Glossary entry

Permittivity and dielectric constant

How strongly a material polarizes in an electric field, ε = ε_r ε₀ with ε₀ = 8.854 × 10⁻¹² F/m. At optical frequencies the relative permittivity of a non-magnetic material is the square of the refractive index: 2.09 for silica and 12.1 for silicon at 1550 nm. The static value is much larger for silica, about 3.8, and for water, about 80.

Optics fundamentalsUpdated September 2026

When an electric field is applied to a material, its charges shift slightly and it becomes polarized. The permittivity $\varepsilon$ measures how much: the electric displacement is $\mathbf{D} = \varepsilon\mathbf{E} = \varepsilon_r\varepsilon_0\mathbf{E}$ , where $\varepsilon_0$ = 8.8541878 × 10⁻¹² F/m is the vacuum permittivity and $\varepsilon_r$ the relative permittivity, also called the dielectric constant. It is dimensionless and equals 1 in vacuum.

Link to the refractive index

For a non-magnetic material the refractive index is the square root of the relative permittivity at the frequency of the light,

n = \sqrt{\varepsilon_r},

and when the material absorbs, both are complex, $\tilde n^2 = \tilde\varepsilon_r$ , as described under complex refractive index. At 1550 nm fused silica ( $n$ = 1.444) has $\varepsilon_r$ = 2.09 and silicon ( $n$ ≈ 3.48) about 12.1.

Frequency dependence

The permittivity depends on how fast the field changes, because different polarization mechanisms can follow the field only up to certain frequencies. Permanent molecular dipoles reorient up to microwave frequencies, ions in a lattice move up to the infrared, and only the electrons respond at optical frequencies. The static dielectric constant is therefore often far larger than $n^2$ . Water has a static value near 80 but an optical value of $1.333^2$ = 1.78; fused silica has about 3.8 at low frequency against 2.09 at 1550 nm. For silicon, a covalent crystal with only electronic polarization, the static value of 11.7 is close to the optical 12.1. This is why capacitor and circuit-board data cannot be used for optical design, and why the Kramers-Kronig relations tie the optical index to absorption bands, some of them far outside the optical range.

Anisotropy and field dependence

In crystals the permittivity is a tensor, which gives birefringence. In some materials it depends on an applied field, the basis of the electro-optic effect, or on carrier density, the basis of the plasma dispersion effect used in silicon modulators. In metals and doped semiconductors the free electrons make the real part of the permittivity negative below the plasma frequency, which is why metals reflect and why surface plasmons exist at metal-dielectric interfaces.

Measurement

At optical frequencies the permittivity is obtained from the measured refractive index and extinction coefficient, by refractometry, prism goniometry or ellipsometry. At radio and microwave frequencies it is measured with capacitance bridges, resonant cavities or transmission-line methods using a vector network analyzer.

References: J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999), Ch. 4 and 7; CODATA recommended values of the fundamental physical constants (NIST).