Solvability of problems of excitation of plane-layered metamaterial media

It is shown that the problem of excitation of a magnetodielectric layer with parameters ? and μ equal to minus unity by a point source is not always solvable. Conditions under which the problem has a solution are established. It is found that, in the vicinity of the singular point ? = μ = ?1, determination of the field is an illposed problem: Small variations in these parameters result in large changes of the field.