Singular modes of the electromagnetic field

Abstract

We show that the mode corresponding to a point of the essential spectrum of the electromagnetic scattering operator is a vector-valued distribution representing the square root fo the three-dimensional Dirac's delta function. An explicit expression for this singular mode in terms of the Weyl sequence is provided and analysed. The essential resonance occurs if the permittivity of an object gets close to zero, which is often the case in plasmas and negative-permittivity metamaterials. Such resonance would lead to a perfect localization (confinement) of the electromagnetic field. Simultaneously, however, a portion of electromagnetic energy is removed from the Hilbert spcae and therefore the whole process may be viewed as absorption.