Alternative Expression for the Phase Velocity of Electromagnetic Homogeneous Plane Waves

We have established a different method to analyze various electromagnetic media. An analytical investigation has been carried out into the relation between the phase velocity, momentum density vector (MDV), and Poynting vector of plane waves in linear, homogeneous, and time-invariant media. Based on it, we have derived a novel dispersion relation for homogeneous plane waves and found an interesting expression for the phase velocity in terms of the fields' intensities and densities. We have been also able to determine the relative orientation of the wave vector with respect to the direction of the Poynting vector. In addition, the group velocity has been expressed in terms of the Poynting vector and MDV. We have applied all the results to several media and obtained valuable outcomes. It is shown that the orthogonality of phase velocity is not feasible for homogeneous plane waves.