FDTD Computation of Space/Time Integrated Electromagnetic Lagrangian: New Insights on Mutually Coupled Wide-band Antenna Design

In this paper, we develop a formalism based on either spatially or temporally integrated electromagnetic (EM) Lagrangian, which provides new insights about the near-field reactive energy around generic antennas for arbitrary spatio-temporal excitation signals. Using electric and magnetic fields calculated via FDTD technique and interpolation routines, we compute and plot the normalized values of space/time integrated EM Lagrangian around antennas. While the time-integration of EM Lagrangian sheds light onto the spatial distribution of inductive/capacitive reactive energy, time-variation of spatially integrated EM Lagrangian can help in design of ultra-wideband (UWB) MIMO antennas with low mutual coupling. The EM Lagrangian approach can assist in design of energy harvesting and wireless power transfer systems, as well as for electromagnetic interference mitigation applications.