Electromagnetic energy in a dispersive metamaterial

An expression for the electromagnetic field energy density in a dispersive, lossy, left-handed metamaterial, consisting of an array of split-ring resonators and an array of wires is derived. An electromagnetic field with general time-dependence is considered. The outcome is compared with previously published results. In the absence of losses, agreement with the general result for the energy density in a dispersive material is obtained. The formulae are verified using the finite-difference time-domain (FDTD) numerical method. The applicability of two commonly used permeability models to the problem of calculating the energy stored in an array of split-ring resonators is discussed.