Cavities Involving Metamaterials With an Uncountable Set of Resonant Frequencies

In this letter, it is shown that cavity resonators involving lossless and nondispersive (in a frequency band) double negative metamaterials can behave in a completely different way with respect to the cavities involving only traditional nondispersive double positive media. More precisely, it is proven that resonators with only nondispersive media may have an uncountable set of resonant frequencies. As practical consequences, it is outlined that this fact can represent an unsurmountable difficulty for present-day numerical simulators of electromagnetic eigenproblems and a cause of troubles for numerical solvers of electromagnetic driven problems. The presented result should warn users of numerical simulators against the employment of simplified models of metamaterials.