We consider media with complex polarizability properties. For linear r
eciprocal media with arbitrary dyadic permittivity and permeability fo
r the field components in a certain plane, analytical solution for pla
ne eigenwaves is constructed. Such media can be modeled or practically
realized as knotted media, i.e., as composite structures with inclusi
ons in form of simple knots. Basic properties of knotted media are dis
cussed, a simple model for the frequency dispersion of the material pa
rameters is suggested.