Trapped-Mode Resonance Regime of Thin Microwave Electromagnetic Arrays with Two Concentric Rings in Unit Cell

We present a theoretical study of reflection and transmission characteristics of a microwave planar array on a thin dielectric substrate with unit cell made of two concentric rings. This array possesses high quality factor transmission resonance with polarization insensitivity for normally incident plane wave. This resonance is defined by the trapped-mode regime. We show that for oblique incidence, there are some differences in characteristics of the array and a small change in quality factor of the trapped-mode resonance. 1. Introduction Planar arrays consisting of a single resonant element (patch or aperture) in the unit cell, often called frequency selective surfaces (FSS) are traditionally used in the microwave and optical regions as filters, in the design of antennas and antenna radomes, and in the far-infrared region, as polarizers, beam splitters, and laser cavity mirrors [1]. An intrinsic feature of these FSSs is a resonance with relatively low quality ( ) factor. The low value of quality factor is explained by the fact that a thin open structure cannot have inner resonating volume and the resonating inclusions are strongly coupled with the free space. However, for some applications, a thin surface with high -factor resonance is desired. There exists a method to produce very thin structures possessing high -factor frequency resonances using the so-called trapped-mode resonance regime [2]. The trapped-mode can be excited in two element arrays when the resonance frequencies of the elements are approximately equal. This mode is characterized by a sharp resonance and strong current intensities which are of opposite directions in the two elements. Due to the almost complete cancelation of the dipole moments, the fields radiated by this current distribution are very weak and also the coupling of this mode with free space is weak. As a consequence, the radiation loss of the trapped-mode resonance is dramatically reduced resulting in a high -factor compared with the usual resonance of array with one element in unit cell. Some applications of these planar metamaterials are described in [3, 4]. In [3], the authors show that these arrays can be used in a spaser (surface plasmon amplification by stimulated emission of radiation) to produce a spatially and temporally coherent electromagnetic radiation source designated as laser spaser. In [4], an approach for sensing a small amount of chemical and biochemical material using an array constituted by asymmetrically double split ring elements is discussed. In [5], the authors presented a detailed study of the