The Maxwell operator with periodic coefficients in a cylinder

TL;DR

This paper proves that the spectrum of the Maxwell operator with periodic coefficients in a cylindrical domain is absolutely continuous for certain cross-sections, advancing understanding of electromagnetic wave behavior in structured media.

Contribution

It establishes the absolute continuity of the Maxwell operator's spectrum in cylinders with specific cross-sections, extending spectral theory in periodic electromagnetic structures.

Findings

Spectrum is absolutely continuous for circular cross-section

Spectrum is absolutely continuous for rectangular cross-section

Results apply to three-dimensional cylindrical domains

Abstract

In the paper we consider the Maxwell operator in a three-dimensional cylinder with coefficients periodic along the axis of a cylinder. It is proved that for cylinders with circular and rectangular cross-section the spectrum of the Maxwell operator is absolutely continuous.