Comment on “Poynting vector, heating rate, and stored energy in structured materials: A first-principles derivation”

Abstract

In Phys. Rev. B 80, 235120 ͑2009͒, M. G. Silveirinha criticizes our work on Poynting's theorem and energy conservation in systems with bounded media ͓EPL 81, 67005 ͑2008͔͒, especially with regard to our argumentation toward S = 1 0 ͑E ϫ B͒ as a generally valid energy flux vector. We fully rebut the criticism, point out that it is based on undue comparison, clear up some misunderstandings and show that Silveirinha's approach is rather a restricted than a general one.is a purely electromagnetic energy flux vector ͑Poynting vec-tor͒, which constitutes together with the electromagnetic field energy densityand the dissipation −jE a universally valid energy conservation law ͑Poynting theorem͒,in which all quantities are well defined and have a clear physical meaning. We also point out problems that exist with the historical form of the Poynting vector,when general ͑realistic͒ media properties are considered. ͑In absence of magnetization, of course, both variants coincide, since H = 1 0 B in this case.͒ In Ref. 2, a "macroscopic Poynting vector" is derived together with other quantities in a composite medium, which the author eventually finds to coincide with "usual textbook formulas." Comparing his findings to ours, he blames our work for "erroneous conclusions," "unsubstantiated claims," and "fundamental misconceptions and mistakes."We will show here that there are rather misunderstandings and mistakes from the author's part, and take the chance to clarify things from our perspective. We need to proceed carefully because the author's notion of several terms is different from ours. We underline that our results do not contradict classical textbooks, 3,4 but rather extent and concretize their accounts. The warnings contained in these books concerning the validity of Eq. ͑4͒ seemingly have been largely overlooked.Our approach 1 starts from a consideration of the system under study as a classical ensemble of charged pointlike particles which are subjected to Newton's laws of motion and are in interaction with physical electromagnetic fields E, B governed by Maxwell's equations and the Lorentz force law. This constitutes a fundamental and purely axiomatic basis for the theory. Its quantum-statistical generalization is straightforward and leads to identical relations for the expectation values. The author of Ref. 2 interprets this as a "phenomenological model," an interpretation which we strongly reject.Matter may be arbitrarily complex, but it will always be possible to decompose it into an ensemble of charged particles. This way, there is neither a need to describe the properties of matter, nor to consider medium boundaries, to establish proper boundary conditions or even to find a proper definition of where the boundary of a medium in a microscopic picture lies.The electromagnetic fields E, B in our approach are not averaged in any sense, neither spatially nor temporally ͑except for the quantum-statistical expectation value being taken͒, and are always given in the space and time domains. Here, our notion of the term "mi...

On the current-driven model in the classical electrodynamics of continuous media

“…which is, indeed, consistent with the Landau and Lifshitz textbook formula [15]. However, the transition from (14) to (17) explicitly requires that Im k = 0. As was shown above, k here is not a mathematically independent variable but must be computed from the dispersion relation which is specific to the medium.…”

“…In particular, Silveirinha writes that the conclusions of [12,13] 'are founded on fundamental misconceptions and mistakes'. These claims have been contested recently on rather general grounds [14]. However [14], did not consider the technical details of Silveirinha's derivations.…”

“…Therefore, Silveirinha cannot claim that he has confirmed the textbook result by using a more first principle or fundamental approach than the approach used by Landau and Lifshitz [15]. On the other hand, it is possible to evaluate (14) without making any assumptions about k. If we assume that all currents inside the medium are induced and thus abandon the unphysical current-driven model, we can use the two Maxwell's equations…”

Reply to “Comment on ‘Poynting vector, heating rate, and stored energy in structured materials: A first-principles derivation’ ”

“…I also emphasize that the macroscopic Poynting vector derived in my paper is coincident with the most general form of the Poynting vector reported in the literature for reciprocal stationary spatially dispersive media. In the Comment, 1 Richter et al argued that s = e ϫ b / 0 can be regarded as a completely general energy flux vector in bounded media, and acknowledged and clarified that the results of their letter 2 are valid if and only if the electromagnetic fields are not averaged in any sense. I certainly agree with Richter et al that the energy conservation theorem derived in their work 2 is correct as long as one considers only "microscopic" electromagnetic fields, and that if that was the intended scope of their work, my considerations in Ref.…”

Electromagnetic-Energy Flow in Anisotropic Metamaterials: The Proper Choice of Poynting’s Vector

“…, and that the accumulation of energy at the interface causes no conceptual problem because in magnetic materials the source of energy dissipation at the interface are the induced surface currents [22] [28] [31]. It is appropriate to recall that these proposals have been recently re-examined, due somewhat to the current work done around the phenomenon of negative refraction in metamaterials [32]- [38].…”