Magnetic field effects in optical harmonics generation by excitons

Mechanisms responsible for the optical harmonics generation in several classes of materials at excitonic transitions are considered. In the cubic semiconductor GaAs, magnetically induced second harmonic generation (SHG) was observed in the region of orbital quantization for the valence and conduction bands. An unusually strong third harmonic generation was detected in the region of the 1s exciton in an external magnetic field due to the exciton-polariton resonance. Magnetic field induced SHG was revealed in the hexagonal wide bandgap semiconductor ZnO at exciton resonances 1$s$, 2$s$, and 2$p$. Depending on the symmetry of the exciton states, the SHG mechanisms are determined by the spin and orbital Zeeman effects, and the magneto-Stark effect. Magnetically induced contribution to SHG was studied in the antiferromagnet Cr$_2$O$_3$ at exciton transitions in an external magnetic field.