Theory of parametric x-ray optical wavemixing processes

TL;DR

This paper develops a quantum electrodynamics framework to describe and analyze x-ray optical wavemixing processes, enabling new spectroscopic imaging techniques with potential applications in material characterization.

Contribution

It introduces a comprehensive theoretical model for x-ray parametric wavemixing processes, linking observable scattering patterns to medium response functions.

Findings

Agreement with recent sum-frequency experimental results

Identification of the imaged quantity as a response function

Framework enables microscopic reconstruction of medium properties

Abstract

Enabled by x-ray free-electron lasers, nonlinear optical phenomena can be explored in the x-ray domain nowadays. Among the multitude of newly accessible processes, this theoretical study focuses parametric x-ray optical wavemixing for closer investigation. Specifically, we develop a framework based on non-relativistic QED to describe x-ray optical sum- and difference-frequency generation as well as x-ray parametric down-conversion on equal footing. All of these processes promise imaging capabilities similar to regular x-ray diffraction with additional spectroscopic selectivity that is tunable via the optical admixture. Based on our derivation, we identify the imaged quantity as we relate the observable scattering pattern to an underlying response function of the medium. The resulting relation, furthermore, enables the microscopic reconstruction of this response function from nonlinear analogues of crystallographic measurements. We benchmark our approach on recent experimental sum-frequency results, for which we find encouraging agreement with our theory.