Energy Density of Macroscopic Electric and Magnetic Fields in Dispersive Medium With Losses

Abstract

Abstract-Electric permittivity and magnetic permeability of linear passive dispersive medium were defined using the circuit equation of an electrically small antenna (scatterer) with resonant and antiresonant properties. It was shown that the average macroscopic energy stored by the scatterers is proportional to frequency derivative of the input admittance of corresponding antenna. It was found that the average macroscopic energy density of electric and magnetic fields in dispersive lossy medium is a function of frequency derivatives of its effective constitutive parameters in accordance with Poynting's theorem in dispersive lossy medium clarified for this case in the paper.

Lagrangian dynamics approach for the derivation of the energy densities of electromagnetic fields in some typical metamaterials with dispersion and loss

“…for harmonic electromagnetic waves are given by The constitutive relations equations (15) to (19) are derived from the dynamical equations which implies that any term proportional to ¶ ( ) P t 2 in the Lagrangian or the dissipation function is not different from a term proportional to M 2 . Therefore, only one of these two terms will show up in the Lagrangian and the dissipation function.…”

“…It also has theoretical interest because the fundamental problem of energy propagation velocity related to causality and relativity is based on it [7][8][9]. A number of solutions for this problem have already been proposed [4,5,[7][8][9][10][11][12][13][14][15][16][17][18][19][20], but so far most of them dealt only with the dispersion of permittivity, without considering the corresponding dispersion of the permeability [4,5,[16][17][18]20]. Besides, some results are controversial [16].…”

“…Besides, some results are controversial [16]. For example, there is no consensus on whether a negative energy density is physically acceptable, although most believe energy density should be positive [4][5][6][7][8][9][10][11][12][13][14][15][18][19][20].…”

State‐space models and stored electromagnetic energy for antennas in dispersive and heterogeneous media

“…Dispersion is often neglected for antenna modeling in the microwave range by considering antennas in free space or embedded in nondispersive dielectrics; however, it is usually necessary for modeling of phenomena in the mm, THz, and optical range. Electromagnetic energy density in dispersive media builds on the classical results in Landau and Lifshitz [1960] with extensions to applications such as antennas, metamaterials, and photonics [Ruppin, 2002;Tretyakov, 2005;Vorobyev, 2012;Yaghjian et al, 2013].…”

Electromagnetic energy storage and power dissipation in nanostructures

“…The electromagnetic energy storage and power dissipation in nanostructures rely both on the materials properties and on the structure geometry. The effect of materials optical property on energy storage and power dissipation density has been studied by many researchers, including early works by Loudon [5], Barash and Ginzburg [6], Brillouin [7], and Landau [8], and more recent works by Ruppin [9], Shin et al [10], and Vorobyev [11,12] to name a few.…”