Second-Harmonic Generation in Quantum Wells with Anisotropic and Tilted Valleys: Effect of Coulomb Interaction

Abstract

Analytical expressions for the components of second-harmonic susceptibility tensor for the L-valley quantum well structures are derived employing the perturbative density-matrix formulation within the time dependent local density approximation (TDLDA). Indirect and direct Coulomb interactions are shown to affect the second-harmonic generation (SHG) spectra differently from each other depending upon the polarization of the pumped and generated light and upon the kind of many-subband system. It is found that the nonlinear dependence of the exchange-correlation potential upon the electron density influences the peak value of the spectrum connected only with the normal-incidence intersubband transitions. The effect of the Coulomb interaction, both direct and indirect, is shown to reveal itself strongly for a near-doubly resonant three-subband system even with a big intersubband gap (of more than 100 meV), while in case of a two-subband system it is best if the gap is of about 10 meV. The numerical calculations show that very fine near-doubly resonant step quantum well systems are required for the SHG and the TDLDA should be used to determine the near-doubly resonance condition.