Abstract
We show that the nonlinear interactions between x rays and longer wavelengths in crystals depend strongly on the band structure and related properties. Consequently, these types of interactions can be used as a powerful probe for fundamental properties of crystalline bulk materials. In contrast to previous work that highlighted that these types of nonlinear interactions can provide microscopic information on the valence electrons at the atomic scale resolution, we show that these interactions also contain information that is related to the periodic potential of the crystal. We explain how it is possible to distinguish between the two contributions. Our work indicates on the possibility for the development of novel multi-dimensional pump-probe metrology techniques that will provide spectroscopic information combined with structural information including ultrafast dynamics at the atomic scale.
Highlights
The possibility to utilize nonlinear interactions between x rays and radiation at wavelengths ranging from infrared (IR) to ultraviolet (UV) as an atomic-scale probe for intermolecular interactions and for properties of valence electrons has been discussed in several publications [1,2,3,4,5,6,7,8,9]
The technique relies on the atomic scale wavelengths of the x-rays, which provide the high resolution, while the longer wavelengths (UV/optical) are used to enhance the interactions with the valence electrons, which are usually weak for x rays
The strong wavelength dependence of spontaneous parametric down conversion (SPDC) of x rays into UV, which has been observed in recent experiments [3,6,8,9,10,11] suggests that nonlinear interactions between x rays and longer wavelengths can be used as new spectroscopy tools for the investigation of phenomena that traditionally are probed by using long-wavelength radiation with the advantage of providing microscopic atomic-scale information
Summary
The possibility to utilize nonlinear interactions between x rays and radiation at wavelengths ranging from infrared (IR) to ultraviolet (UV) as an atomic-scale probe for intermolecular interactions and for properties of valence electrons has been discussed in several publications [1,2,3,4,5,6,7,8,9]. Since the goal of the measurements is to probe microscopic information, the use of crystals introduces a new challenge for the interpretation of the results since the measured signal depends not just on the atomic or inter unit cell interactions between the valence electrons and on the periodic potential of the materials. Most theoretical models that have been considered for the description of nonlinear interactions between x rays and longer wavelengths have focused on the ability to observe microscopic information and on the estimation of the strength of the effects [2,3,4,5,7,17,18,19,20] They have not addressed the challenge of the separation of the inter unit cell information from the periodic information. With eigenvalues εn(q), where n is the band number and q is the wave vector associated with the Bloch state
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