Surface plasmon resonanceSurface plasmon resonance (SPR) is a phenomenon that occurs where electrons in a thin metal sheet become excited by light that is directed to the sheet with a particular angle of incidence, and then travel parallel to the sheet. Assuming a constant light source wavelength and that the metal sheet is thin, the angle of incidence that triggers SPR is related to the refractive index of the material and even a small change in the refractive index will cause SPR to not be observed.
Surface plasmonSurface plasmons (SPs) are coherent delocalized electron oscillations that exist at the interface between any two materials where the real part of the dielectric function changes sign across the interface (e.g. a metal-dielectric interface, such as a metal sheet in air). SPs have lower energy than bulk (or volume) plasmons which quantise the longitudinal electron oscillations about positive ion cores within the bulk of an electron gas (or plasma). The charge motion in a surface plasmon always creates electromagnetic fields outside (as well as inside) the metal.
Matrix (mathematics)In mathematics, a matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object. For example, is a matrix with two rows and three columns. This is often referred to as a "two by three matrix", a " matrix", or a matrix of dimension . Without further specifications, matrices represent linear maps, and allow explicit computations in linear algebra.
Prostate-specific antigenProstate-specific antigen (PSA), also known as gamma-seminoprotein or kallikrein-3 (KLK3), P-30 antigen, is a glycoprotein enzyme encoded in humans by the KLK3 gene. PSA is a member of the kallikrein-related peptidase family and is secreted by the epithelial cells of the prostate gland. PSA is produced for the ejaculate, where it liquefies semen in the seminal coagulum and allows sperm to swim freely. It is also believed to be instrumental in dissolving cervical mucus, allowing the entry of sperm into the uterus.
Localized surface plasmonA localized surface plasmon (LSP) is the result of the confinement of a surface plasmon in a nanoparticle of size comparable to or smaller than the wavelength of light used to excite the plasmon. When a small spherical metallic nanoparticle is irradiated by light, the oscillating electric field causes the conduction electrons to oscillate coherently. When the electron cloud is displaced relative to its original position, a restoring force arises from Coulombic attraction between electrons and nuclei.
Diagonalizable matrixIn linear algebra, a square matrix is called diagonalizable or non-defective if it is similar to a diagonal matrix, i.e., if there exists an invertible matrix and a diagonal matrix such that , or equivalently . (Such , are not unique.) For a finite-dimensional vector space , a linear map is called diagonalizable if there exists an ordered basis of consisting of eigenvectors of .
Multi-parametric surface plasmon resonanceMulti-parametric surface plasmon resonance (MP-SPR) is based on surface plasmon resonance (SPR), an established real-time label-free method for biomolecular interaction analysis, but it uses a different optical setup, a goniometric SPR configuration. While MP-SPR provides same kinetic information as SPR (equilibrium constant, dissociation constant, association constant), it provides also structural information (refractive index, layer thickness). Hence, MP-SPR measures both surface interactions and nanolayer properties.
Surface plasmon polaritonSurface plasmon polaritons (SPPs) are electromagnetic waves that travel along a metal–dielectric or metal–air interface, practically in the infrared or visible-frequency. The term "surface plasmon polariton" explains that the wave involves both charge motion in the metal ("surface plasmon") and electromagnetic waves in the air or dielectric ("polariton"). They are a type of surface wave, guided along the interface in much the same way that light can be guided by an optical fiber.
Hermitian matrixIn mathematics, a Hermitian matrix (or self-adjoint matrix) is a complex square matrix that is equal to its own conjugate transpose—that is, the element in the i-th row and j-th column is equal to the complex conjugate of the element in the j-th row and i-th column, for all indices i and j: or in matrix form: Hermitian matrices can be understood as the complex extension of real symmetric matrices.
Logarithm of a matrixIn mathematics, a logarithm of a matrix is another matrix such that the matrix exponential of the latter matrix equals the original matrix. It is thus a generalization of the scalar logarithm and in some sense an inverse function of the matrix exponential. Not all matrices have a logarithm and those matrices that do have a logarithm may have more than one logarithm. The study of logarithms of matrices leads to Lie theory since when a matrix has a logarithm then it is in an element of a Lie group and the logarithm is the corresponding element of the vector space of the Lie algebra.
