Poynting’s theorem and luminal total energy transport in passive dielectric media

Without approximation the energy density in Poynting’s theorem for the generally dispersive and passive dielectric medium is demonstrated to be a system total dynamical energy density. Thus the density in Poynting’s theorem is a conserved form that by virtue of its positive definiteness prescribes important qualitative and quantitative features of the medium-field dynamics by rendering the system dynamically closed. This fully three-dimensional result, applicable to anisotropic and inhomogeneous media, is model independent, relying solely on the complex-analytic consequences of causality and passivity. As direct applications of this result, we show (1) that a causal medium responds to a virtual, “instantaneous” field spectrum, (2) that a causal, passive medium supports only a luminal front velocity, (3) that the spatial “center-of-mass” motion of the total dynamical energy is also always luminal and (4) that contrary to (3) the spatial center-of-mass speed of subsets of the total dynamical energy can be arbitrarily large. Thus we show that in passive media superluminal estimations of energy transport velocity for spatially extended pulses is inextricably associated with incomplete energy accounting.