Analyticity of the Dirichlet-to-Neumann map for the time-harmonic Maxwell's equations

TL;DR

This paper investigates the analyticity properties of the electromagnetic Dirichlet-to-Neumann map in time-harmonic Maxwell's equations for complex media, linking it to Herglotz functions in composite materials.

Contribution

It establishes the analyticity of the Dirichlet-to-Neumann map for Maxwell's equations in multicomponent media and explores its relation to Herglotz functions in composites.

Findings

Proves analyticity of the Dirichlet-to-Neumann map in electromagnetic media.

Connects the map to Herglotz functions for isotropic and anisotropic composites.

Provides theoretical foundation for inverse problems in electromagnetism.

Abstract

In this chapter of the book entitled, "Extending the Theory of Composites to Other Areas of Science" [edited by Graeme W. Milton, 2016] we derive the analyticity properties of the electromagnetic Dirichlet-to-Neumann map for the time-harmonic Maxwell's equations for passive linear multicomponent media. Moreover, we discuss the connection of this map to Herglotz functions for isotropic and anisotropic multicomponent composites.