Electromagnetic Media with no Dispersion Equation

It has been known through some examples that parameters of an electromagnetic medium can be so defined that there is no dispersion equation (Fresnel equation) to restrict the choice of the wave vector of a plane wave in such a medium, i.e., that the dispersion equation is satisfied identically for any wave vector. In the present paper, a more systematic study to define classes of media with no dispersion equation is attempted. The analysis makes use of coordinate-free four-dimensional formalism in terms of multivectors, multiforms and dyadics.