We describe the development of an ambient-temperature continuously-rotating half-wave plate (HWP) for study of the Cosmic Microwave Background (CMB) polarization by the POLARBEAR-2 (PB2) experiment. Rapid polarization modulation suppresses 1/f noise due to unpolarized atmospheric turbulence and improves sensitivity to degree-angular-scale CMB fluctuations where the inflationary gravitational wave signal is thought to exist. A HWP modulator rotates the input polarization signal and therefore allows a single polarimeter to measure both linear polarization states, eliminating systematic errors associated with differencing of orthogonal detectors. PB2 projects a 365-mm-diameter focal plane of 7,588 dichroic, 95/150 GHz transition-edge-sensor bolometers onto a 4-degree field of view that scans the sky at $sim$ 1 degree per second. We find that a 500-mm-diameter ambient-temperature sapphire achromatic HWP rotating at 2 Hz is a suitable polarization modulator for PB2. We present the design considerations for the PB2 HWP, the construction of the HWP optical stack and rotation mechanism, and the performance of the fully-assembled HWP instrument. We conclude with a discussion of HWP polarization modulation for future Simons Array receivers.
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