We generalize a recently formulated theory of high-order harmonic generation by low-frequency laser fields [Anne L'Huillier et al., Phys. Rev. A 48, R3433 (1993)] to the case of an elliptically polarized light. Our theoretical description includes both the single-atom response and propagation. Phase matching significantly modifies the results obtained in the single-atom response. The results of our calculations, including propagation for both the intensity and polarization properties of harmonics as a function of laser ellipticity, compare very well with recent experimental observations.
Antoine, P., LHuillier, A., Lewenstein, M., Salieres, P., & Carre, B. (2004). Theory of high-order harmonic generation by an elliptically polarized laser field. Physical review. A, Atomic, molecular, and optical physics, 53(3), 1725-1745. https://doi.org/10.1103/PhysRevA.53.1725 (Original work published 2004)