Design and characterization of a 60-cm reflective half-wave plate for the CLASS 90 GHz band telescope

Front-end polarization modulation enables improved polarization measurement stability by modulating the targeted signal above the low-frequency $1/f$ drifts associated with atmospheric and instrumental instabilities and diminishes the impact of instrumental polarization. In this work, we present the design and characterization of a new 60-cm diameter Reflective Half-Wave Plate (RHWP) polarization modulator for the 90 GHz band telescope of the Cosmology Large Angular Scale Surveyor (CLASS) project. The RHWP consists of an array of parallel wires (diameter $50~\mathrm{μm}$, $175~\mathrm{μm}$ pitch) positioned $0.88~\mathrm{mm}$ from an aluminum mirror. In lab tests, it was confirmed that the wire resonance frequency ($f_\mathrm{res}$) profile is consistent with the target, $139~\mathrm{Hz}<f_\mathrm{res}<154~\mathrm{Hz}$ in the optically active region (diameter smaller than $150~\mathrm{mm}$), preventing the wire vibration during operation and reducing the RHWP deformation under the wire tension. The mirror tilt relative to the rotating axis was controlled to be $<15''$, corresponding to an increase in beam width due to beam smearing of $<0.6''$, negligible compared to the beam's full-width half-maximum of $36'$. The median and 16/84th percentile of the wire--mirror separation residual was $0.048^{+0.013}_{-0.014}~\mathrm{mm}$ in the optically active region, achieving a modulation efficiency $ε=96.2_{+0.5}^{-0.4}\%$ with an estimated bandpass of 34 GHz. The angular velocity of the RHWP was maintained to an accuracy of within $0.005\%$ at the nominal rotation frequency ($2.5~\mathrm{Hz}$). The RHWP has been successfully integrated into the CLASS 90 GHz telescope and started taking data in June 2024, replacing the previous modulator that has been in operation since June 2018.