Electric field effect on optical harmonic generation at the exciton resonances in GaAs

An electric field applied to a semiconductor reduces its crystal symmetry and modifies its electronic structure which is expected to result in changes of the linear and nonlinear response to optical excitation. In GaAs, we observe experimentally strong electric field effects on the optical second (SHG) and third (THG) harmonic generation. The SHG signal for the laser-light $k$ vector parallel to the [001] crystal axis is symmetry forbidden in the electric-dipole approximation, but can be induced by an applied electric field in the vicinity of the $1s$ exciton energy. Surprisingly, the THG signal, which is allowed in this geometry, is considerably reduced by the electric field. We develop a theory which provides good agreement with the experimental data. In particular, it shows that the optical nonlinearities for the $1s$ exciton resonance are modified in an electric field by the Stark effect, which mixes the $1s$ and $2p$ exciton states of opposite parity. This mixing acts in opposite way on the SHG and THG processes, as it leads to the appearance of forbidden SHG in (001)-oriented GaAs and decreases the crystallographic THG.