Nonlinear optics of semiconductors is an important field of fundamental and applied research, but surprisingly the role of excitons in the coherent processes leading to harmonics generation has remained essentially unexplored. Here we report on some examples of experimental and theoretical study of the second- (SHG) and third (THG) harmonic generation involving the exciton resonances in the noncentrosymmetric semiconductors ZnO and GaAs. External electric and magnetic fields are used to modify exciton states and their nonlinear optical properties. Depending on the particular symmetry of the exciton states SHG/THG can originate from the electric- and magnetic-field-induced perturbations of the excitons due to the Stark effect, the spin as well as orbital Zeeman effects, or the magneto-Stark effect. A microscopic theory of SHG and THG on excitons is developed, which shows that the nonlinear interaction of coherent light with excitons has to be considered beyond the electric-dipole approximation.
Currently coherent spin phenomena are in the focus of wide research activity in such multidisciplinary fields
as spintronics, quantum communication and information processing.<sup>1-3</sup> Among those, the optical orientation
based on the transfer to media of the angular momentum carried by the circularly-polarized light plays very
important role for disclosing basic processes that govern generation and relaxation of spin and orbital states.
By using ultrafast pump-probe spectroscopy we show that optical pumping can induce spin-polarization in
antiferromagnetic Mott insulators R<sub>2</sub>CuO<sub>4</sub> (R = Pr, Nd, Sm) providing a way for fast nonlinear manipulation
of spin states on time scale of 100 fs and less. The driving mechanisms of the ultrafast spin orientation and
dynamics in Mott insulators are the strong spin-orbit, spin-phonon and exchange interaction as inherent features
of strongly-correlated systems both in the ground and excited states. High values of the corresponding nonlinear
susceptibilities may have significant impact for novel ultrafast all-optical technologies.