SOLBOX-17: Cylindrical lens structures

Zero-index and near-zero-index (NZI) materials are artificial structures that have recently attracted great interest in the electromagnetics and optics communities, thanks to their potentials in manipulating electromagnetic waves for a plethora of applications [1-5]. As with all other types of metamaterials, NZI structures are built of small unit cells, such as dielectric, metallic, and plasmonic particles, although they are often homogenized and represented by using effective electromagnetic properties in their numerical simulations. In fact, when accurately performed, homogenization can provide excellent analysis abilities, particularly when these structures are integrated with other devices to construct larger systems. At the same time, even when an NZI structure is greatly simplified by using a homogeneous model, the resulting electromagnetic problem may still possess several numerical challenges, considering that the conventional implementations are developed for ordinary materials. Some of these difficulties, e.g., handling numerically small or large values in the computer environment, may be easier to overcome, while there are also challenges that arise due to inherent properties of the developed methods and algorithms and that need more elaborate techniques to solve.