Type:2-Tensor, or section
Range:[v_1, …, v_9]
Default:[1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0]

Specifies the relative permittivity \TField{\varepsilon}^{(\mathrm{rel})}. The relative permittivity is dimensionless. It defines the permittivity as \varepsilon=\varepsilon_0 \TField{\varepsilon}^{(\mathrm{rel})}, where \varepsilon_0 is the vacuum permittivity in units farads per meter, \units{F/m} (which equals to units coulomb per volt per meter, \units{CV^{-1}m^{-1}}). The permittivity \varepsilon relates the electric displacement \TField{D} to the electric field strength \TField{E},

\TField{D} &=\varepsilon \TField{E}

For the extension to bi-anistropic materials see RelBiPermittivity.

A constant relative permittivity can be defined by assigning a rank-2 tensor:

Material {
  # defines a constant relative permittivity
  RelPermittivity =
      [..., ..., ...
       ..., ..., ...
       ..., ..., ...]

Assign a scalar for an isotropic relative permittivity:

Material {
  RelPermittivity = 2.25

For more general cases, the relative permittivity may be given as a section in order to deal with space, time, frequency and parameter dependent definitions:

# define the relative permittivity as a section
RelPermittivity {
  Python {...}
  PhotoElasticCorrection { ... }
  ThermoOpticalCorrection { ... }

Field definitions within the section RelPermittivity are summed up. Consult the subsequent sections to see which types of field definitions are allowed.


The refractive index (index of refraction, n) of an optical medium relates to the relative permittivity \TField{\varepsilon}^{(\mathrm{rel})} and relative permeability \TField{\mu}^{(\mathrm{rel})} as n=\sqrt{\TField{\varepsilon}^{(\mathrm{rel})} \TField{\mu}^{(\mathrm{rel})}}. In most cases, \TField{\mu}^{(\mathrm{rel})}=1. Therefore, e.g., for an isotropic material with refractive index n=1.5, the relative permittivity is specified as RelPermittivity = 2.25.

Lossy materials can be modeled using a complex refractive index, \tilde{n}=n+i\kappa, with \kappa>0, e.g., \tilde{n}=1.5+0.1i . In this example, a complex relative permittivity is specified: RelPermittivity = 2.24+0.3i. (Please note the sign convention, where a positive \kappa relates to absorption, c.f., TimeHarmonic.)