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The phase conjugated response from nonmagnetic multi-level metallic quantumwells is analyzed and an essentially complete analytical solution is presentedand discussed. The description is based on a semi-classical local-field theoryfor degenerate four-wave mixing in mesoscopic interaction volumes of condensedmedia developed by the present authors [T. Andersen and O. Keller, Phys.Scripta 58, 132 (1998)]. The analytical solution is supplemented by a numericalanalysis of the phase conjugated response from a two-level quantum well in thecase 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 whichthe light-matter interaction can be tuned to resonance. The phase conjugatedresponse is examined in the case where all the scattering takes place in oneplane, and linearly polarized light is used in the mixing. In the numericalwork we study a two-monolayer thick copper quantum well using the infinitebarrier model potential. Our results show that the phase conjugated responsefrom such a quantum-well system is highly dependent on the spatial dispersionof the matter response. The resonances showing up in the numerical results areanalytically identified from the expressions for the linear and nonlinearresponse tensors. In addition to the general discussion of the phase conjugatedresponse with varying frequency and parallel component of the wavevector, wepresent the phase conjugated response in the special case where the light is inresonance with the interband transition.Comment: 18 pages, 12 figures, 3 tables, accepted for publication in The  Physical Review B. Figs. 3-6 reduced quality due to size limi

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