Terahertz (THz) spectroscopy provides a powerfull method to characterize different quasi-particles in optically excited semiconductors (see, e.g., experiments [1, 2]). When the intra-excitonic 1s-to-2p transition is excited with a strong THz pulse, all kinds of nonlinear and extreme nonlinear effects are observed [3, 4] including Rabi flopping, THz high harmonics, and the excitonic dynamical Franz-Keldysh effect. We present a theoretical analysis of the nonlinear THz response from the internal transitions of coherent [3] and incoherent [4] excitons based on our microscopic THz theory [5, 6]. Moreover, the response of unexcited semiconductors to extremely intense THz fields is investigated (see Fig. 1(a)). For field strengths larger than about 3MV/cm, frequency components up to 200 times the excitation frequency V{sub}0=12THz are generated. This extreme nonlinear high-harmonic generation is caused by the nontrivially coupled dynamics of intraband acceleration and nonresonantly excited interband transitions. Even though the THz field is strongly nonresonant with the bandgap, charge carriers are excited due to multi-photon processes and are then accelerated by the THz field.
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