Design of the frequency independent optic axis of the Pancharatnam base achromatic half-wave plate for CMB polarization experiment

Pancharatnam base achromatic half-wave plate (AHWP) achieves high polarization efficiency over broadband. It generally comes with a feature of which the optic axis of AHWP has dependence of the electromagnetic frequency of the incident radiation. When the AHWP is used to measure the incident polarized radiation with a finite detection bandwidth, this frequency dependence causes an uncertainty in the determination of the polarization angle due to the limited knowledge of a detection band shape and a source spectral shape. To mitigate this problem, we propose new designs of the AHWP that eliminate the frequency dependent optic axis over the bandwidth of which the polarization efficiency also achieves the same broadband width. We carried out the optimization by tuning the relative angles among the individual half-wave plates (HWP) of the five-and nine-layer AHWP. The optimized set of the relative angles achieves the frequency independent optic axis and covers the fractional bandwidth of 1.3 and 1.5 for five-and nine-layer AHWPs, respectively. We also study the susceptibility of the alignment accuracy, which can be chosen based on the requirement in each application.