Poynting’s theorem for plane waves at an interface: A scattering matrix approach

Abstract

We write Poynting’s theorem in a form that allows us to introduce a natural definition of the scattering matrix S. For a dielectric-dielectric interface this balance equation leads to energy flux conservation and the unitarity property of S. For the dielectric-conductor interface the scattering matrix is no longer unitary due to the presence of losses in the conductor, and we denote it by S̃. The dissipative term in Poynting’s theorem can be interpreted as due to a single parasitic channel or excitation of the absorptive interface. We define an S matrix that includes the parasitic channel, so that S is unitary.