Edward F. Kuester

An Overview of the Theory and Applications of Metasurfaces: The Two-Dimensional Equivalents of Metamaterials

Metamaterials are typically engineered by arranging a set of small scatterers or apertures in a regular array throughout a region of space, thus obtaining some desirable bulk electromagnetic behavior. The desired property is often one that is not normally found naturally (negative refractive index, near-zero index, etc.). Over the past ten years, metamaterials have moved from being simply a theoretical concept to a field with developed and marketed applications. Three-dimensional metamaterials can be extended by arranging electrically small scatterers or holes into a two-dimensional pattern at a surface or interface. This surface version of a metamaterial has been given the name metasurface (the term metafilm has also been employed for certain structures). For many applications, metasurfaces can be used in place of metamaterials. Metasurfaces have the advantage of taking up less physical space than do full three-dimensional metamaterial structures; consequently, metasurfaces offer the possibility of less-lossy structures. In this overview paper, we discuss the theoretical basis by which metasurfaces should be characterized, and discuss their various applications. We will see how metasurfaces are distinguished from conventional frequency-selective surfaces. Metasurfaces have a wide range of potential applications in electromagnetics (ranging from low microwave to optical frequencies), including: (1) controllable “smart” surfaces, (2) miniaturized cavity resonators, (3) novel wave-guiding structures, (4) angular-independent surfaces, (5) absorbers, (6) biomedical devices, (7) terahertz switches, and (8) fluid-tunable frequency-agile materials, to name only a few. In this review, we will see that the development in recent years of such materials and/or surfaces is bringing us closer to realizing the exciting speculations made over one hundred years ago by the work of Lamb, Schuster, and Pocklington, and later by Mandelshtam and Veselago.

A low-frequency model for wedge or pyramid absorber arrays-I: theory

The interaction of electromagnetic waves with an array of absorbing wedges or pyramid cones is studied in the low-frequency limit; i.e., when the period of the array is small compared with wavelength. A theoretical model is obtained using the method of homogenization, which replaces the transversely periodic structure with a transversely uniform medium possessing a certain (generally anisotropic) effective permittivity and permeability. Plane-wave reflection from such structures can then be modeled using well-known techniques for one-dimensionally inhomogeneous media; a Riccati equation for the reflection coefficient is used in this work. This model is appropriate for use with absorbers found in anechoic chambers used for electromagnetic compatibility and electromagnetic interference (EMC/EMI) measurements over the frequency range of 30-1000 MHz. >

A quasi-closed form expression for the conductor loss of CPW lines, with an investigation of edge shape effects

In previous work, we used a matched asymptotic technique to investigate the fields near an edge of a finitely conducting strip with nonzero thickness. It was demonstrated that with this asymptotic solution of the fields, the power loss in the region local to the edge could be determined accurately. In this paper, we will show how the accurate representation of the power loss can be used to obtain a closed form expression for the attenuation constant due to conductor loss of coplanar waveguide (CPW) structures. This expression is valid for an arbitrarily shaped edge and any conductor thickness. Results obtained with this expression are compared to and closely agree with both experimental results and other techniques found in the literature. We also investigated conductors with different edge shapes (45/spl deg/ and 90/spl deg/ edges) to explore their effect on the attenuation constant (or loss) of CPW structures.

A low-frequency model for wedge or pyramid absorber arrays-II: computed and measured results

Based on the theoretical model developed in Part I of this two-part paper, we present numerical results for the plane-wave reflection coefficient from arrays of pyramid-cone absorbers when the period of the array is smaller than half a wavelength. Comparison is made with results of a moment-method calculation, as well as with experimental measurements. The model is then used to modify the design of some existing types of commercially available absorbers for reduced reflection in the frequency range of 30-300 MHz. These improved absorbers have been installed in an anechoic chamber used for electromagnetic compatibility and electromagnetic interference (EMC/EMI) measurements. Site attenuation measurements from this chamber are presented which show closer correspondence to an ideal open-field test site. >

Power loss associated with conducting and superconducting rough interfaces

In recent work, a generalized impedance boundary condition for two-dimensional conducting rough interfaces was derived. In this study, the impedance boundary condition is used to calculate the power loss associated with conducting rough interfaces. Results for two-dimensional conducting and superconducting roughness profiles are shown in this paper, and comparisons to other results in the literature are given. The importance of these roughness effects in microwave and millimeter-wave integrated circuits is also discussed. Suggestions are made to extend this study to three dimensional random rough interfaces.

The thin-substrate approximation for reflection from the end of a slab-loaded parallel-plate waveguide with application to microstrip patch antennas

Integrals arising in the Wiener-Hopf solution for wide microstrip antennas are approximated in closed form for the case of an electrically thin substrate. The resulting expressions are used to obtain simple, closed-form expressions for resonant frequency and unloaded radiation Q for rectangular microstrip patch antennas which are valid when commonly used quasi-static formulas no longer hold. Numerical comparisons show significant shifts in resonant frequencies as compared with existing theories.

Numerical computation of the incomplete Lipschitz-Hankel integral Je o ( a, z )

Abstract Two factorial-Neumann series expansions are derived for the incomplete Lipschitz-Hankel integral Je 0 ( a , z ). These expansions are used together with the Neumann series expansion, given by Agrest, in an algorithm which efficiently computes Je 0 ( a , z ) to a user defined number of significant digits. Other expansions for Je 0 ( a , z ), which are found in the literature, are also discussed, but these expansions are found to offer no significant computational advantages when compared with the expansions used in the algorithm.

Comparison of approximations for effective parameters of artificial dielectrics

Formulas available in the literature for approximating the effective permittivity and permeability of a periodic array of (possibly lossy) dielectric rods of arbitrary cross section are assessed for their accuracy by comparing them with precise numerical values for special forms of the arrays. The literature on effective properties of arrays of dielectric rods is reviewed, covering what is known about general bounds, as well as the numerical results that are available for two specific arrays of square rods. It is found that while no single formula is capable of very high precision in every case, it is possible to construct good approximate formulas in individual cases as a result of this comparison. >

Surface-wave radiation loss from curved dielectric slabs and fibers

A newly developed systematic procedure to calculate the real and imaginary parts of the change in propagation constant of a surface-wave mode on a curved open waveguide of general cross section is used here to determine these quantifies for the TE modes of an asymmetric slab waveguide and for all the modes of an optical fiber. Comparison of these results with the existing literature points up the care which must be taken in making approximations in this problem, since errors of significant factors in the radiation loss have been made in previous work.

Characterizing Metasurfaces/Metafilms: The Connection Between Surface Susceptibilities and Effective Material Properties

A metafilm is a type of metasurface, a two-dimensional equivalent of a metamaterial, and is essentially a surface distribution of electrically small scatterers arranged in a judiciously chosen pattern. In previous work, we have shown that the most appropriate way to characterize a metafilm is by its effective electric and magnetic surface susceptibilities, and we discussed methods for retrieving these surface susceptibilities. Nevertheless, some researchers have continued to characterize metasurfaces in terms of bulk effective material properties. In this letter, we first clarify sign conventions (and nomenclature) used for surface susceptibilities and correct sign errors in previous publications. We then discuss the connection between the surface susceptibilities of a metafilm and effective material properties of a thin material slab. The two subtle but important aspects discussed here are: 1) the interpretation of a thin material slab by its surface susceptibilities, and 2) the equating of a metafilm (which has its own unique surface susceptibilities) to a thin material slab with effective material properties.