Time-Averaged Energy Flow and Momentum of Electromagnetic Waves in Homogeneous Isotropic Linear Media

There exist multiple different even non-equivalent expressions describing characteristics of electromagnetic wave energy flow and momentum in media, which makes the issue confusing. For simplicity (without loss of generality), we shall consider a case where a harmonic homogeneous plane wave (HHPW) travels in a homogeneous isotropic linear medium (HILM); thus, both time-dependent Poynting's vector S(t) and time-dependent momentum density G(t) are rigorously derived from continuity equations. Then, referring to recent studies of stored and dissipated energies of electromagnetic waves in lossy media, time-averaged Poynting's vector <S> and time-averaged momentum density <G> are obtained according to the time dependence of the terms arising in the expressions of S(t) and G(t), respectively. On this basis, a new way is proposed to determine the direction relation between <S> and <G> of HHPWs in an HILM, and it is demonstrated that, in an HILM, the propagation direction of <S> is always consistent with that of <G>, which may be applied to explain why the predicted reversal of electromagnetic wave momentum in a left-handed material has not been observed up to now. This work may be helpful to further discuss, and even eliminate, the confusion arising in related issues, and deepen the understanding of the energy flow and momentum of electromagnetic waves in media.