An ordering is nonperiodic if it lacks translational symmetry, which means that a shifted copy will never match exactly with its original. The ability to diffract comes from the existence of an indefinitely large number of elements with a regular spacing, a property loosely described as long-range order. Experimentally the aperiodicity is revealed in the unusual symmetry of the diffraction pattern.

The first officially reported case of what came to be known as quasicrystals was made by Dan Shechtman and coworkers in 1984. Between a mathematical model of a quasicrystal, such as the Penrose tiling, and the corresponding physical systems, the distinction is taken to be evident and usually does not have to be emphasized.

The study of the physical and optical properties of photonic crystals has generated a burst of new ideas for optical devices and systems. Special mention needs to be made here of photonic crystal silica fibres, which appear as the first application of photonic crystals to the real world of optical communications.

In the field of semiconductors and metals, the fabrication of photonic crystals has represented an important challenge for micro- and nanotechnology. In turn, these technologies have benefited from the validation of processes which has thus been completed. In this respect, the evolution of photonics has paralleled the revolution which has been taking place in the field of electronics with the development of nanotransistors and quantum dot memories.

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