Miller's Rule (optics)
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Miller's Rule (optics)
In optics, Miller's rule is an empirical rule which gives an estimate of the order of magnitude of the nonlinear coefficient. More formally, it states that the coefficient of the second order electric susceptibility response (\chi_) is proportional to the product of the first-order susceptibilities (\chi_) at the three frequencies which \chi_ is dependent upon. The proportionality coefficient is known as Miller's coefficient \delta. Definition The first order susceptibility response is given by: \chi_1(\omega) = \frac \frac where: * \omega is the frequency of oscillation of the electric field An electric field (sometimes E-field) is the physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical field fo ...; * \chi_1 is the first order electric susceptibility, as a function of \omega; * ''N'' is the number density of oscillating charge car ...
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Optics
Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultraviolet, and infrared light. Because light is an electromagnetic wave, other forms of electromagnetic radiation such as X-rays, microwaves, and radio waves exhibit similar properties. Most optical phenomena can be accounted for by using the classical electromagnetic description of light. Complete electromagnetic descriptions of light are, however, often difficult to apply in practice. Practical optics is usually done using simplified models. The most common of these, geometric optics, treats light as a collection of rays that travel in straight lines and bend when they pass through or reflect from surfaces. Physical optics is a more comprehensive model of light, which includes wave effects such as diffraction and interference that cannot be ...
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Electric Field
An electric field (sometimes E-field) is the physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical field for a system of charged particles. Electric fields originate from electric charges and time-varying electric currents. Electric fields and magnetic fields are both manifestations of the electromagnetic field, one of the four fundamental interactions (also called forces) of nature. Electric fields are important in many areas of physics, and are exploited in electrical technology. In atomic physics and chemistry, for instance, the electric field is the attractive force holding the atomic nucleus and electrons together in atoms. It is also the force responsible for chemical bonding between atoms that result in molecules. The electric field is defined as a vector field that associates to each point in space the electrostatic ( Coulomb) for ...
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Electron
The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no known components or substructure. The electron's mass is approximately 1/1836 that of the proton. Quantum mechanical properties of the electron include an intrinsic angular momentum ( spin) of a half-integer value, expressed in units of the reduced Planck constant, . Being fermions, no two electrons can occupy the same quantum state, in accordance with the Pauli exclusion principle. Like all elementary particles, electrons exhibit properties of both particles and waves: They can collide with other particles and can be diffracted like light. The wave properties of electrons are easier to observe with experiments than those of other particles like neutrons and protons because electrons have a lower mass and hence a longer de Broglie wavele ...
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Fundamental Charge
The elementary charge, usually denoted by is the electric charge carried by a single proton or, equivalently, the magnitude of the negative electric charge carried by a single electron, which has charge −1 . This elementary charge is a fundamental physical constant. In the SI system of units, the value of the elementary charge is exactly defined as e =  coulombs, or 160.2176634 zeptocoulombs (zC). Since the 2019 redefinition of SI base units, the seven SI base units are defined by seven fundamental physical constants, of which the elementary charge is one. In the centimetre–gram–second system of units (CGS), the corresponding quantity is . Robert A. Millikan and Harvey Fletcher's oil drop experiment first directly measured the magnitude of the elementary charge in 1909, differing from the modern accepted value by just 0.6%. Under assumptions of the then-disputed atomic theory, the elementary charge had also been indirectly inferred to ~3% accuracy from black ...
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Vacuum Permittivity
Vacuum permittivity, commonly denoted (pronounced "epsilon nought" or "epsilon zero"), is the value of the absolute dielectric permittivity of classical vacuum. It may also be referred to as the permittivity of free space, the electric constant, or the distributed capacitance of the vacuum. It is an ideal (baseline) physical constant. Its CODATA value is: : ( farads per meter), with a relative uncertainty of It is a measure of how dense of an electric field is "permitted" to form in response to electric charges, and relates the units for electric charge to mechanical quantities such as length and force. For example, the force between two separated electric charges with spherical symmetry (in the vacuum of classical electromagnetism) is given by Coulomb's law: :F_\text = \frac \frac Here, ''q''1 and ''q''2 are the charges, ''r'' is the distance between their centres, and the value of the constant fraction 1/4 \pi \varepsilon_0 (known as the Coulomb constant, ''k''e) is ...
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Anharmonicity
In classical mechanics, anharmonicity is the deviation of a system from being a harmonic oscillator. An oscillator that is not oscillating in harmonic motion is known as an anharmonic oscillator where the system can be approximated to a harmonic oscillator and the anharmonicity can be calculated using perturbation theory. If the anharmonicity is large, then other numerical techniques have to be used. In reality all oscillating systems are anharmonic, but most approximate the harmonic oscillator the smaller the amplitude of the oscillation is. As a result, oscillations with frequencies 2\omega and 3\omega etc., where \omega is the fundamental frequency of the oscillator, appear. Furthermore, the frequency \omega deviates from the frequency \omega_0 of the harmonic oscillations. See also intermodulation and combination tones. As a first approximation, the frequency shift \Delta \omega=\omega-\omega_0 is proportional to the square of the oscillation amplitude A: :\Delta \omeg ...
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