Local-field study of phase conjugation in metallic quantum wells with probe fields of both propagating and evanescent character

The phase conjugated response from nonmagnetic multilevel metallic quantum wells is analyzed and an essentially complete analytical solution is presented and discussed. The description is based on a semiclassical local-field theory for degenerate four-wave mixing in mesoscopic interaction volumes of condensed media developed by the present authors [T. Andersen and O. Keller, Phys. Scr. 58, 132 (1998)]. The analytical solution is supplemented by a numerical analysis of the phase conjugated response from a two-level quantum well in the case where one level is below the Fermi level and the other level is above. This is the simplest configuration of a quantum-well phase conjugator in which the light-matter interaction can be tuned to resonance. The phase conjugated response is examined in the case where all the scattering takes place in one plane, and linearly polarized light is used in the mixing. In the numerical work we study a two-monolayer thick copper quantum well using the infinite barrier model potential. Our results show that the phase conjugated response from such a quantum-well system is highly dependent on the spatial dispersion of the matter response. The resonances showing up in the numerical results are analytically identified from the expressions for the linear and nonlinear response tensors. In addition to the general discussion of the phase conjugated response with varying frequency and parallel component of the wave vector, we present the phase conjugated response in the special case where the light is in resonance with the interband transition.