Complex Poynting vector in gyromagnetic media and its impact on power flow in guided modes

In this paper, we show the relation between the time-varying spinning nature of the instantaneous Poynting vector and the phasor form of the complex Poynting vector in the bulk of the gyromagnetic medium. We show the presence of a transverse reactive power component in the bulk of the gyrotropic medium, even for plane wave propagation. We use a simple quantification technique of Poynting vector spin to analyze the rotation of the instantaneous Poynting vector using the complex phasor form of the time-averaged Poynting vector. For a transverse electric mode, we show the similarity between the Poynting vector spin and the photonic spin of the magnetic field. The Poynting vector spin is then used to represent the transverse power transfer across a ferrite-air interface supporting TE surface wave modes. Considering a gyromagnetic ferrite-filled rectangular waveguide following the TE mode profile, we show the correspondence between the Poynting vector spin and the overall positive and backward power flow. We analytically propose a mechanism to engineer the region of the waveguide supporting backward and forward power propagation.