Polarization (electrostatics)

In electrostatics, the polarization is the vector field that results from permanent or induced electric dipole moments in a dielectric material. The polarization vector P is defined as the dipole moment per unit volume.

In a homogeneous linear and isotropic dielectric medium, the polarization is aligned with and proportional to the electric field E. In an anisotropic material, the polarization and the field are not necessarily in the same direction. Then, the i^th component of the polarization is related to the j^th component of the electric field according to:

Pi =	∑	ε0χijEj,
	j

where ε₀ is the permittivity of free space, and χ is the electric susceptibility tensor of the medium.

If the polarization P is not proportional to the electric field E, the medium is termed nonlinear and is described by the field of nonlinear optics. If the direction of P is not aligned with E, as in many crystals, the medium is anisotropic and is described by crystal optics.