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 polarizationpower-law dependence on the external electric field.
- Mathematically it is defined as the electric dipole moment change per volume resulting from absorption of radiation of optical frequencies, defined as , where is the electric displacement, the electric constant (vacuum permittivity) , and the strength of the radiation electric field. A dielectric medium is characterized by the constitutive relation where 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 , 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 nth-order in the field is denoted as Thus, the following equations apply,andwhere is the i-th component of the electric field strength and is the usual 'susceptibility' in the absence of higher terms and is the order of the field-induced polarization in the material.In an anisotropic medium, , and are the medium 'hyper-susceptibilities'; they are tensors of rank 2, 3, and 4, respectively.Linear optical responses such as absorption, light propagation, reflection, and refraction, involving a weak incoming field, are related to . Non-linear techniques are connected to the non-linear polarization . Low order non-linear techniques, such as three-wave mixing, are related to the second order optical polarization . For a random isotropic medium (such as a liquid) or for a crystal with a centrosymmetric unit cell, 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, , and the corresponding hyper-susceptibility.
PAC, 2007, 79, 293 (Glossary of terms used in photochemistry, 3rd edition (IUPAC Recommendations 2006)) on page 402