Nonlinear response of quantum-confined electrons in nonparabolic subbands

Abstract

We show that quantum confinement can dramatically alter the density-dependence of the third-order susceptibility, χ(3)NP, that arises from band nonparabolicity. Our results predict an oscillatory dependence of the efficiencies for third-harmonic generation and four-wave mixing on the subband occupation of quantum wells, and for narrow wells with high charge densities predict an enhancement over the bulk susceptibility. We also make a simple estimate of the fields required to saturate this nonparabolicity contribution to χ(3). We discuss these results in light of recent experiments on third-harmonic generation from narrow-gap quantum wells at frequencies of ∼1 THz, and show that nonparabolicity may not be the only nonlinearity contributing to the large χ(3) observed.