Time domain power flow in hyperbolic metmaterial excited by a pulsed dipole

From a frequency domain point of view, the field emitted by a dipole in free space translates into two parts: the real power, that is propagating, and the reactive power. The latter is the average stored energy, in a sense that it is a stationary one. From a time domain point of view, a finite pulse results in a net propagating wave and also power flow that oscillates forward and backward or around the dipole (A Shlivinski and E. Heyman, IEEE Trans. on Antennas and Propat., 47, 280–286, 1999). Adopting a frequency domain formulation, the propagating spectrum in hyperbolic medium (HM) is indefinite, in contrast to an ordinary medium where the propagating spectrum is finite.