Why Periodic Structures May Not Be Able to Synthesize Negative Indices of Refraction

In this paper we first list some of the features that are widely accepted as being facts regarding materials with simultaneously negative mu and epsiv, namely: (a) negative index of refraction; (b) advance of the phase of a signal as it moves away from the source; (c) an increase of the evanescent waves as they get further away from the source; and (d) while the E-and H-field in an ordinary material form a right handed triplet with the direction of phase propagation, they will in a material with negative mu and epsiv form a left handed triplet. Such materials have never been found in nature. However, numerous researchers have suggested ways to produce them artificially. Periodic structures of elements varying from simple straight wires to very elaborate concoctions have been claimed to produce negative index of refraction. Nevertheless, we shall here show that according to a well known theory based on expansion into inhomogeneous plane waves, it does not seem possible to obtain the features that are characteristic for materials with negative mu and epsiv as listed above. Thus, it seems logical to re-examine Veselago's original paper. We find that it is mathematically correct. However, when used in certain practical applications like, for example, the well known flat lens, it may lead to negative time. While such a solution might be mathematically acceptable, it will violate the causality principle from a physical point of view. So it should not surprise us that we so far have encountered difficulties when trying to create materials with negative mu and epsiv, in particular negative index of refraction.