Why a harmonic solution for lossless, perfectly homogeneous, left-handed material cannot exist

In a preceding paper [J. Opt. Soc. Am. A 21, 122 (2004)], we proposed proof of the nonexistence of harmonic solutions for a perfectly homogeneous left-handed material with both relative permittivity and relative permeability equal to -1 using the theorem of analytic continuation of an analytic function. The use of this theorem of analyticity has been questioned in a recent paper [Phys. Rev. E 73, 046608 (2006)], arguing the possible inadequacy of the conditions of application of the theorem. We avoid the use of the analyticity theorem and propose a direct and simple proof of the nonexistence of such solutions. Furthermore, this proof is extended to any left-handed material with negative permeability and permittivity. (c) 2008 Optical Society of America.