Antenna Mutual Coupling in Near-field: Insights using Reactive Helicity and EM Lagrangian Density

In this letter, we provide new insights into the mutual coupling between antennas, using spatial distribution of near-field reactive Helicity and period-averaged EM Lagrangian density. First, we analytically show that reactive Helicity (given by the real part of complex Helicity) in frequency domain always becomes zero in the far-field region of generic linearly and circularly polarized antennas. Furthermore, we introduce the concept of ‘instantaneous Helicity’ (analogous to instantaneous Poynting vector) to calculate reactive Helicity for antennas excited by arbitrary time-domain signals (eg. short-duration pulses). We analytically demonstrate the fundamental connection between this instantaneous Helicity, EM inertia density and EM Lagrangian density. Finally, using MoM-based MATLAB Antenna Toolbox, we compute the distribution (contour-plots) of normalized reactive Helicity and period-averaged Lagrangian density around a two-port system of thin-wire dipoles in frequency domain, revealing complex near-field inter-element interactions. Such visualization of mutual coupling via reactive Helicity and period-averaged EM Lagrangian density can enable antenna array designers to go beyond the traditional S-parameter approach, and identify regions containing near-zone non-TEM fields and non-propagating energy density, which may contribute constructively/destructively to the port-to-port mutual coupling.