Manipulating microwaves with ‘spoof’ surface plasmons

The newly discovered ability to confine, guide, and manipulate microwaves in open structures on scales that are much smaller than their wavelengths appears to be heralding a new era in microwave technology. Since the days of Marconi, metal surfaces have been known to support surface electromagnetic waves. In many ways, such waves are identical to simple grazing radiation because the electromagnetic fields in the air above the planar metal surface extend over distances of order many tens of wavelengths and are almost completely excluded from the metal. Since these waves are only weakly localized at the surface, they are readily perturbed by objects placed some distance away. They are consequently not particularly useful for forming surface-guided wave structures. However, if the distance over which the electromagnetic field extends above the metal is considerably reduced, so that the mode is much more strongly bound to the surface, ideally over distances of less than the wavelength of the incident radiation, then surface-wave manipulation of microwaves is more readily achieved.

Figure 1. Schematic representation of electric fields associated with a mode propagating along the surface of a metal. (a) At microwave frequencies, the metal is almost perfectly conducting and the field (E_z) extends far beyond the metal. (b) By perforating the substrate with an array of subwavelength holes, the field is localized near the interface.

By patterning a metal surface with grooves or holes with a characteristic dimension less than the wavelength of the incident radiation, one can alter the electromagnetic boundary conditions to strongly localize microwave radiation to that surface (see Figure 1). This highly localized wave is—using language borrowed from optical technology—a ‘spoof’ or ‘designer’ surface plasmon. In the visible regime, a surface plasmon is the trapped surface wave associated with density oscillations of the conduction electrons. (Observations of surface-plasmon excitation in the visible domain were first recorded, unknowingly, by Wood in 1902, who found that—for light impinging on a metal grating—a strong absorption of power occurred for a particular angle of incidence.) For the visible region, the degree of trapping of the mode at the metal surface and the usefulness of the surface plasmon depend strongly on the metal used. However, at microwave wavelengths, all metals may be treated as almost perfect conductors that completely screen out the electromagnetic field. Therefore, the ability to design even perfect conducting surfaces with specific spoof surface-plasmon properties essentially means that one can design, in any metal, a particular response dictated not by the choice of metal but by the specific patterning chosen.

Figure 2. (a) Prism-coupling setup. E: Electric-field direction, n: Index of refraction. (b) Sample surface where the side of the wax-filled holes is 7mm and the periodicity 9.5mm. (c) Reflectivity spectra from the sample surface for θ_int=46.5°in a plane of incidence oriented along the diagonal of the holes (φ=45°). The predictions from a finite-element-method (FEM) numerical model are also shown (using Ansoft's HFSS^TMsoftware). (d) Electromagnetic-field predictions of the resonance shown in (c). The colorscale and arrows on the left show the electric field at a phase corresponding to maximum field enhancement. Red shades indicate field intensities of at least five times the incident field. The figure on the right shows the Poynting vector (magnitude and direction) on resonance. Here, red shading corresponds to power enhancements of at least ten times.

From the middle of the twentieth century,^1,2 radar engineers have been aware that addition of a subwavelength corrugation to the metal surface strongly binds the surface mode to the interface, even in this long-wavelength regime. In its simplest form, such a surface is an array of closely spaced, narrow vertical slots in a metal substrate. If the slots are designed to be resonant, e.g., approximately one-quarter of a wavelength deep, then the short circuit (i.e., their closed end) at the bottom is transformed by the length of the slot into an open circuit at the open end such that the surface impedance becomes large and imaginary. Such surfaces can completely prevent surface-wave propagation and reflect an incoming wave without phase shift. However, if the depth of the slots is less than one-quarter wavelength, the effective surface impedance is positive and imaginary and enhanced compared to that of a planar metal. Such surfaces can support transverse-magnetic bound surface waves below the quarter-wavelength resonant frequency, which is then analogous to the limiting surface-plasmon frequency of metals in the visible regime.

Figure 3. (a) Photograph and (b) schematic of our ‘Sievenpiper-mushroom’ sample, comprised of copper patches of side length a=1.3mm, arranged in an array of pitch λ_g=1.6mm. Each patch is separated from the ground plane by h=0.79mm of low-loss dielectric, but connected to this plane by a copper pin.

This idea was recently revisited by John Pendry and his coworkers,³ who proposed that, “Although a flat perfectly conducting surface supports no bound states, the presence of holes, however small, produces a surface-plasmon polariton-like bound surface state.” This highlighted the possibility of creating designer (or spoof) surface modes with almost arbitrary dispersion through structure rather than material composition. We have since experimentally confirmed the existence of these modes in the microwave domain using grating coupling,⁴ rather like Wood's original observations. However, the ultimate test of this new principle is to use—as Otto did for the visible domain—simple prism coupling.⁵ Using prism coupling with microwaves, we determined the dispersion of the spoof surface plasmon (see Figure 2)⁶ and provided—for the first time—a complete formalism for its analytical derivation.⁷

Figure 4. (a) Resonance of surface-plasmon-like mode. (b) Dispersion of this mode at optimum coupling is experimentally derived by varying θ_int (circles). Also shown are the predictions from the numerical model (solid line).

However, these structures are still relatively thick and do not readily lend themselves to applications where light weight and flexibility may be important. Since all one is doing by patterning the surface with holes is making a high-impedance surface for a certain wavelength regime, a more familiar interpretation of the high-impedance surface, the thin ‘Sievenpiper-mushroom’ structure (see Figure 3),⁸ may be used instead. Such a structure has a thickness of only a fraction of the wavelength (<1mm), compared to the much thicker ‘Pendry’ and corrugated-slab structures. In a very recent study,⁹ we demonstrated strong coupling of incident microwave radiation to a bound transverse-magnetic surface mode on such structures (see Figure 4).

We have thus paved the way for a new generation of microwave structures using thin patterned metals to strongly localize surface waves that may be confined to a scale on the order of or smaller than their wavelength. Further patterning will provide in-plane focusing, splitting, and a variety of ways of controlling microwaves on a surface.