Stored Electromagnetic Field Energies in General Materials

TL;DR

This paper derives the most general expressions for stored electromagnetic energies in complex media from the time-domain Poynting theorem and introduces a new energy conservation law that extends traditional understanding.

Contribution

It presents a novel energy conservation law for time-harmonic electromagnetic fields based on general stored energy expressions, enhancing the analysis of energy storage in complex media.

Findings

Derived general expressions for stored electromagnetic energies.

Introduced a new energy conservation law involving stored and dissipated energies.

In lossless media, established a physical interpretation of stored energy related to radiating systems.

Abstract

The most general expressions of the stored energies for time-harmonic electromagnetic fields are derived from the time-domain Poynting theorem, and are valuable in characterizing the energy storage and transport properties of complex media. A new energy conservation law for the time-harmonic electromagnetic fields, which involves the derived general expressions of the stored energies, is introduced. In contrast to the well-established Poynting theorem for time-harmonic fields, the real part of the new energy conservation law gives an equation for the sum of stored electric and magnetic field energies; the imaginary part involves an equation related to the difference between the dissipated electric and magnetic field energies. In a lossless isotropic and homogeneous medium, the new energy conservation law has a clear physical implication: the stored electromagnetic field energy of a radiating system enclosed by a surface is equal to the total field energy inside the surface subtracted by the field energy flowing out of the surface.