polarization, $P$

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 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.
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.

Source:

PAC, 2007, 79, 293 (Glossary of terms used in photochemistry, 3rd edition (IUPAC Recommendations 2006)) on page 402