Interfacing light and single atoms with a lens

We characterize the interaction between a single atom or similar microscopic system and a light field via the scattering ratio. For this, we first derive the electrical field in a strongly focused Gaussian light beam, and then consider the atomic response. Following the simple scattering model, the fraction of scattered optical power for a weak coherent probe field leads to unphysical scattering ratios above 1 in the strong focusing regime. A refined model considering interference between the exciting and scattered field into finite-sized detectors or optical fibers is presented, and compared with experimental extinction measurements for various focusing strengths.