Method of Moments Simulation of Modulated Metasurface Antennas With a Set of Orthogonal Entire-Domain Basis Functions

A family of orthogonal and entire-domain basis functions (named Fourier-Bessel) is proposed for the analysis of circular modulated metasurface (MTS) antennas. In the structures at hand, the MTS is accounted for in the electric field integral equation (EFIE) as a sheet transition impedance boundary condition on the top of a grounded dielectric slab. The closed-form Hankel transform of the Fourier-Bessel basis functions (FBBFs) allows one to use a spectral domain formulation in the method-of-moments (MoM) solution of the EFIE. Moreover, these basis functions are fully orthogonal, which implies that they are able to represent the global evolution of the current distribution in a compact form. FBBFs also present a better filtering capability of their spectrum compared to other well-known orthogonal families such as the Zernike functions. The obtained MoM matrix is sparse and compact, and it is thus very well-conditioned and can be efficiently computed and inverted. The numerical results based on the proposed decomposition are presented and compared with those based on the use of the Gaussian ring basis functions and with the full-wave analysis of MTS antennas implemented with small printed elements. A very good agreement is observed.

I. Introduction

In recent years, a lot of interest has been attracted by artificial surfaces able to provide electromagnetic properties that one cannot find in nature [1], [2]. Such structures, commonly referred to as metasurfaces (MTSs), can be employed in a wide range of frequencies, from microwaves [3] to optics [4]. Although MTSs may also be used to tailor the transmission of space waves [4], [5], they have found a vast number of applications in the control of surface-wave (SW) wavefronts [6], [7] and the design of aperture antennas [8]–[14]. At microwave frequencies, MTSs may be implemented as dense textures of subwavelength elements (typically , with being the free-space wavelength) printed on a grounded dielectric slab [10]. The resulting number of printed patches is generally around 10⁴ for devices with a diameter. Indeed, MTS antennas [11] generally consist of circular apertures, where an SW launcher [15] is used to excite the structure. This paper will focus on circular apertures, bearing in mind that a proper stretching of the proposed basis functions may enable the treatment of elliptical ones [12], [16], [17].