Equivalence of permittivity/permeability conditions and source conditions for the existence of TE or TM waves in nonhomogeneous, sourced media

It is argued that the conditions permitting TE (transverse electric) or TM (transverse magnetic) waves in nonhomogeneous media with sources could be reduced to conditions on the source only if the latter took into account the polarization charges and magnetization currents. The resulting formulation was confirmed as being mathematically equivalent. The advantages of the new formulation are compactness and generality (the new formulation applies to nonlinear and nonisotropic media). Its disadvantage is arcaneness; it may be difficult to assess the bound sources until after the problem is completely solved