Nonlinear opticsNonlinear optics (NLO) is the branch of optics that describes the behaviour of light in nonlinear media, that is, media in which the polarization density P responds non-linearly to the electric field E of the light. The non-linearity is typically observed only at very high light intensities (when the electric field of the light is >108 V/m and thus comparable to the atomic electric field of ~1011 V/m) such as those provided by lasers. Above the Schwinger limit, the vacuum itself is expected to become nonlinear.
Circular polarizationIn electrodynamics, circular polarization of an electromagnetic wave is a polarization state in which, at each point, the electromagnetic field of the wave has a constant magnitude and is rotating at a constant rate in a plane perpendicular to the direction of the wave. In electrodynamics, the strength and direction of an electric field is defined by its electric field vector. In the case of a circularly polarized wave, the tip of the electric field vector, at a given point in space, relates to the phase of the light as it travels through time and space.
Polarization (physics)Polarization (also polarisation) is a property of transverse waves which specifies the geometrical orientation of the oscillations. In a transverse wave, the direction of the oscillation is perpendicular to the direction of motion of the wave. A simple example of a polarized transverse wave is vibrations traveling along a taut string (see image); for example, in a musical instrument like a guitar string. Depending on how the string is plucked, the vibrations can be in a vertical direction, horizontal direction, or at any angle perpendicular to the string.
Plane of incidenceIn describing reflection and refraction in optics, the plane of incidence (also called the incidence plane or the meridional plane) is the plane which contains the surface normal and the propagation vector of the incoming radiation. (In wave optics, the latter is the k-vector, or wavevector, of the incoming wave.) When reflection is specular, as it is for a mirror or other shiny surface, the reflected ray also lies in the plane of incidence; when refraction also occurs, the refracted ray lies in the same plane.
Angle of incidence (optics)The angle of incidence, in geometric optics, is the angle between a ray incident on a surface and the line perpendicular (at 90 degree angle) to the surface at the point of incidence, called the normal. The ray can be formed by any waves, such as optical, acoustic, microwave, and X-ray. In the figure below, the line representing a ray makes an angle θ with the normal (dotted line). The angle of incidence at which light is first totally internally reflected is known as the critical angle.
PolarizerA polarizer or polariser (see spelling differences) is an optical filter that lets light waves of a specific polarization pass through while blocking light waves of other polarizations. It can filter a beam of light of undefined or mixed polarization into a beam of well-defined polarization, that is polarized light. The common types of polarizers are linear polarizers and circular polarizers. Polarizers are used in many optical techniques and instruments, and polarizing filters find applications in photography and LCD technology.
BirefringenceBirefringence is the optical property of a material having a refractive index that depends on the polarization and propagation direction of light. These optically anisotropic materials are said to be birefringent (or birefractive). The birefringence is often quantified as the maximum difference between refractive indices exhibited by the material. Crystals with non-cubic crystal structures are often birefringent, as are plastics under mechanical stress.
WaveplateA waveplate or retarder is an optical device that alters the polarization state of a light wave travelling through it. Two common types of waveplates are the half-wave plate, which shifts the polarization direction of linearly polarized light, and the quarter-wave plate, which converts linearly polarized light into circularly polarized light and vice versa. A quarter-wave plate can be used to produce elliptical polarization as well.
Fresnel equationsThe Fresnel equations (or Fresnel coefficients) describe the reflection and transmission of light (or electromagnetic radiation in general) when incident on an interface between different optical media. They were deduced by Augustin-Jean Fresnel (freɪˈnɛl) who was the first to understand that light is a transverse wave, even though no one realized that the "vibrations" of the wave were electric and magnetic fields.
Inflection pointIn differential calculus and differential geometry, an inflection point, point of inflection, flex, or inflection (rarely inflexion) is a point on a smooth plane curve at which the curvature changes sign. In particular, in the case of the graph of a function, it is a point where the function changes from being concave (concave downward) to convex (concave upward), or vice versa.
Quantum Hall effectThe quantum Hall effect (or integer quantum Hall effect) is a quantized version of the Hall effect which is observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields, in which the Hall resistance Rxy exhibits steps that take on the quantized values where VHall is the Hall voltage, Ichannel is the channel current, e is the elementary charge and h is Planck's constant. The divisor ν can take on either integer (ν = 1, 2, 3,...) or fractional (ν = 1/3, 2/5, 3/7, 2/3, 3/5, 1/5, 2/9, 3/13, 5/2, 12/5,.
Stationary pointIn mathematics, particularly in calculus, a stationary point of a differentiable function of one variable is a point on the graph of the function where the function's derivative is zero. Informally, it is a point where the function "stops" increasing or decreasing (hence the name). For a differentiable function of several real variables, a stationary point is a point on the surface of the graph where all its partial derivatives are zero (equivalently, the gradient is zero).
International Linear ColliderThe International Linear Collider (ILC) is a proposed linear particle accelerator. It is planned to have a collision energy of 500 GeV initially, with the possibility for a later upgrade to 1000 GeV (1 TeV). Although early proposed locations for the ILC were Japan, Europe (CERN) and the USA (Fermilab), the Kitakami highland in the Iwate prefecture of northern Japan has been the focus of ILC design efforts since 2013. The Japanese government is willing to contribute half of the costs, according to the coordinator of study for detectors at the ILC.
GrapheneGraphene (ˈgræfiːn) is an allotrope of carbon consisting of a single layer of atoms arranged in a hexagonal lattice nanostructure. The name is derived from "graphite" and the suffix -ene, reflecting the fact that the graphite allotrope of carbon contains numerous double bonds. Each atom in a graphene sheet is connected to its three nearest neighbors by σ-bonds and a delocalised π-bond, which contributes to a valence band that extends over the whole sheet.
MetamaterialA metamaterial (from the Greek word μετά meta, meaning "beyond" or "after", and the Latin word materia, meaning "matter" or "material") is any material engineered to have a property that is rarely observed in naturally occurring materials. They are made from assemblies of multiple elements fashioned from composite materials such as metals and plastics. These materials are usually arranged in repeating patterns, at scales that are smaller than the wavelengths of the phenomena they influence.
Critical point (mathematics)Critical point is a wide term used in many branches of mathematics. When dealing with functions of a real variable, a critical point is a point in the domain of the function where the function is either not differentiable or the derivative is equal to zero. When dealing with complex variables, a critical point is, similarly, a point in the function's domain where it is either not holomorphic or the derivative is equal to zero. Likewise, for a function of several real variables, a critical point is a value in its domain where the gradient is undefined or is equal to zero.
Particle acceleratorA particle accelerator is a machine that uses electromagnetic fields to propel charged particles to very high speeds and energies, and to contain them in well-defined beams. Large accelerators are used for fundamental research in particle physics. The largest accelerator currently active is the Large Hadron Collider (LHC) near Geneva, Switzerland, operated by the CERN. It is a collider accelerator, which can accelerate two beams of protons to an energy of 6.5 TeV and cause them to collide head-on, creating center-of-mass energies of 13 TeV.
Geometrical opticsGeometrical optics, or ray optics, is a model of optics that describes light propagation in terms of rays. The ray in geometrical optics is an abstraction useful for approximating the paths along which light propagates under certain circumstances. The simplifying assumptions of geometrical optics include that light rays: propagate in straight-line paths as they travel in a homogeneous medium bend, and in particular circumstances may split in two, at the interface between two dissimilar media follow curved paths in a medium in which the refractive index changes may be absorbed or reflected.
Magnetic fieldA magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to the magnetic field. A permanent magnet's magnetic field pulls on ferromagnetic materials such as iron, and attracts or repels other magnets.
Reciprocal latticeIn physics, the reciprocal lattice represents the Fourier transform of another lattice. The direct lattice or real lattice is a periodic function in physical space, such as a crystal system (usually a Bravais lattice). The reciprocal lattice exists in the mathematical space of spatial frequencies, known as reciprocal space or k space, where refers to the wavevector. In quantum physics, reciprocal space is closely related to momentum space according to the proportionality , where is the momentum vector and is the reduced Planck constant.
