Energy density and velocity of electromagnetic waves in lossy chiral medium

Abstract

The average energy density of the macroscopic quasimonochromatic electromagnetic field U ts (t, r) in a linear passive chiral lossy medium described by the constitutive E-H relations is determined using a microscopic model. According to the model, U ts (t, r) is equal to the sum of the average energy densities of the electromagnetic field in free space U t0 (t, r) and electromagnetic oscillations in structural elements U s (t, r) induced by the electromagnetic wave. Making use of the Poynting theorem, the energy density U ts (t, r) U t0 (t, r) and power density of losses are derived as functions of the Poynting vector, polarization of the electromagnetic waves, phase shift between the field vectors and refractive index of a chiral medium. The exact energy velocity of the quasimonochromatic electromagnetic waves satisfying relativistic causality is determined using U ts (t, r). The approximate energy velocities of the quasimonochromatic electromagnetic wave are determined using energy density components approximating U ts (t, r) (e.g., the sum of the positive energy densities of the macroscopic electric and magnetic fields as well as the energy density of magnetoelectric cross-coupling). Comparison of the exact and approximate energy velocities with the group velocity in the case of a chiral lossy medium with a single-resonant frequency clarifies the concept of the electromagnetic energy and demonstrates the fundamental significance of the exact energy velocity.

Minimum Q for Lossy and Lossless Electrically Small Dipole Antennas

“…The quality-factor energy densities defined here are not circuit-model dependent [25,26] but depend only on the macroscopic constitutive parameters and fields of the antenna media (and thus are useful for antenna design). The Q-energy differs considerably from both the equivalent-circuit energy of Tretyakov [25,26] and the energy obtained by Vorobyev [27] in determining electromagnetic wave velocities in lossy dispersive material, but only slightly from the magnetic electrodynamic energy of Boardman and Marinov [28] in the frequency range where their magnetic energy is positive.…”

“…Since the surface S a contains the equivalent electric and magnetic currents that reduce the fields to zero inside V a , one can divide E e into separate contributions, E e1 and E e2 , respectively, from electric and magnetic surface currents on S a ; that is, E e (r) = E e1 (r) + E e2 (r) (27) such that E e (r) ≈ 0 for r ∈ V a with the approximation becoming more accurate as ka gets smaller. In the far field, both E e1 and E e2 represent electric dipoles with dipole moments that can be designated as…”

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

“…Energy density in lossy chiral media has been studied in recent papers [8][9][10]. These papers determine the energy density for the case of linear polarization and complement our studies, which focus on the effects of polarization selectivity of interaction with circularly polarized radiation in composites with helices of different shapes.…”

“…In comparison with the solutions obtained here, solutions from Ref. [10] cannot be used to study the pitch angle dependence and optimization of the electromagnetic properties of chiral media.…”

“…These papers determine the energy density for the case of linear polarization and complement our studies, which focus on the effects of polarization selectivity of interaction with circularly polarized radiation in composites with helices of different shapes. Using microscopic and macroscopic models, paper [10] provides solutions for the average total energy density of the macroscopic quasimonochromatic electromagnetic field in regions of normal dispersion with negligible losses of a magnetoelectric medium and for the average energy density of the macroscopic quasimonochromatic electromagnetic field in a chiral medium with losses as a function of the refractive index and characteristic impedance of the medium. In comparison with the solutions obtained here, solutions from Ref.…”