Universal Expression of the Optical Power Dissipation in Multilayer Structures with Complex Permittivity and Permeability

Abstract

A general simple expression is derived for the time-average optical power dissipation Q in plasmonic or metamaterial-based multilayer structures, which have complex permittivity and/or complex permeability. We demonstrate that the derived general expression for Q, including the optical interference effect, is in the same form as one based on the Poynting's energy theorem, where the optical interference effect is not explicitly considered. The universal expression of Q, derived under the assumption of complex permittivity and permeability, reduces to other well-known simple forms, which are only valid when either permittivity or permeability is complex. The derived general expression of Q provides with a strong theoretical background to predict the optical absorption or loss in the design of plasmonic or metamaterial-based nanostructures.