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

TL;DR

This paper provides an analytical and numerical study of phase conjugation in metallic quantum wells, revealing how the response depends on spatial dispersion and resonance conditions, with potential applications in nonlinear optics.

Contribution

It offers a complete analytical solution for phase conjugation in metallic quantum wells and explores the effects of spatial dispersion and resonance through numerical analysis.

Findings

Phase conjugated response depends strongly on spatial dispersion.

Resonances are identified from response tensor expressions.

Response is significant when light is in resonance with interband transitions.

Abstract

The phase conjugated response from nonmagnetic multi-level metallic quantum wells is analyzed and an essentially complete analytical solution is presented and discussed. The description is based on a semi-classical 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. Scripta 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 wavevector, we present the phase conjugated response in the special case where the light is in resonance with the interband transition.