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...