Solving the current element problem over lossy half-space without Sommerfeld integrals

Abstract

An approach is presented for efficient computation of the vector potentials arising in the problem of a current element radiating over a lossy half-space. The present approach departs from the conventional ones in that it works primarily with the transform domain representations rather than with the Sommerfeld integrals which are the corresponding spatial domain counterparts. The key step in the present method is to approximate the transforms using a suitable approximation which is valid for a wide range of parameters of practical interest. The approximated transforms can be inverted in a closed form for the horizontal component of the vector potentials ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\Pi_{z}</tex> ) and can be expressed in a computationally efficient form for the vertical component ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\Pi_{z}</tex> ). Numerical results illustrating the accuracy of the method are presented and some estimates of comparative computational times are also included.