Impact of the effective thickness from anti-reflective sub-wavelength structures in achromatic half-wave plate design

We develop a continuously rotating achromatic half-wave plate (HWP) for LiteBIRD. An achromatic HWP is made of five-layer sapphire plates following a Pancharatnam design. The two surfaces employ broadband anti-reflection (AR) sub-wavelength structures (SWS) fabricated with ultra-short pulsed laser ablation. For designing AHWP with SWS, we fabricated three representative structures using laser ablation. One has a symmetric SWS shape and the other two have different asymmetric shapes in ordinary and extraordinary directions. We modeled five-layer AHWP with SWS based on fabricated shapes and numerically evaluated their transmittance, modulation efficiency, and phase of the modulated signal using the rigorous coupled-wave analysis (RCWA) method. We also added instrumental polarization (IP) as the figure-of-merit, which is a conversion of unpolarized to polarized light. IP creates an undesired modulated signal, which may cause a non-linear response in a bolometric detector. The typical cause of IP is the imperfection of AR SWS. From calculations, we did not find a significant difference in IP among the three cases. However, we found the impact on the modulation efficiency because the retardance depends on the SWS shapes. Furthermore, the retardance depends on frequency. We numerically analyzed the impact of the extra retardance from SWS on the overall AHWP performance. We show one of the three cases has the broadest modulation efficiency by compensating for the frequency dependence of the retardance from the SWS and the AHWP sapphire stacks.