On a Steklov spectrum in Electromagnetics

TL;DR

This paper explores Steklov eigenproblems related to Maxwell's equations, providing theoretical insights and explicit eigenvalue computations in a 3D ball, advancing understanding in electromagnetic spectral analysis.

Contribution

It introduces rigorous results for Steklov boundary problems for curlcurl operators and explicitly computes eigenvalues and eigenfunctions in a 3D unit ball.

Findings

Rigorous results for Steklov problems in Maxwell's equations

Explicit eigenvalue and eigenfunction calculations in a unit ball

Enhanced understanding of electromagnetic spectral properties

Abstract

After presenting various concepts and results concerning the classical Steklov eigenproblem, we focus on analogous problems for time-harmonic Maxwell's equations in a cavity. In this direction, we discuss recent rigorous results concerning natural Steklov boundary value problems for the curlcurl operator. Moreover, we explicitly compute eigenvalues and eigenfunctions in the unit ball of the three-dimensional Euclidean space by using classical vector spherical harmonics.