A Global Uniqueness on Spherically Stratified Dielectric Medium in Time-Harmonic Maxwell Equation with Interior Transmission Eigenvalues

TL;DR

This paper investigates the uniqueness of determining the refractive index in a spherically stratified dielectric medium using interior transmission eigenvalues derived from the time-harmonic Maxwell equations, employing entire function theory.

Contribution

It introduces a novel approach linking interior transmission eigenvalues to entire function theory for uniqueness in inverse electromagnetic problems.

Findings

Density function generated by transmission eigenvalues determines the indicator function.

Reduction of the inverse problem to an entire function uniqueness problem.

Main parameter is the integral of the square root of the refraction index.

Abstract

A set of regularly distributed transmission eigenvalues generates a density function. We use such a density function inversely determines the form of the indicator function. Using the entire function theory, we reduce an uniqueness problem with interior transmission eigenvalues induced by time-harmonic Maxwell equation to an uniqueness problem in entire function theory. In such an inverse problem, the definite integral of the square root of refraction index is the main parameter.