Theory of high-order sum and difference frequency mixing in a strong bichromatic laser field

We generalize the recently formulated theory of high-order harmonic generation by low-frequency laser fields to the case of high-order sum and difference frequency mixing in a two-color field of noncommensurate frequencies in the optical-infrared regime. Our theoretical description includes both the single-atom response and propagation. We observe a different behavior of the sum and difference frequency mixing processes, in the single-atom response as well as in the propagation results. The results of our calculations including propagation compare very well with recent experimental observations.