Local-field study of the optical second-harmonic generation in a symmetric quantum-well structure

A nonlocal analysis of the infrared second-harmonic generation associated with intersubband transitions in a symmetric semiconductor quantum-well structure is presented. Taking as a starting point a fundamental self-consistent integral equation for the local field, the p-polarized first-harmonic field inside the quantum well is studied. By using the infinite-barrier wave functions and taking into account only the two lowest subbands, analytical expressions are obtained for the local field. The result of the local-field calculation at the first-harmonic frequency, in turn, is used to calculate the p-polarized second-harmonic local field. The conversion efficiency of the second-harmonic generation from the quantum well is thus determined. Numerical calculations of the frequency and angular spectra of the second-harmonic intensities are presented for a symmetric GaAs/${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As quantum well. The numerical results show that strong second-harmonic generation occurs in the vicinity of the resonance frequencies for both the first- and second-harmonic local field inside the quantum well. The influence of the dynamic local-field interaction of the electrons on the optical second-harmonic generation is investigated. It is demonstrated that the dynamic screening can lead to a notable upward shift of the locations of the resonant peaks in the frequency spectra of the second-harmonic conversion coefficient.