when the constitutive parameters have the form(2.29)-(2. 31). Physically, this term describes both the energy stored in the electromagnetic field and the energy dissipated by the material because of time lags between the application of e and h and the polarization or magnetization of the atoms(and thus the response fields D and B). In principle this term can also be used to describe active media that transfer mechanical or chemical energy of the material into field energy. nstead of attempting to interpret(4.40), we concentrate on the physical me V·S(r,1)=-V·[E(r,t)×H(r,t)] We shall postulate that this term describes the net flow of electromagnetic energy into the point r at time t. Then(4.39)shows that in the absence of impressed sources the energy How must act to(1) increase or decrease the stored energy density at r, (2) dissipate energy in ohmic losses through the term involving J, or 3)dissipate(or provide)energy through the term(40). Assuming linearity we may write S(r, t) (r, t)+=Wm(r, t) (4.41) re the terms on the right-hand side represent the time rates of change of, respectively, ed electric, stored magnetic, and dissipated energies 4.5.1 Dissipation in a dispersive material Although we may, in general, be unable to separate the individual terms (4.41),we can examine these terms under certain conditions. For example, consider a field that builds from zero starting from time t -oo and then decays back to zero at t v·S(dt=ucm(t=∞)-U-m(t=-∞)+u(=0)-u(=-0) where Wen We+Wm is the volume density of stored electromagnetic energy. This stored energy is zero at t= +oo since the fields are zero at those times. Thus, △uQ v·S(n)dt=o(t=∞)-uQ(t=-0) presents the volume density of the net energy dissipated by a lossy med um (or su by an active medium). We may thus classify materials according to the scheme active For an anisotropic material with the constitutive relations E·E,B=乒·H,J INote that in this section we suppress the r-dependence of most quantities for clarity of presentation 2001 by CRC Press LLCwhen the constitutive parameters have the form (2.29)–(2.31). Physically, this term describes both the energy stored in the electromagnetic field and the energy dissipated by the material because of time lags between the application of E and H and the polarization or magnetization of the atoms (and thus the response fields D and B). In principle this term can also be used to describe active media that transfer mechanical or chemical energy of the material into field energy. Instead of attempting to interpret (4.40), we concentrate on the physical meaning of −∇ · S(r, t) = −∇ · [E(r, t) × H(r, t)]. We shall postulate that this term describes the net flow of electromagnetic energy into the point r at time t. Then (4.39) shows that in the absence of impressed sources the energy flow must act to (1) increase or decrease the stored energy density at r, (2) dissipate energy in ohmic losses through the term involving Jc, or (3) dissipate (or provide) energy through the term (40). Assuming linearity we may write −∇· S(r, t) = ∂ ∂t we(r, t) + ∂ ∂t wm(r, t) + ∂ ∂t wQ(r, t), (4.41) where the terms on the right-hand side represent the time rates of change of, respectively, stored electric, stored magnetic, and dissipated energies. 4.5.1 Dissipation in a dispersive material Although we may, in general, be unable to separate the individual terms in (4.41), we can examine these terms under certain conditions. For example, consider a field that builds from zero starting from time t = −∞ and then decays back to zero at t = ∞. Then by direct integration1 − ∞ −∞ ∇ · S(t) dt = wem(t = ∞) − wem(t = −∞) + wQ(t = ∞) − wQ(t = −∞) where wem = we +wm is the volume density of stored electromagnetic energy. This stored energy is zero at t = ±∞ since the fields are zero at those times. Thus, wQ = − ∞ −∞ ∇ · S(t) dt = wQ(t = ∞) − wQ(t = −∞) represents the volume density of the net energy dissipated by a lossy medium (or supplied by an active medium). We may thus classify materials according to the scheme wQ = 0, lossless, wQ > 0, lossy, wQ ≥ 0, passive, wQ < 0, active. For an anisotropic material with the constitutive relations D˜ = ˜¯ · E˜ , B˜ = µ˜¯ · H˜ , J˜ c = σ˜¯ · E˜ , 1Note that in this section we suppress the r-dependence of most quantities for clarity of presentation.