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: **

- Mathematically it is defined as the @E01929@ change per volume resulting from absorption of radiation of optical frequencies, defined as \(P = D - \epsilon_{0}E\), where \(D\) is the @E01930@, \(\varepsilon_{0}\) the electric constant (vacuum @P04507@) , and \(E\) the strength of the radiation electric field. A dielectric medium is characterized by the constitutive relation \(D = \epsilon_{0}\, \chi ^{(1)}\) where \(\chi ^{(\text{1})} = \varepsilon_{r} - 1\) 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.
- The polarization component to the
*n*th-order in the field is denoted as \(P^{(\text{n})}\) Thus, the following equations apply,

\(P = P^{(\text{1})} + P_{\text{NL}}\) and \(P_{\text{NL}} = P^{(\text{2})} + P^{(\text{3})} + \dots\)

\(P = \epsilon _{0}\left [ \chi _{e}^{(1)}E\: + (1/2)\chi _{e}^{(2)}E^{2}\: + (1/6)\chi _{e}^{(3)}E^{3} + \dots \right ] = P^{(1)} + P^{(2)} + P^{(3)} + \dots\) where \(E^{\text{i}}\) is the*i*-th component of the electric field strength and \(\chi _{\text{e}}^{(\text{n})}\) is the usual 'susceptibility' \(\chi ^{(\text{1})} = \varepsilon_{r} - 1\) in the absence of higher terms and \(P^{(\text{n})}\) is the order of the field-induced polarization in the material.

In an anisotropic medium, \(\chi _{\text{e}}^{(1)}\), \(\chi _{\text{e}}^{(2)}\) and \(\chi _{\text{e}}^{(3)}\) 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 \(P^{(\text{1})}\). Non-linear techniques are connected to the non-linear polarization \(P_{\text{NL}}\). Low order non-linear techniques, such as three-wave mixing, are related to the second order optical polarization \(P^{(\text{2})}\). For a random @I03353@ medium (such as a liquid) or for a crystal with a centrosymmetric @U06562@, \(\chi _{\text{e}}^{(2)}\) 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, \(P^{(\text{3})}\), and the corresponding hyper-susceptibility.

PAC, 2007, 79, 293. 'Glossary of terms used in photochemistry, 3rd edition (IUPAC Recommendations 2006)' on page 402 (https://doi.org/10.1351/pac200779030293)