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.

The approximate orbital-approach of Jha and Bloembergen is used to calculate the non-dispersive part of the bilinear optical susceptibility,χ⁽²⁾, for various compounds. Using bonding and antibonding states of the molecular orbital theory it is shown thatχ⁽²⁾ satisfies a simple relation in terms of other measurable physical quantities. This relation is used to calculateχ⁽²⁾ for various III–V, II–VI and I–VII semiconductors, both with cubic zinc blende structure and with hexagonal wurtzite structure. The same procedure is used to obtainχ⁽²⁾ for potassium dihydrogen phosphate (KDP). The calculated values are compared with the experimentally observed values and it is found that the present model gives excellent results for II–VI compounds and for KDP.