Energy spectrum of electromagnetic normal modes in dissipative media: modes between two metal half spaces

TL;DR

This paper clarifies the nature of electromagnetic normal modes in dissipative media, showing they form a continuum with real frequencies, which impacts the calculation of van der Waals and Casimir interactions.

Contribution

It resolves the contradiction between complex-valued mode energies and real physical spectra by demonstrating the true spectrum is a continuum with real frequencies.

Findings

Normal modes in dissipative media form a continuum with real frequencies.

Contour integration yields a real-valued spectrum, resolving previous contradictions.

Implications for accurate van der Waals and Casimir force calculations.

Abstract

The energy spectrum of the electromagnetic normal modes plays a central role in the theory of the van der Waals and Casimir interaction. In dissipative media it appears as if there are distinct normal modes with complex valued energies. The summation of the zero-point energies of these modes render a complex valued result. Using the contour integration, resulting from the use of the generalized argument principle, gives a real valued and different result. We resolve this contradiction and show that the spectrum of true normal modes form a continuum with real frequencies. We illustrate the problem in connection with the van der Waals interaction between two metal half spaces.