Absorption cross-section fluctuations driven by continuous and discrete laser frequency variations

Though the operational definition of a photon’s absorption cross-section is straightforward, the definition has a fundamental and well-known subtlety. In order to make contact with theory, the incident photons must be monoenergetic and should impinge on the target atom or molecule at a constant rate. To some extent, however, these two constraints are always violated: no field is perfectly monochromatic and laser photons bunch (for both technical and fundamental reasons). Thus, the textbook definition of cross-section must be understood in terms of a mean, in which case the quantum nature of a field and the practicability of its realization must be recognized as sources of cross-section variance. Here, we consider the role that continuous and discrete random frequency fluctuations play in determining the variance of an absorption cross-section. In particular, we investigate the differing roles of phase diffusion and mode-partition noise, finding that discontinuous mode variations have a significant and not easily discerned effect on an absorption cross-section’s variance. As a by-product of our studies, agreement between theory and experiment highlights the utility of a hybrid absorption cross-section for use in the quasi-static approximation, and also suggests an exponential relationship between the rate of mode hops and injection current in cleaved-facet diode lasers.