Electromagnetic field energy density in artificial microwave materials with negative parameters

TL;DR

This paper derives physically consistent formulas for electromagnetic energy density in passive and active artificial microwave materials with negative parameters, addressing dispersion, absorption, and stability issues.

Contribution

It establishes general relations for energy density in negative parameter metamaterials that include dispersion and absorption effects, ensuring physical validity.

Findings

Energy density formulas are valid even with negative real parts of parameters.

Passive metamaterials always have positive energy density values.

Non-dispersive negative parameter materials are unstable.

Abstract

General relations for the stored reactive field energy density in passive linear artificial microwave materials are established. These relations account for dispersion and absorption effects in these materials, and they are valid also in the regions where the real parts of the material parameters are negative. These relations always give physically sound positive values for the energy density in passive metamaterials. The energy density and field solutions in active metamaterials with non-dispersive negative parameters are also considered. Basic physical limitations on the frequency dispersion of material parameters of artificial passive materials with negative real parts of the effective parameters are discussed. It is shown that field solutions in hypothetical materials with negative and non-dispersive parameters are unstable.