Model system for optical nonlinearities: Asymmetric quantum wells

Optical nonlinearities in asymmetric quantum wells due to resonant intersubband transitions are analyzed using a compact density-matrix approach. The large dipolar matrix elements obtained in such structures are partly due to the small effective masses of the host materials and are interpreted in terms of the participation of the whole band structure to the optical transitions. The other origin of the large second-order susceptibilities lies in the possibility of tuning independently the potential shape and the width of asymmetric quantum wells in order to obtain resonances (single or double) for a given excitation wavelength. Using a model based on an infinite-barrier quantum well, we have obtained very general and tractable formulas for second-order susceptibilities at resonance. This model allows us to fix additional fundamental quantum limitations to second-order optical nonlinearities. The ‘‘best potential shapes’’ maximizing the different susceptibilities are obtained, together with scaling laws as a function of photon energy. Experimental results on different GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As asymmetric quantum wells optimized for second-harmonic generation and optical rectifications are given, with optical rectification coefficients more than ${10}^6$ higher than in bulk GaAs. These asymmetric quantum wells may be considered as giant ‘‘pseudomolecules’’ optimized for large optical nonlinearities in the 8–12-μm range.