity to polarization ($I{rightarrow}P$) leakage of the optics, which becomes a source of 1/f noise and also causes differential gain systematics that arise from CMB temperature fluctuations. In this paper, we present the performance of a CRHWP installed in the POLARBEAR experiment, which employs a Gregorian telescope with a 2.5 m primary illumination pattern. The CRHWP is placed near the prime focus between the primary and secondary mirrors. We find that the $I{rightarrow}P$ leakage is larger than the expectation from the physical properties of our primary mirror, resulting in a 1/f knee of 100 mHz. The excess leakage could be due to imperfections in the detector system, i.e. detector non-linearity in the responsivity and time-constant. We demonstrate, however, that by subtracting the leakage correlated with the intensity signal, the 1/f noise knee frequency is reduced to 32 mHz ($ell sim$39 for our scan strategy), which is very promising to probe the primordial B-mode signal. We also discuss methods for further noise subtraction in future projects where the precise temperature control of instrumental components and the leakage reduction will play a key role.
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