Quasicrystals, or crystals that display the unusual property of non-periodicity (while remaining ordered), were discovered in the 1980s by Dan Shechtman. A highly controversial topic, Shechtman did not produce a paper describing them for over two years after their discovery. However, within the past 30 years, the scientific community has come to accept them, reproduce them for study, and even award Dan Shechtman with a Nobel Prize for their discovery. Naturally found but very rare, they are typically synthesized in labs. Quasicrystals display distinctive qualities in areas such as adhesion, corrosion, friction and hardness, but scientists have recently found that they, along with other ordered non-periodic structures, exhibit unique optical effects as well, specifically negative refraction.
To understand how ordered non-periodic structures are tested in the field of optics, one must first understand photonic crystals: crystals which exhibit effects of photon-directing similar to the electron-directing effects of semi-conductor crystals. The resulting phenomena occur by the fact that photonic crystals have dielectric constants which are periodically modulated (causing effects such as varying refractive indices, as seen in the figure below). Photonic crystals can be fabricated, but they can occur in nature: like the commonly known gemstone, opal.
Photonic crystals can be fabricated in one, two, or three dimensions; the 3D crystals are the most challenging to create and model mathematically, which is why 2D quasi-periodic models are preferred.
Crystals are periodic and ordered, which is evident in the representation of the above figure. The order is apparent in the straightness of lines, consistency of size and span, etc. The periodicity is apparent in the distances between each line and the sameness of the pattern throughout the entire crystal. Quasicrystals, as we previously...