## polarization, \(P\)

https://doi.org/10.1351/goldbook.P04712
The relevant material property that couples with the radiation field. May be called optical or dielectric polarization. Optical spectroscopies may be classified according to the dielectric polarization power-law dependence on the external electric field.
Notes:
1. Mathematically it is defined as the @E01929@ change per volume resulting from absorption of radiation of optical frequencies, defined as P = D - ɛ0E, where D is the @E01930@, ɛ0 the electric constant (vacuum @P04507@) , and E the strength of the radiation electric field. A dielectric medium is characterized by the constitutive relation D = ɛ0.χ(1) where χ(1) = ɛr - 1 is the linear 'susceptibility' for a transparent singly refracting medium. Depending on the molecular or atomic restoring force on the electron with respect to the displacement D, the field-induced motion of the electron can introduce other frequency components on the electron motion, and this in turn leads to non-linear optical effects.
2. The polarization component to the nth-order in the field is denoted as P(n) Thus, the following equations apply,
P = P(1) + PNL and PNL = P(2) + P(3) + …
P = ɛ 0[χe(1)E + (1/2)χe(2)E^{2} + (1/6)χe(3)E^{3} ...] where Ei is the i-th component of the electric field strength and χe(n) is the usual 'susceptibility' χ(1) = ɛr - 1 in the absence of higher terms and P(n) is the order of the field-induced polarization in the material.
In an anisotropic medium, χe(1), χe(2) and χe(3) are the medium 'hyper-susceptibilities'; they are tensors of rank 2, 3, and 4, respectively.
Linear optical responses such as absorption, light @P04881@, reflection, and refraction, involving a weak incoming field, are related to P(1). Non-linear techniques are connected to the non-linear polarization PNL. Low order non-linear techniques, such as three-wave mixing, are related to the second order optical polarization P(2). For a random @I03353@ medium (such as a liquid) or for a crystal with a centrosymmetric @U06562@, χe(2) is zero by symmetry and then the lowest order non-linear techniques, as well as the higher order, are related to the third-order optical polarization, P(3), and the corresponding hyper-susceptibility.
Source:
PAC, 2007, 79, 293. 'Glossary of terms used in photochemistry, 3rd edition (IUPAC Recommendations 2006)' on page 402 (https://doi.org/10.1351/pac200779030293)