This paper introduces simple analytical formulas for the grid impedance of electrically dense arrays of square patches and for the surface impedance of high-impedance surfaces based on the dense arrays of metal strips or square patches over ground planes. Emphasis is on the oblique-incidence excitation. The approach is based on the known analytical models for strip grids combined with the approximate Babinet principle for planar grids located at a dielectric interface. Analytical expressions for the surface impedance and reflection coefficient resulting from our analysis are thoroughly verified by full-wave simulations and compared with available data in open literature for particular cases. The results can be used in the design of various antennas and microwave or millimeter wave devices which use artificial impedance surfaces and artificial magnetic conductors (reflect-array antennas, tunable phase shifters, etc.), as well as for the derivation of accurate higher-order impedance boundary conditions for artificial (high-) impedance surfaces. As an example, the propagation properties of surface waves along the high-impedance surfaces are studied. I. INTRODUCTIONIn this paper we consider planar periodic arrays of infinitely long metal strips and periodic arrays of square patches, as well as artificial high-impedance surfaces based on such grids. [17]. Capacitive strips and square patches have been studied extensively in the literature (e.g., [18]-[20]). However, to the best of the authors' knowledge, there is no known easily applicable analytical model capable of predicting the plane-wave response of these artificial surfaces for large angles of incidence with good accuracy.Models of planar arrays of metal elements excited by plane waves can be roughly split into two categories: computational and analytical methods. Computational methods as a rule are based on the Floquet expansion of the scattered field (see, e.g., [2], [3], [21], [22]). These methods are electromagnetically strict and general (i.e., not restricted to a particular design geometry). Periodicity of the total field in tangential directions allows one to consider the incidence of a plane wave on a planar grid or on a high-impedance surface as a single unit cell problem. The field in the unit cell of the structure can be solved using,

The authors propose to use microelectromechanical systems (MEMS) to produce novel phase shifters based on an electronically reconfigurable high-impedance surface (HIS). Typically, HIS is a textured metal surface with reactive impedance varying from an initial value to a very high value. Such phase shifters can be developed with introducing a surface with variable impedance in, e.g., a rectangular metal or dielectric rod waveguide. Placed along narrow walls of the rectangular metal waveguide or adjacent to the dielectric waveguide, the HIS affects the propagation constant, which results in changing the phase of the propagating wave. The authors manufactured a prototype of the microelectromechanical systems-based HIS consisting of a dielectric layer placed on a ground plane, and two arrays of metal patches. The gap between the upper and lower arrays of patches was fixed and filled with SiO 2 . The measured phase of the wave reflected from the prototype HIS varies in the range of 50°, and its insertion loss is below 0.5 dB (out of resonance).

Materials with tunable dielectric properties are valuable for a wide range of electronic devices, but are often lossy at terahertz frequencies. Here we experimentally report the tuning of the dielectric properties of single-walled carbon nanotubes under light illumination. The effect is demonstrated by measurements of impedance variations at low frequency as well as complex dielectric constant variations in the wide frequency range of 0.1-1 THz by time domain spectroscopy. We show that the dielectric constant is significantly modified for varying light intensities. The effect is also practically applied to phase shifters based on dielectric rod waveguides, loaded with carbon nanotube layers. The carbon nanotubes are used as tunable impedance surface controlled by light illumination, in the frequency range of 75-500 GHz. These results suggest that the effect of dielectric constant tuning with light, accompanied by low transmission losses of the carbon nanotube layer in such an ultra-wide band, may open up new directions for the design and fabrication of novel Terahertz and optoelectronic devices.

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