In the last decades there has been a great deal of interest in the study of complex artificial structures (metamaterials) that may interact in an unusual way with electromagnetic radiation [1]. Wire metamaterials have attracted particular attention due to their potential to manipulate waves in the subwavelength scale [2, 3].
In this work, we investigate the guided modes supported by a metamaterial slab formed by two mutually orthogonal and nonconnected arrays of parallel metallic wires. Specifically, one set of wires is parallel to the interface, whereas the other is perpendicular. The wires are embedded in a simple dielectric. Our analysis relies on a homogenization technique known as transverse averaged (TA)-field approach [4] and additional boundary conditions [5].
Remarkably, the analysis reveals that in the continuum limit (i.e., when the granularity of the metamaterial is neglected) the structured slab supports a diverging (infinite) number of guided mode branches that accumulate near the light line for low frequencies. We explain this peculiar effect as a consequence of the strong hyperbolic response of the wire medium near the static limit [6]. An interesting feature of the guided modes is that even though they are weakly bounded to the slab, they may vary extremely fast along the transverse direction (i.e. perpendicular to the direction of propagation). This property may be advantageously exploited to detect subwavelength particles. Furthermore, we discuss the impact of the granular structure of the wire metamaterial on the modal dispersion, showing that in a realistic structure the number of guided modes branches depends on the number of metallic wires parallel to the interface.