Regular crystals have translational symmetry, where the same unit part is repeated over and over again with no rotation. Quasicrystals have rotational symmetry, where the same unit part is repeated over and over, but with a rotation about an angle.
Quasicrystals are structural forms that are both ordered and nonperiodic. They form patterns that fill all the space but lack translational symmetry. The term and the concept were introduced originally to denote a specific arrangement observed in solids which can be said to be in a state intermediary between crystal and glass. Producing Bragg diffraction, they share a defining property with crystals, but differ from them by lacking a simple repeating structure.
Mathematical artefacts known as ‘aperiodic tilings’ were invented in the early 1960s, but some twenty years later physical experiments gave conclusive evidence of their material existence. Within the field of crystallography and solid state physics the discovery has produced a paradigm shift which is indeed a minor scientific revolution.
 It was realized that quasicrystals had been investigated and observed earlier
 but until then the prevailing views about atomic structure of matter lead to their being explained away.
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.
Nanophotonics are now being recognized as a special branch of optics, in much the same way as nanoelectronics form a special branch of electronics. Some of the technological problems that had appeared at the time of the first studies on photonic crystals, are currently in the process of being solved. However, it should be stressed that future development and applications of photonic crystals are definitively dependent on the degree of accuracy which can be achieved in the fabrication of micro- and nanostructures, and thus on the overall dimensions of the corresponding devices.
One of the most striking illustrations of the fruitfulness of research on metallo-dielectric photonic crystals is probably the development of the so-called metamaterials, which are expected to provide a new approach towards negative refraction, through the simultaneous control of the effective permittivity and the effective permeability.
Since metamaterials are dependent upon the structure of the material rather than the properties of the atoms that make up it’s composition, it is possible to build photonic metamaterials using packed nanospheres. Recently major breakthroughs have occurred in Nonlinear Liquid Crystal Nano-Metamaterials which use nanosphere- and nanoshell-doped liquid crystals can produce metamaterials with a tunable refractive index!
Important links and info on Quasicrystals:
Structural Stability and Kinetics of Hydrogen in TiZrNi Quasicrystals
When hydrogen atoms slowly diffuse into a metastable structure, a coherence length of thin TiZrNi quasicrystal metallic ribbons is increased. Improved atomic order with addition of hydrogen is an uncommon phenomenon in metals, and may reflect the unordinary structural property of quasicrystals. Metastable TiZrNi quasicrystals prepared by rapid quenching of molten ingots were hydrogenated in a low pressure of hydrogen (lower than 1000 Torr) at high temperature. After completion of the pressure-composition-temperature measurements between 200 to 300 °C, X-ray diffraction data revealed that the full width at half maximum values of the diffraction peaks were decreased suggesting that the quasicrystal phase may stabilized by hydrogen inclusion. Annealing of the same sample at 200 °C without hydrogen yields no change of the relative intensity of diffraction peaks.
The aim of this book is to acquaint the reader with what the author regards as the most basic characteristics of quasicrystals — structure, formation and stability, properties — in relationship with the applications of quasicrystalline materials.
Quasicrystals are fascinating substances that form a family of specific structures with strange physical and mechanical properties as compared to those of metallic alloys. This, on the one hand, is stimulating intensive research to understand the most basic properties of quasicrystals in the frame of a generalized crystallography. On the other hand, these properties open the way to technological applications, demonstrated or potential, mostly regarding energy savings.
This valuable book discusses those various facets of quasicrystals in five chapters, ending with the author’s own interpretation of the properties with respect to their unique structure.
New method for trapping light may improve communications technologies
Posted August 18, 2005; 12:12 p.m.
by Eric Quiñones
A discovery by Princeton researchers may lead to an efficient method for controlling the transmission of light and improve new generations of communications technologies powered by light rather than electricity.
The discovery could be used to develop new structures that would work in the same fashion as an elbow joint in plumbing by enabling light to make sharp turns as it travels through photonic circuits. Fiber-optic cables currently used in computers, televisions and other devices can transport light rapidly and efficiently, but cannot bend at sharp angles. Information in the light pulses has to be converted back into cumbersome electrical signals before they can be sorted and redirected to their proper destinations.
In an experiment detailed in the Aug. 18 issue of Nature, the researchers constructed a three-dimensional model of a quasicrystal made from polymer rods to test whether such structures are useful for controlling the path of light. A quasicrystal is an unusual form of solid composed of two building blocks, or groups of atoms, that repeat regularly throughout the structure with two different spacings. Ordinary crystals are made from a single building block that repeats with all equal spacings. The difference enables quasicrystals to have more spherical symmetries that are impossible for crystals.
Ordinary crystals had been considered the best structure for making junctions in photonic circuits. But the researchers proved for the first time that quasicrystal structures are better for trapping and redirecting light because their structure is more nearly spherical. Their model, which had the same symmetry as a soccer ball, showed that the quasicrystal design could block light from escaping no matter which direction it traveled.
The finding represents an advance for the burgeoning field of photonics — in which light replaces electricity as a means for transmitting and processing information — and could lead to the development of faster telecommunications and computing devices.
“The search for a structure that blocks the passage of light in all directions has fascinated physicists and engineers for the past two decades,” said Princeton physicist Paul Steinhardt , a co-author of the Nature paper, who invented the concept of quasicrystals with his student Dov Levine at the University of Pennsylvania in 1984.
“Controlled light can be directed, switched and processed like electrons in an electronic circuit, and such photonic devices have many applications in research and in communications,” Steinhardt noted.
Co-author Paul Chaikin, a former Princeton professor now at the Center for Soft Matter Research at New York University, said, “Ultimately, photonics is a better method for channeling information than electronics — it consumes less energy and it’s faster.”
The paper’s other co-authors are Weining Man, who worked on the project as part of her doctoral thesis in Princeton’s physics department, and Mischa Megens, a researcher at Philips Research Laboratories in the Netherlands.
To conduct their experiment, the researchers constructed the world’s first model of a three-dimensional photonic quasicrystal, which was a little larger than a softball and made from 4,000 centimeter-long polymer rods. They observed how microwaves were blocked at certain angles in order to gauge how well the structure would control light passing through it.
Building the physical model was a breakthrough that proved more valuable than using complex mathematical calculations, which had been a hurdle in previous efforts to evaluate the effectiveness of photonic quasicrystals in blocking light.
“The pattern in which photons are blocked or not blocked had never really been computed,” Steinhardt said. “In the laboratory, we were able to construct a device that was effectively like doing a computer simulation to see the patterns of transmission.”
Chaikin added, “We showed that it has practical applications, and we also found out some properties of quasicrystals that we didn’t know before.”
The researchers are now exploring ways of miniaturizing the structure in order to utilize the device with visible light instead of microwaves. They also are examining whether the quasicrystal designs may be useful in electronic and acoustic applications.
Further details and images related to the study are available at: http://wwwphy.princeton.edu/~steinh/quasiphoton/