Impact of the continuity of spinning rate function on circular SOP conversion performance in spun quarter wave plate

Spun quarter wave plate (SQWP) exhibits superior state of polarization (SOP) conversion performance compared to the conventional quarter wave plate (QWP), with low loss and high accuracy, making it a promising choice for fiber optic systems. The spinning rate function, as a crucial component of SQWP, characterizes the process of spinning rate ($\xi$) from 0 to maximum (${\xi }_{max}$), playing a vital role in the performance of SQWP. To enhance circular SOP conversion, the traditional way is that we raise the spinning rate, but this increases ellipticity fluctuation ($\Delta E$), impacting SQWP stability. Urgent exploration of alternative solutions is needed. In order to address this issue, in this study, the impact of the continuity of spinning rate function on circular SOP conversion performance in SQWP is thoroughly investigated through theoretical research and numerical simulation. The results show that spinning rate functions with higher order continuity decrease ellipticity fluctuation and enhance the circular SOP conversion performance in SQWP more effectively. We introduce and compare two novel higher order continuous spinning rate functions with the conventional linear and cosine functions regarding their robustness ($\sigma$) on circular SOP conversion performance. The average values of $\sigma$ for the two proposed spinning rate functions are $4.01\times 10^{-5}$ and $2.17\times 10^{-6}$, respectively. They are one and two orders of magnitude smaller than the linear and cosine functions. The results demonstrate that the proposed spinning rate functions outperform conventional linear and cosine functions in both circular SOP conversion performance and robustness. The research findings of this study are expected to offer valuable insights and guidance for the future development and design of SQWP.