Waves in man-made materials: superlattice to metamaterials

Abstract

While artificial or man-made structures date back to Lord Rayleigh, the work started by Lewin in 1947, placing spheres onto cubic lattices, greatly enriched microwave materials and devices. It was very suggestive of both metamaterials and photonics crystals. Effective medium models were used to describe bulk properties with some success. The concept of metamaterials followed photonic crystals, and these both were introduced after the introduction of the man-made superlattices designed to enrich the class of materials for electronic devices. The work on serrated ridged waveguides by Kirschbaum and Tsu for the control of the refractive index of microwave lenses as well as microwave matching devices in 1959 used a combination of theory, such as Floquet’s theory, Bloch theory in one dimension, as well as periodic lumped loading. There is much in common between metamaterials and superlattices, but in this paper, we discuss some practical limitations to both. It is pointed out that unlike superlattices where kl > 1 is the most important criterion, metamaterials try to avoid involve such restrictions. However, the natural random fluctuations that limit the properties of naturally occurring materials are shown to take a toll on the theoretical predictions of metamaterials. The question is how great that toll, i.e. how significant those fluctuations will be, in diminishing the unusual properties that metamaterials can exhibit.