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/* Dispersive Materials */
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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</submath> \Delta \varepsilon_p = ε<sub>\varepsilon_{sp</sub> } - ε<sub>∞\varepsilon_{\infty}</submath> represents the change in permittivity due to the p''th'' pole.
Unmagnetized plasmas are typically modeled as Drude materials. The complex permittivity of a Drude material with N poles is given by:
:<math> \varepsilon(\omega) = \varepsilon_{\infty} - \sum_{p=1}^N \dfrac{{\omega_p}^2}{\omega^2 - j\omega \nu_p} </math>
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The complex permittivity of a Lorentz material with N poles is given by:
:<math> \varepsilon(\omega) = \varepsilon_{\infty} - \sum_{p=1}^N \dfrac{\Delta \varepsilon_p {\omega_p}^2}{\omega^2 - 2j\omega \delta_p - {\omega_p}^2}, \quad \Delta \varepsilon_p = \varepsilon_{sp} - \varepsilon_{\infty} </math><!--[[Image:FDTD20.png]]-->
where ω<sub>p</sub> and delta δ<sub>p</sub> are the angular resonant frequency and angular damping frequency corresponding to the p''th'' pole, respectively, and both are expressed in rad/s. Similar to a Debye material, Δε<sub>p</submath> \Delta \varepsilon_p = ε<sub>\varepsilon_{sp</sub> } - ε<sub>∞\varepsilon_{\infty}</submath> represents the change in permittivity due to the p''th'' pole.
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