Frequency-domain Integral Equations in Linear Electrodynamics

A general formulation is presented for integral equations in the most general linear media, for which only the free-space Green's function is needed. The frequency-domain integral equations thus obtained contain all previously derived integral equations as particular cases. The derivation is based on the equivalency between a macroscopic and a microscopic formulation of Maxwell's equations. Possible extensions to time-domain electromagnetic fields, that take into account the dispersive properties of the media, are discussed.