Sculpting metals for anomalous transmission phenomena, complex waves and negative refractive metamaterials: underlying physics and applications Miguel Navarro-Cía Millimeter and Terahertz Waves Laboratory, Universidad Pública de Navarra, Campus Arrosadía, 31006 Pamplona, Spain E-mail: miguel.navarro@unavarra.es Abstract In this talk, the potential of controlling the electromagnetic propagation by periodically-textured surfaces is reviewed. It is shown that backward-wave- and slow-wave-propagation, superluminal, effective negative refractive index and highly-confined complex surface waves are obtained with these metallic surfaces. The role of periodicity, complex surface waves and resonant-electric-coupling in all these phenomena is emphasized and compared against equivalent circuit models. The explanation of the underlying physics is combined with exemplary applications focused on the millimetre- and submillimetre-wave band. Introduction Over the last few years we have seen dramatic advances in controlling the propagation of electromagnetic waves. The two main fields in this direction are metamaterials [1] and plasmonics [2]. Metamaterials took off at the beginning of the 21 st century as a result of the experimental realization of a double-negative medium [3] and the firestorm of controversy brought by the perfect lens concept [4]. Nowadays, there is a race toward low-loss and high frequency metamaterials. On the other hand, the inflection point on plasmonics research was extraordinary (optical) transmission, which was brought to attention in the seminal paper of Ebbesen et al. [5]. Equally, extraordinary transmission has revitalized the field of gratings, which traces back more than a century ago. The recent convergence of both fields - metamaterials and plasmonics - via extraordinary transmission [6 ,7] has sparked considerable excitement since it has made it possible to proof experimentally negative refraction by double-negativity at high frequencies [8, 9]. The aim of this talk is threefold: firstly, to show a thorough analysis of subwavelength aperture arrays exhibiting not only extraordinary transmission, but also other unusual transmission or reflection features (either in the phase or magnitude response) when more complex systems are considered. For instance, when compound periods are contemplated [10], additional complex surface waves are generated by dielectric loading of the array which can interact with the modes supported by the arrays [11] or Babinet’s concepts are applied [12]; secondly, to bring the attention to patterned metals with more complex topologies such as complementary-split-ring-resonators [13] for enhanced field confinement [14]; thirdly, to exploit subwavelength hole arrays to achieve low-loss double negative