Diffraction by a truncated planar array of dipoles:A Wiener–Hopf approach

Miguel Camacho,Alastair P Hibbins,Filippo Capolino,Matteo Albani

doi:10.1016/j.wavemoti.2019.03.004

Miguel Camacho, Alastair P Hibbins + Show 2 more

Open Access

https://doi.org/10.1016/j.wavemoti.2019.03.004

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Abstract

We present a rigorous solution to the problem of scattering of a semi-infinite planar array of dipoles, i.e., infinite in one direction and semi-infinite in the other direction, thus presenting an edge truncation, when illuminated by a plane wave. Such an arrangement represents the canonical problem to investigate the diffraction occurring at the edge-truncation of a planar array. By applying the Wiener–Hopf technique to the Z-transformed system of equations derived from the electric field integral equation, we provide rigorous close form expressions for the dipoles’ currents. We find that such currents are represented as the superposition of the infinite array solution plus a perturbation, which comprises both edge diffraction and bound surface waves excited by the edge truncation. Furthermore, we provide an analytical approximation for the double-infinite sum involved in the calculation which drastically reduces the computational effort of this approach and also provides physically-meaningful asymptotics for the diffracted currents.

Highlights

The study of the scattering of electromagnetic waves has remained a topic of interest for both physics and engineering communities since the past century
In this paper we provide a rigorous solution to the problem of the scattering of a plane wave that impinges obliquely on a semi-infinite array of dipolar metallic patches using the Wiener–Hopf technique [33,34]
We have presented a rigorous analysis of the scattering by a semi-infinite array of dipoles using the Wiener–Hopf technique in the Z-transformed domain due to the discrete nature of the planar current distribution

Summary

Introduction

The study of the scattering of electromagnetic waves has remained a topic of interest for both physics and engineering communities since the past century. Throughout the development of frequency selective surfaces in the past decade and the subsequent emergence of metasurfaces [4,5], physical optics has allowed for the solution of these periodic problems using the so-called local periodicity approximation to reduce the analysis to a single unit cell with periodic boundary conditions [6,7] This approximation, valid in some cases, cannot completely reproduce the behavior of real systems that are finite. Due to the discrete nature of the problem the Wiener–Hopf method is implemented in the Z-transformed spectral domain for an infinite linear system of equations derived from the electric field integral equation This technique was previously utilized by some of the authors for the solution of the scattering of a semi-infinite array of metallic strips illuminated by a plane wave [35]. We need to mention that though the Wiener–Hopf technique applied to the rigorous solution in the Z-transformed domain for discrete current distributions in periodic arrayed structured is rather unusual, there have been important previous contributions [35,36,37,38,39,40,41,42,43]

Integral equation formulation

Wiener–Hopf approach

Approximate factorization

Asymptotic evaluation of the diffracted currents

Illustrative examples

Conclusions