Exact closed-form expression of a Sommerfeld integral for the impedance plane problem

Title
Exact closed-form expression of a Sommerfeld integral for the impedance plane problem
Authors
Koh, I.S.
Keywords
Dyadic Green's function, impedance half plane, Lipschitz-Hankel integral, Sommerfeld integral
Issue Date
2006-09
Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Abstract
A Sommerfeld integral for an impedance half-plane is one of the classical problems in electromagnetic theory. In this paper, the integral is evaluated into two series representations, which are expressed in terms of the exponential integral and the Lommel function, respectively. It is shown that the series expansions absolutely converge for any parameters, such as distance or surface impedance. Then based on the Lommel function expansion, an exact closed-form expression of the integral is formulated. This expression is written in terms of incomplete Weber integrals, which are directly related to incomplete cylindrical functions such as incomplete Lipschitz-Hankel integrals. Additionally, a complete asymptotic series of the integral is obtained based on the exponential integral expansion. With conventional methods such as steepest descent method, it is cumbersome to derive the divergent series. The validity of all the formulations derived in this paper is demonstrated through a comparison with a numerical integration of the integral for various situations.
URI
http://dspace.inha.ac.kr/handle/10505/1574
ISSN
0018-926X
Appears in Collections:
College of Engineering(공과대학) > Electronic Engineering (전자공학) > Journal Papers, Reports(전자공학 논문, 보고서)
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