Zeros of the Bessel function and the role of continuous spectrum in the problem of electromagnetic diffraction by a finitely conducting sphere

Abstract

This paper is a short review in the area of asymptotic theory of the Bessel function and its application to the diffraction of electromagnetic waves by a sphere of finite conductivity. Location of zeros of the Bessel function in the complex plane of index is addressed on the basis of Debye's asymptotic approximations. It is shown that for complex values of the argument, there exist two branches of zeros. The branch of zeros located in the upper half plane of the complex plane plays a key role in the analysis of the electromagnetic field diffracted by a dielectric sphere. The paper presents simple qualitative estimations of contributions coming from discrete and continuous parts of the spectrum.