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 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.