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Polarizability is responsible for a material's dielectric constant and, at high (optical) frequencies, its refractive index. The polarizability of an atom or molecule is defined as the ratio of its induced dipole moment to the local electric field; in a crystalline solid, one considers the dipole moment per unit cell. [1]
The Lorentz–Lorenz equation is similar to the Clausius–Mossotti relation, except that it relates the refractive index (rather than the dielectric constant) of a substance to its polarizability. The Lorentz–Lorenz equation is named after the Danish mathematician and scientist Ludvig Lorenz , who published it in 1869, and the Dutch ...
In electromagnetism, the absolute permittivity, often simply called permittivity and denoted by the Greek letter ε , is a measure of the electric polarizability of a dielectric material. A material with high permittivity polarizes more in response to an applied electric field than a material with low permittivity, thereby storing more energy ...
The relative permittivity (in older texts, dielectric constant) is the permittivity of a material expressed as a ratio with the electric permittivity of a vacuum. A dielectric is an insulating material, and the dielectric constant of an insulator measures the ability of the insulator to store electric energy in an electrical field.
A dielectric resonator oscillator (DRO) is an electronic component that exhibits resonance of the polarisation response for a narrow range of frequencies, generally in the microwave band. It consists of a "puck" of ceramic that has a large dielectric constant and a low dissipation factor. Such resonators are often used to provide a frequency ...
is the dielectric polarization. For the full coupling between the phonon and the photon, we need the four Maxwell's equations in matter. Since, macroscopically, the crystal is uncharged and there is no current, the equations can be simplified. A phonon polariton must abide all of these six equations.
where ε 0 is the electric constant, and χ is the electric susceptibility of the medium. Note that in this case χ simplifies to a scalar, although more generally it is a tensor. This is a particular case due to the isotropy of the dielectric. Taking into account this relation between P and E, equation becomes: [3]
Therefore, the dielectric constant (and the conductivity) has contributions from both terms. This approach can be generalized to compute the frequency dependent dielectric function. [38] It is possible to calculate dipole moments from electronic structure theory, either as a response to constant electric fields or from the density matrix. [39]