FDTD Computation of Space/Time Integrated Electromagnetic Lagrangian: New Insights Into Design of Mutually Coupled Antennas

In this paper, we develop a formalism based on electromagnetic Lagrangian which provides new insights about the near-field reactive energy density around generic antennas for arbitrary spatio-temporal excitation signals. Using electric and magnetic fields calculated via FDTD technique and interpolation routines,we compute the EM Lagrangian density around antennas (thin-wire dipoles, Yagi-Uda Arrays and planar UWB Monopoles). Spatial maps of time-integrated EM Lagrangian density sheds light onto the capacitive/inductive nature of reactive energy density distribution around antennas and highlight its inherent connection with inter-element mutual coupling. Furthermore, we demonstrate that by minimizing the temporal fluctuations of spatially integrated EM Lagrangian density, it is possible to design MIMO antennas with wide impedance bandwidth and low mutual coupling.