Stored and absorbed energy of fields in lossy chiral single-component metamaterials

Abstract

Here we present theoretical results for estimation of electromagnetic field energy density and absorbed energy in dispersive lossy chiral single-component metamaterials which consist of an ensemble of identical helical resonators as inclusions. The shape of the helical resonator can vary over a wide range, from a straight wire to a flat split ring. An interaction of the inclusions with harmonic circularly polarized electromagnetic plane waves is studied. We focus on how the inclusion shape influences the mentioned metamaterial properties. The derived general solution for the problem is in good agreement with previous partial and alternative solutions obtained for split ring resonators, straight wires, and helices. The study reveals the optimal geometry of helical lossy resonators for their strongest selectivity of interaction with circularly polarized radiation.

Effective Electrodynamics Theory for the Hyperbolic Metamaterial Consisting of Metal–Dielectric Layers

“…We now consider some numerical results of Equations (18), (27) and (28) (see Figure 2). In our simulation, the filling fraction is f = 0.5, and the relative permittivity of the dielectric layers is ε d = 2.5.…”

“…However, for a frequency too close to the resonance frequency 0 ω ω = p , the power loss rate (see Equation (28)) gets so high; thus, the stored energy becomes heat in a short time. (18) and (27). The relative permittivity of the dielectric layers is assumed to be 18).…”

“…In the first subsection, we will propose a Lagrangian density and show that the EM field Figure 2. Numerical results for Equations (18) and (27). The relative permittivity of the dielectric layers is assumed to be ε d = 2.5, and the filling fraction is chosen as f = 0.5.…”

“…The resonance and directionality of the constituent components imply that the metamaterials are inherently dispersive, absorptive, and anisotropic. A fundamental problem concerning dispersive media is how to calculate the stored electromagnetic energy density [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]. For dispersive media with negligible absorption, the time-averaged energy density as a function of the (complex valued) electric and magnetic fields (in the frequency domain) can be derived by considering the adiabatically varying electromagnetic field [29].…”

“…For the wire-SRR metamaterials, time-averaged energy density formula can be derived using the equivalent circuit (EC) method [10,16,17]. On the other hand, instantaneous energy density formula (the time domain formula) can be obtained using the electrodynamics (ED) method with Poynting theorem [9,[12][13][14][15][18][19][20]24,27,28]. However, quite a few controversies exist in the literature, and they need to be resolved [16][17][18][19][20].…”