I understand where the high energy cutoff comes from in high harmonic generation, with $E_{max}\approx I_p+3U_p$. However, I do not understand how, in the harmonic spectrum, radiation of frequency $1\omega$ is produced. When the electron recombines with its parent atom, there is at least the ionization potential energy which is released as a photon. The energy of the ionization potential $I_p$, even for Hydrogen, is way more energy than one laser photon with frequency $\omega$. It would seem that even with zero kinetic energy, the radiation would be of energy much larger than $\omega$.
Given that the absorption of the electron is a time-reversed process of photoionization, I can think of two possible solutions, neither of which sound right:
First, the absorption could be a multiphoton process and some low-energy photons are emitted alongside some larger ones. However, multiphoton processes are higher order and therefore less common, which would seem to be at odds with the fact that in the harmonic spectrum, the lowest order harmonics have the highest intensities.
Second, the absorption could be a second tunneling process. This would bypass the $I_p$, but brings in a new problem. A tunneling process doesn't require a photon, and so even if the electron managed only $1\omega$ of kinetic energy at the time of tunneling re-absorption, there would be no requisite radiation.
Where do these low frequency harmonics come from, and why are they of dominant intensity?
