Discrete Huygens’ source representations: Applications to loaded-wire gratings

Abstract

This paper presents a novel approach to discrete Huygens’ source representations and their application to loaded-wire grating problems in various environments. We begin by introducing a method using an array of line sources in free space to reproduce fields from primary sources with finite cross-sections to an arbitrarily high degree of accuracy. This technique employs exact plane-wave representations and far-field functions to determine the current strengths of equally spaced line sources. The use of far-field functions avoids the singularities of the plane-wave spectra when equating the fields of two sources. Numerical examples demonstrate the accuracy of this approach and highlight the significant contribution of evanescent waves. We then extend this concept to solve loaded-wire grating problems in free space, utilizing two Huygens’ source representations to determine the required wire impedances for achieving desired field transformations. The theory is validated through numerical simulations, showcasing the conversion of real point-source fields into complex point-source fields using strategically designed gratings. Furthermore, we adapt the discrete Huygens’ source representation for scenarios involving dielectric slabs backed by conducting ground planes, and solve the corresponding loaded-wire grating problems.