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 results of a comprehensive experimental and theoretical study of the three-photon process of optical second harmonic generation (SHG) involving the exciton resonances of the noncentrosymmetric hexagonal wide-band-gap semiconductor ZnO in the photon energy range of 3.2 − 3.5 eV. Resonant crystallographic SHG is observed for the 1s(A, B), 2s(A, B), 2p(A, B), and 1s(C) excitons. We show that strong SHG signals at these exciton resonances are induced by the application of a magnetic field when the incident and the SHG light wave vectors are along the crystal z-axis where the crystallographic SHG response vanishes. A microscopic theory of SHG generation through excitons is developed, which shows that the nonlinear interaction of coherent light with excitons has to be considered beyond the electric-dipole approximation. Depending on the particular symmetry of the exciton states SHG 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. The importance of each mechanism is analyzed and discussed by confronting experimental data and theoretical results for the dependencies of the SHG signals on photon energy, magnetic field, electric field, crystal temperature, and light polarization. Good agreement is obtained between experiment and theory proving the validity of our approach to the complex problem of nonlinear interaction of light with ZnO excitons. This general approach can be applied also to other semiconductors.

The magneto-Stark effect of excitons is demonstrated to be an efficient source of optical nonlinearity in hexagonal ZnO. Strong resonant second harmonic generation signals induced by an external magnetic field are observed in the spectral range of 2s and 2p excitons. The microscopic theoretical analysis shows that for excitons with a finite wave vector, exciton states of opposite parity are mixed by an effective odd parity electric field induced by the magnetic field despite its even parity. The field, spectral, and polarization dependencies of the second harmonic generation intensity validate the proposed mechanism. The observed phenomenon is not limited to a certain symmetry class and therefore must be effective in other semiconductors.

EuTe possesses the centrosymmetric crystal structure m3m of rocksalt type in which the second-harmonic generation is forbidden in electric dipole approximation but the third-harmonic generation ͑THG͒ is allowed. We studied the THG spectra of this material and observed several resonances in the vicinity of the band gap at 2.2-2.5 eV and at higher energies up to 4 eV, which are related to four-photon THG processes. The observed resonances are assigned to specific combinations of electronic transitions between the ground 4f 7 state at the top of the valence band and excited 4f 6 5d 1 states of Eu 2+ ions, which form the lowest energy conduction band. Temperature, magnetic field, and rotational anisotropy studies allowed us to distinguish crystallographic and magnetic-field-induced contributions to the THG. A strong modification of THG intensity for the 2.4 eV band and suppression of the THG for the 3.15 eV band was observed in applied magnetic field. Two main features of the THG spectra were assigned to 5d͑t 2g ͒ and 5d͑e g ͒ subbands at 2.4 eV and 3.15 eV, respectively. A microscopic quantum-mechanical model of the THG response was developed and its conclusions are in qualitative agreement with the experimental results.

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Third harmonic generation (THG) has been studied in europium selenide EuSe in the vicinity of the band gap at 2.1-2.6 eV and at higher energies up to 3.7 eV. EuSe is a magnetic semiconductor crystalizing in centrosymmetric structure of rock-salt type with the point group m3m. For this symmetry the crystallographic and magnetic-fieldinduced THG nonlinearities are allowed in the electric-dipole approximation. Using temperature, magnetic field, and rotational anisotropy measurements, the crystallographic and magnetic-field-induced contributions to THG were unambiguously separated. Strong resonant magnetic-field-induced THG signals were measured at energies in the range of 2.1-2.6 eV and 3.1-3.6 eV for which we assign to transitions from 4f 7 to 4f 6 5d 1 bands, namely involving 5d(t 2g ) and 5d(e g ) states.