Optimization strategies for modulation transfer spectroscopy applied to laser stabilization

We present a general analysis for determining the optimal modulation parameters for the modulation transfer spectroscopy scheme. The results are universally valid and can be applied to spectroscopy of any atomic species requiring only the knowledge of the effective linewidth $\Gamma_{eff}$. A signal with optimized slope and amplitude is predicted for a large modulation index $M$ and a modulation frequency comparable to the natural linewidth of the spectroscopic transition. As a result of competing practical considerations, a modulation index in the range of $3 \le M \le 10$ has been identified as optimal. This parameter regime is experimentally accessible with a setup based on an acousto-optic modulator. An optimized signal for spectroscopy of the rubidium D2 line is presented. The signal shape and the dependence on the modulation parameters are in very good agreement with the theoretical description given. An experimental procedure for achieving a strong suppression of residual amplitude modulation is presented. Based on the optimized signal, we demonstrate long-term laser stabilization resulting in a laser linewidth of 150\,kHz (16\,s average) and a frequency stability of 18\,kHz (rms) over 15 hours.