polarization, P in spectrochemical analysis

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.
  1. Mathematically it is defined as the electric dipole moment change per volume resulting from absorption of radiation of optical frequencies, defined as P = D − ɛ 0 E, where D is the electric displacement, ɛ 0 the electric constant (vacuum permittivity) , and E the strength of the radiation electric field. A dielectric medium is characterized by the constitutive relation D = ɛ 0 χ (1) where χ (1) = ɛ 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.
  2. The polarization component to the nth-order in the field is denoted as P (n) Thus, the following equations apply,
    P = P (1) + P NL and P NL = P (2) + P (3) + …
    P = ɛ 0 χ e (1) E + 1/2 χ e (2) E 2 + 1/6 χ e (3) E 3 + … = P (1) + P (2) + P (3) + …
    where E i is the i-th component of the electric field strength and χ e (n) is the usual 'susceptibility' χ (1) = ɛ r − 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, χ e (1), χ e (2) and χ e (3) 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 P (1). Non-linear techniques are connected to the non-linear polarization P NL. Low order non-linear techniques, such as three-wave mixing, are related to the second order optical polarization P (2). For a random isotropic medium (such as a liquid) or for a crystal with a centrosymmetric unit cell, χ 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 (3), and the corresponding hyper-susceptibility.
PAC, 2007, 79, 293 (Glossary of terms used in photochemistry, 3rd edition (IUPAC Recommendations 2006)) on page 402