  We theoretically study nonlinear optics of excitons under intense THz
irradiation. In particular, the linear near infrared absorption and resonantly
enhanced nonlinear sideband generation are described. We predict a rich
structure in the spectra which can be interpreted in terms of the quasienergy
spectrum of the exciton, via a remarkably transparent expression for the
susceptibility, and show that the effects of strongly avoided quasienergy
crossings manifest themselves directly, both in the absorption and transmitted
sidebands.
