Microscopic optical fields and mixing coefficients of X-ray and optical frequencies in solids

Abstract

Simple approximation schemes are developed to calculate induced optical fields and local field corrections to the linear optical dielectric function in metals like aluminium and in insulators like germanium. In these calculations, the unperturbed electronic states in Ge are described within the framework of the bonding orbital approach, whereas the nearly-free-electron approximation is used for Al. As expected, explicit numerical calculations show that the contribution to secondary longitudinal induced fields is more appreciable in Ge. The second order susceptibility describing the non-linear mixing of an optical frequency with an x-ray frequency, which depends upon the magnitude of the microscopic induced optical charge density, is also calculated for these solids. For most relevant wavevectors of secondary optical fields, it is found to be of the order of 10^-12 esu in Ge and 10^-14 esu in Al.