International Journal of Mathematics and Mathematical Sciences
Volume 32 (2002), Issue 5, Pages 301-312
doi:10.1155/S0161171202110246

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 need to be included. A second order tensor equation is formulated, and it 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 second order can be calculated for the material.