Surface modes and photonic modes in Casimir calculations for a compact cylinder

Abstract

A rigorous formulation of the problem of calculating the electromagnetic vacuum energy of an infinite dielectric cylinder is discussed. It is shown that the physically relevant spectrum of electromagnetic excitations includes the surface modes and photonic modes. The mathematical procedure of summing over this spectrum is proposed, and the transition to imaginary frequencies is accomplished. As a result, it is justified the imaginary-frequency representation for the vacuum energy which has been used in previous Casimir studies for this configuration.