Excimer lampAn excimer lamp (or excilamp) is a source of ultraviolet light based on spontaneous emission of excimer (exciplex) molecules. Excimer lamps are quasimonochromatic light sources operating over a wide range of wavelengths in the ultraviolet (UV) and vacuum ultraviolet (VUV) spectral regions. Operation of an excimer lamp is based on the formation of excited dimers (excimers), which spontaneously transiting from the excited state to the ground state result in the emission of UV-photons.
Argon fluoride laserThe argon fluoride laser (ArF laser) is a particular type of excimer laser, which is sometimes (more correctly) called an exciplex laser. With its 193-nanometer wavelength, it is a deep ultraviolet laser, which is commonly used in the production of semiconductor integrated circuits, eye surgery, micromachining, and scientific research. "Excimer" is short for "excited dimer", while "exciplex" is short for "excited complex".
Excimer laserAn excimer laser, sometimes more correctly called an exciplex laser, is a form of ultraviolet laser which is commonly used in the production of microelectronic devices, semiconductor based integrated circuits or "chips", eye surgery, and micromachining. Since 1960s excimer lasers are widely used in high-resolution photolithography machines, one of the critical technologies required for microelectronic chip manufacturing. The term excimer is short for 'excited dimer', while exciplex is short for 'excited complex'.
Group representationIn the mathematical field of representation theory, group representations describe abstract groups in terms of bijective linear transformations of a vector space to itself (i.e. vector space automorphisms); in particular, they can be used to represent group elements as invertible matrices so that the group operation can be represented by matrix multiplication. In chemistry, a group representation can relate mathematical group elements to symmetric rotations and reflections of molecules.
Fiber Bragg gratingA fiber Bragg grating (FBG) is a type of distributed Bragg reflector constructed in a short segment of optical fiber that reflects particular wavelengths of light and transmits all others. This is achieved by creating a periodic variation in the refractive index of the fiber core, which generates a wavelength-specific dielectric mirror. Hence a fiber Bragg grating can be used as an inline optical fiber to block certain wavelengths, can be used for sensing applications, or it can be used as wavelength-specific reflector.
Induced representationIn group theory, the induced representation is a representation of a group, G, which is constructed using a known representation of a subgroup H. Given a representation of H, the induced representation is, in a sense, the "most general" representation of G that extends the given one. Since it is often easier to find representations of the smaller group H than of G, the operation of forming induced representations is an important tool to construct new representations.
Representation theoryRepresentation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essence, a representation makes an abstract algebraic object more concrete by describing its elements by matrices and their algebraic operations (for example, matrix addition, matrix multiplication).
Krypton fluoride laserA krypton fluoride laser (KrF laser) is a particular type of excimer laser, which is sometimes (more correctly) called an exciplex laser. With its 248 nanometer wavelength, it is a deep ultraviolet laser which is commonly used in the production of semiconductor integrated circuits, industrial micromachining, and scientific research. The term excimer is short for 'excited dimer', while exciplex is short for 'excited complex'. An excimer laser typically contains a mixture of: a noble gas such as argon, krypton, or xenon; and a halogen gas such as fluorine or chlorine.
Weight (representation theory)In the mathematical field of representation theory, a weight of an algebra A over a field F is an algebra homomorphism from A to F, or equivalently, a one-dimensional representation of A over F. It is the algebra analogue of a multiplicative character of a group. The importance of the concept, however, stems from its application to representations of Lie algebras and hence also to representations of algebraic and Lie groups. In this context, a weight of a representation is a generalization of the notion of an eigenvalue, and the corresponding eigenspace is called a weight space.
Unitary representationIn mathematics, a unitary representation of a group G is a linear representation π of G on a complex Hilbert space V such that π(g) is a unitary operator for every g ∈ G. The general theory is well-developed in the case that G is a locally compact (Hausdorff) topological group and the representations are strongly continuous. The theory has been widely applied in quantum mechanics since the 1920s, particularly influenced by Hermann Weyl's 1928 book Gruppentheorie und Quantenmechanik.
