The complex permittivity of a Debye material with N poles is given by:
:<math> \varepsilon (\omega) = \varepsilon_\infty + \sum_{p=1}^N \dfrac{\Delta \varepsilon_p}{1 + j\omega \tau_p}, \quad \Delta \varepsilon_p = \varepsilon_{sp} - \varepsilon_\infty </math><!--[[Image:FDTD18(2).png]]-->
where ε<sub>∞</sub> is the value of the permittivity at infinite frequency, τ<sub>p</sub> is the relaxation time corresponding to the p''th'' pole having the unit of seconds, and ε<sub>sp</sub> is the value of the static permittivity (at DC) corresponding to the p''th'' pole. Δε<sub>p</sub> = ε<sub>sp</sub> - ε<sub>∞</sub> represents the change in permittivity due to the p''th'' pole.