Distribution of Reactive Energy Density around Antennas in Time-Harmonic Regime: An Electromagnetic Lagrangian Approach

In this paper, we present an electromagnetic (EM) Lagrangian approach to quantify the reactive energy density distribution around generic antenna systems operating in the time-harmonic regime. First, we introduce the `period-averaged EM Lagrangian density' for radiating EM fields and present its intrinsic relations with the complex Poynting vector, total EM energy density, complex Helicity density, antenna reactive energy and radiation Q-factor. Furthermore, utilising full-wave MoM (method-of-moments) based MATLAB Antenna Toolbox, we compute contour plots of period-averaged EM Lagrangian density around thin-strip dipoles as well as printed microstrip patch antennas. It is demonstrated that such contour plots can not only distinguish between the capacitive and inductive nature of reactive energy density around multiple antenna systems, but also assist in the visualization of the links of inter-element mutual coupling via reactive fields. Such spatial maps of period-averaged EM Lagrangian density can be potentially useful for engineers working in the design of antenna arrays, MIMO (multiple-input multiple-output) and full-duplex systems, as well as EMI/EMC (Electromagnetic Interference/Compatibility) compliant devices.