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

TL;DR

This paper rigorously formulates the calculation of electromagnetic vacuum energy for an infinite dielectric cylinder, including surface and photonic modes, and justifies the use of imaginary-frequency representation in Casimir effect computations.

Contribution

It provides a rigorous mathematical framework for summing over electromagnetic modes in a dielectric cylinder, validating the imaginary-frequency approach used in Casimir energy calculations.

Findings

Surface and photonic modes are essential in the electromagnetic spectrum of the cylinder.

The imaginary-frequency representation for vacuum energy is mathematically justified.

The proposed method improves the accuracy of Casimir energy computations for cylindrical geometries.

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.