We provide a general and rigorous formulation of antenna localized electromagnetic radiation energy in generic antenna systems based on Poynting flow instead of the spectral approach proposed earlier. The main theory is first developed using the principles of energy-momentum conservation and the center-of-energy theorem, culminating in the derivation of a direct localized energy expression. It is rigorously established that this expression satisfies the main features expected of physical energy, mainly positive definiteness and regularity. The obtained formula involves only the radiated fields (no current or charge) source and is easier to compute using specialized direct time-domain EM solvers. The proposed approach is expected to play a role in understanding energy localization in coupled antennas and shed light on gain enhancement methods.
LOCALIZED ENERGY: MOTIVATIONS AND GENERAL CONSIDERATIONSThe subject of localized energy has emerged in recent years as one of the potential critical domains projected to play increasingly important roles in various applications. For example, we mention 5G and mmWave technologies, which are accompanied by interactions and energy exchange at multiple physical scales, often in dense and complex electromagnetic environments; indeed, systems like Ultra-Dense Networks (UDN) and massive MIMO involve interactions in the near-zone and hence increased localization [1,2]. Also, it is now established that near-field nano-optics, subwavelength imaging, plasmonics, and optical antennas all involve highly nontrivial processes of local energy enhancement [3,4]. Electromagnetic energy localization has also been studied in depth within the context of condensed matter physics [5] and is a familiar subject in periodic structures like photonic crystals. Energy localization is now seen as a fundamental factor in electromagnetic therapy in general [6] and microwave hyperthermia in particular [7]. However, while looking into the electromagnetic energy in the near-field of antennas, the applied electromagnetics community mostly focuses the attention towards the "reactive energy" for antennas [8][9][10][11][12][13][14][15]. It should be noted here that near-field focusing is another classical antenna application where energy localization is essential [16][17][18], and the same is true for the closely related subject of wireless power transfer [19]. Also in traditional RF and microwave antenna engineering, localized energy has been singled out as one of the main principles behind ultrawide band (UWB) performance [20,21]. Therefore, it has become essential to look into the near-fields of the antennas more comprehensively and focus on aspects like localized energy, moving beyond the standard notions of reactive-energy and antenna-Q factors [22][23][24][25][26][27].The subject of localized energy was recently treated from a more general perspective, that of the Weyl (plane-wave) expansion [28,29], which was used to propose a spacetime spectral theory of localized energy in [30,31]. Localized energy in th...