Theoretical description of frequency modulation and wavelength modulation spectroscopy

We present a comprehensive theory for heterodyne absorption spectroscopy with phase-modulated light. The general equations presented allow for an arbitrary modulation index and an arbitrary modulation frequency. We use this description for three purposes: First, we review the special cases of so-called frequency modulation and wavelength modulation spectroscopy. Second, we present the additional case of large-index, high-frequency modulation. Third, we present an overview of how the absorption signal depends on the experimental parameters of modulation frequency and modulation index. This overview may be helpful to experimentalists in choosing these parameters, for it provides a systematic understanding of how moving around in parameter space changes certain features of the signal, while leaving other features invariant.