In electromagnetism, the permittivity ε of a medium is the ratio D / E where D is the electric displacement in coulombs per square metre (C/m2) and E is the electric field strength in volts per metre (V/m). In the common case of an isotropic medium, D and E are parallel and ε is a scalar, but in more general anisotropic media this is not the case and ε is a rank-2 tensor (causing birefringence).
Permittivity is specified in farads per metre (F/m). It can also be defined as a dimensionless relative permittivity, or dielectric constant, normalized to the absolute vacuum permittivity ε0 = 8.854 10-12F/m.
When an electric field is applied, a current flows. The total current flowing in a real medium is in general made of two parts: a conduction current and a displacement one. A perfect dielectric is a material that shows displacement current only.
In case of lossy medium (i.e. when the conduction currents are not negligible) the total current density flowing is:
where , σ is the conductivity (responsible for conduction current) of the medium and εd is the relative permittivity (responsible for displacement current).
In this formalism the complex permittivity ε* is defined as:
At a given frequency, the imaginary part of ε leads to absorption loss if it is negative (in the above sign convention for frequency) and gain if it is positive. (More generally, one looks at the imaginary parts of the eigenvalues of the anisotropic dielectric tensor.)