We derive the instantaneous densities of electric energy and electric power dissipation in lossless and lossy dispersive media for a time-harmonic electric field. The instantaneous quantities are decomposed into DC and AC components, some of which are shown to be independent of the dispersion of dielectric constants. The AC component of the instantaneous energy density can be used to visualize propagation of electromagnetic waves through complex 3D structures.
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Shin et al. (2012) studied this question.
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