Source-neutral Green'functions for periodic problems in electrostatics, and their equivalents in electromagnetism
Christopher G. Poulton, L. C. Botten, R. C. McPhedran, A. B. Movchan · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · 1999
We consider source–neutral problems for periodic problems in electrostatics. These may be used to derive an identity due to Lord Rayleigh entirely within the context of the unit cell, and without use of reasoning based on contributions from charges at an outer boundary of the periodic system, or employing conditionally convergent lattice sums. We also consider the equivalent of source–free Green'functions for the Helmholtz equation, which are Green'functions with their specular parts removed. We show that, as the wavenumber tends to zero, the non–specular dynamic Green'functions tend with no divergences to the source–neutral electrostatic Green'function.