Theoretical and experimental exploration of finite sample size effects on the propagation of surface waves supported by slot arrays

Abstract

The propagation of surface waves supported by a finite array of slots perforated on a zero thickness perfect electrically conducting screen is studied both experimentally and theoretically. To generate numerical results, the integral equation satisfied by the electric field in the slots is efficiently solved by means of Galerkin's method, treating the metal as perfectly conducting. The finite size of the array along the direction of propagation creates a family of states of higher momentum and lower amplitude than the single mode for the corresponding infinite array. These modes are spaced in momentum with a periodicity inversely proportional to the length of the array. In addition, the finite width in the transverse direction produces a set of higher frequency modes due to this additional quantization. Both effects arising from finite sample length and width are explained by the theoretical model and validated experimentally. DOI: 10.1103/PhysRevB.95.245425 The existence of strongly localized surface modes supported by corrugated metallic surfaces at frequencies varying from terahertz [1] to microwaves [2] is well established. At optical frequencies, due to the Drude-like properties of the metal, these exist even on flat surfaces, being labeled surface plasmons polaritons (SPPs) [3,4]. However, following the discovery of extraordinary optical transmission (EOT) [5] and the later theoretical calculations, these surface waves were linked to a massively enhanced transmission through subwavelength holes [6,7] due to the diffractive coupling of radiative modes with the SPPs. This theory was, however, essentially developed for optical frequencies relying on the presence of SPPs. The subsequent discovery of EOT at frequencies at which metals behave as near perfect electric conductors (PEC), such as microwaves [8,9], launched the search for a more general theory. Many workers in the field made analogies of the surface waves supported on a patterned PEC with the aforementioned SPP, and due to the similarities with the SPP dispersion, the modes became commonly known as the "spoof surface plasmons" [10][11][12]. It should be noted, however, that there has been a wealth of studies of surface waves on metals at low frequencies, dating back to the 1940s [13,14]. This connection between the surface waves supported by hole arrays and the transmission through them has given rise to much research [15,16] in which the transmission through both infinite and finite arrays of holes and slits has been studied often using a modal matching approach [17,18]. However, there is no corresponding study on the effects of finite sample size on the propagation of surface waves themselves. At microwave frequencies, these surface modes have been explored particularly using metasurfaces [19], subwavelengthstructured metallic surfaces that yield novel properties such as negative refraction [20], band gaps [21], and dispersive behavior leading to the design of surface wave lenses and antennas [22][23][24][25]. With the development of miniaturiza...

Far-Field and Near-Field Physics of Extraordinary THz Transmitting Hole-Array Antennas

“…To confirm the existence of these leaky waves, we consider an infinite array along both x and y-directions and calculate the complex propagation constants of the modes traveling along x in the absence of excitation. More specifically, the procedure consists in finding the complex zeros of the determinant of the system of equations that has the same set of basis functions and the 2-D periodic Green's function, following the Method of Moments approach presented in [40], at a given frequency. In Fig.…”

“…To understand their origin, one needs to remember that, due to the periodicity of the infinite array, the reciprocal space of the x variable can be obtained by periodically repeating the Brillouin zone defined by the region limited by k x ∈ [−π/a, π/a]. In addition, hole arrays are known to support complex waves, which, for the case of holes that are small compared to the wavelength and to the periodicity, present a value of their wavevector that is just slightly larger than the free space wavevector, |k sw x | ≈ k 0 [7], [40]. Hence, when k 0 approaches the Brillouin zone boundary, thanks to the periodicity of the spectrum, some of the harmonics with wavevector k m x = k sw x + 2πm/a may enter the visible region [41] and become a leaky mode.…”

“…5(b), one can see the presence of 12 zeroes. Following the aforementioned rationale, the zeroth harmonics can be identified as those zeroes with a real part of k x slightly larger than k 0 , as the phase velocity of these waves reduces when the frequency approaches the λ/2 resonance of a single hole [40]. Then, using the formula for the space harmonics and what we learned from Fig.…”

Asymmetric surface wave excitation through metasurface-edge diffraction

“…The procedure leads to the total current represented as the sum of three different wave species, i.e., three current terms originating from different physical mechanisms: (1) the residue of the pole at ξ γ is associated with the currents found in the non-truncated problem (double infinite periodic metasurface); (2) the branch cut introduced by the Green's function in the transform of the coupling coefficient k m−n is associated with the so-called "space wave" collecting the continuous wavevector spectrum of the fields diffracted by the edge of the metasurface; and (3) the residues of the poles arising from the zeroes inside the unit circle of the transform of the coupling K(ξ) corresponding to the surface waves supported by the metasurface. The fact that not all of the surface waves supported by the structure are necessarily excited by the edge diffraction is an essential feature of the scattering by a semi-infinite structure, and this constitutes a significant difference with respect to the scattering by a small object/defect over or within the metasurface [12]. Specifically, this is due to the coupling mechanism between the plane wave and the surface wave at the edge; only modes that propagate energy away from the edge are "physical", i.e., excitable by the diffracted wave originated by the edge or by a localized source [11,16].…”

“…Both these techniques require to place objects in the near field of the wave-supporting structure adding unwanted coupling mechanisms. Alternatively, localized sources placed in the vicinity of a metasurface are able to excite all wavector components due to their scattered-field's continuous spectrum [11,12]. However, the main drawback of this technique is the complete lack of selectivity in which surface waves are being excited.…”