Iterative solution of quadratic tensor equations for mutual polarisation

Abstract

To describe mutual polarisation in bulk materials containing high polarisability molecules, local fields beyond the linear approximation needs to be included. A second order tensor equation is formulated that describes this in the case of crystalline or at least locally ordered materials such as an idealised polymer. It is shown that this equation is solved by a set of recursion equations that relate the induced dipole moment, linear polarisability and first hyperpolarisability in the material to the intrinsic values of the same properties of isolated molecules. From these, macroscopic susceptibility tensors up to 2nd order can be calculated for the material.