Numerical study of the line shape changes of modulation transfer spectroscopy depending on the modulation index

This study presents a simple scheme for the numerical calculation of modulation transfer spectroscopy (MTS) signals. The MTS spectra predicted by our approach with the typical parameters show good agreement with the spectra predicted using standard third-order perturbation calculation and Fourier expansion methods. Our succinct calculation scheme enables us to incorporate effects from the higher-order sidebands even in the relatively high modulation index regimes without increasing the number of the additional terms required; this is in stark contrast to the previous standard approaches. We also present a systematic investigation into the line shape of MTS spectra in terms of their modulation index, which is one of the essential factors for optimizing MTS line shape for laser frequency stabilization applications.