Accelerating field decay along nonlocal metasurfaces by suppressing the Norton wave

Abstract

Studying the nature of electromagnetic fields of dipole sources over a homogeneous flat ground or impedance surfaces has a long history. In general, at a long distance $r$ from the source, the near-surface field is mostly contributed by the geometrical optics term (describing the radiation pattern), a guided wave, and the higher-order reactive contribution referred to as the Norton wave. In the special case of a perfect magnetic conductor interface, the first two terms vanish, so the residual Norton wave determines the steepest achievable field decay profile of $~r^{-3/2}$ (for a two-dimensional horizontal magnetic dipole). In this letter, we reveal that in the presence of a nonlocal metasurface described by the second-order impedance boundary condition, the field decay can be further accelerated by suppressing the Norton wave (approaching the profiles $r^{-5/2}$ and $r^{-7/2}$ for electric and magnetic fields, respectively). In a proposed practical realization of a nonlocal metasurface, the effect is numerically verified and shown to reduce the edge diffraction effects by 10 dB for the shield diameter of only one wavelength, paving the way toward compact antenna systems.

Figures (3)

• Figure 1: Fields excited by a HMD placed at height $h\ll\lambda$ above a (a) PEC; (b) PMC and (c) nonlocal impedance boundary with an impedance pole at a grazing angle. The geometry of the 2D problem considered is depicted in the inset of (c).
• Figure 2: Analytical study of fields excited by a 2D HMD on a nonlocal MS with a surface impedance of (\ref{['eq:aprox']}) with $B=1$ (Norton wave suppressed) depending on $A$ and $X/\eta$: (a) normalized excitation coefficient level $|F_{2,E_x}|\eta/C$ of the term decaying as $E_x\sim\Omega^{-5/2}$; (b) normalized excitation coefficient level $|E_{x,0}^{\text{GW}}|\eta/C$ of a SW/LW; (c) exponential decay factor $\Im(\tau_0)$ of the LW (SW propagation regions are uniformly yellow); normalized levels of the tangential electric (d) and magnetic (e) field (solid lines) calculated with (\ref{['eq:ift']}) vs. distance from the source $x/\lambda$ compared with their dominating asymptotic expansion terms from (\ref{['eq:total_ff']}); (f) radiation pattern shape. The case with the set of parameters $B=1$, $A=-3.5$, $X/\eta=3.5$, chosen for the practical implementation, is indicated with cross markers in (a--c) and with red lines in (d--f). The local high-impedance case is shown in (d--f) with blue curves. Markers in (d) show the results of full-wave numerical confirmation for the practical MS implementation.
• Figure 3: Comparison of practical implementations of the local and nonlocal MSs: (a) meta-atoms of the local corrugated HIS (left) and the proposed nonlocal MS (right); (b) numerically extracted (markers) and analytically calculated (solid lines) $Z_{\text{s}}(\gamma)$; (c) analytically estimated $\text{DU}(90^{\circ})$ for $X/\eta=3.5$, $B=1$, and different practically implementable negative values of $A$ (see suppmat); (d) full-wave numerically calculated $\text{DU}(\phi)$ for $D=\lambda$.