Resonant Third-Order Optical Susceptibility ?(3)(3?) in Asymmetric Coupled Si1?xGex/Si Quantum Wells

Abstract

We have calculated the enhancement of the third-order nonlinear optical susceptibility owing to the multi-photon process associated with the intersubband transition in the valence band in asymmetric coupled Si1—xGex/Si quantum wells. The hole states are described by the 6×6 Luttinger-Kohn Hamiltonian which incorporates the heavy-hole, light-hole and spin–orbit split-off bands and the effect of strain of lattice constants in the multi-quantum-well structure has been taken into account. In order to optimize the resonant third-order susceptibility the layer thicknesses of wells and barriers are selected in such a way that the energy spacings between the bound states in the valence band are nearly equal and the product of the dipole matrix elements of the relevant intersubband transitions is maximized. The step structure in the barrier height has been also considered. We found that the susceptibility χ(3)(3ω) is one or two orders of magnitude larger than that of the bulk Si.