# Permittivity (1D FDTD)

**Permittivity** $\varepsilon$ describes the electric response of a material. For the linear medium used by FDTD OpenMP, electric flux density is proportional to the electric field:

$$
D_z=\varepsilon E_z,\qquad \varepsilon=\varepsilon_r\varepsilon_0
$$

Relative permittivity $\varepsilon_r$ compares the material with vacuum. New simulations use $\varepsilon_r = 1$ everywhere. Holding permeability fixed, increasing permittivity lowers the lossless wave speed and changes wave impedance. An interface between regions can therefore reflect part of an incoming wave.

`Fdtd_EzSimSetEps()` assigns absolute permittivity to a half-open cell range. The command-line option `--set-eps-r=4,80,120`, for example, assigns four times the vacuum permittivity to cells 80 through 119. This creates a dielectric layer within the domain.

Permittivity enters the electric [[fdtd-openmp-update-coefficients|update coefficients]], controlling how strongly neighboring magnetic samples change $E_z$. It also enters the electric loss factor when conductivity is nonzero.

The material model stores one scalar permittivity per cell. It does not model a frequency-dependent response, anisotropy, or nonlinear dependence on field strength.