The Essential Modes of the Electromagnetic Scattering Operator

Previously we have shown that apart from discrete spectrum (eigenvalues), the three-dimensional volume integral operator of electromagnetic scattering has a continuous essential spectrum as well. Here we derive the corresponding essential modes. We use the Weyl definition of essential spectrum, where such modes are described in terms of singular sequences. A closed form expression for the required sequence is obtained and its properties are analyzed. We also discuss the physical meaning and the conditions on the excitation of the essential resonance.