Debye Material, Drude Material, and Lorentz Material #

This section describes Debye material, Drude material, and Lorentz material.

Debye material, Drude material, and Lorentz material are types of material models that are determined based on dispersion formulas.

Debye Material #

Debye materials are commonly used for dispersive material models that are represented as $\varepsilon_{total}(f)$. For a Debye material with a single pole ($p = 1$), the relation between the permittivity $\varepsilon_{total}$ and the frequency $f$ is expressed as:

$$\varepsilon_{total}(f) = \varepsilon + \frac{\Delta\varepsilon_p}{1 + i2\pi f \gamma_p }$$

Wherein, $\varepsilon$ represents the permittivity;

$\Delta\varepsilon_p$ represents the change in relative permittivity caused by the Debye pole, also referred to as Debye permittivity ($\varepsilon_p$), which is defined as $\Delta\varepsilon_p = \varepsilon_{s,p} - \varepsilon_ {\infty,p}$; $\varepsilon_{s,p}$ represents relative permittivity at stable or zero frequency; $\varepsilon_{\infty,p}$ represents relative permittivity at infinite frequency;

$\gamma_p$ represents pole relaxation time.

Name	Symbol	Units	Range	Default	Description
Permittivity	$\varepsilon$	~	Real number, $\varepsilon\geq1$	1	Real part of the permittivity $\varepsilon_{total}$, dispersion-free
Debye permittivity	$\Delta\varepsilon_p$	~	Real number, $\Delta\varepsilon_p \geq0$	0	Imaginary part of the complex permittivity $\varepsilon_{total}$, Debye permittivity, dispersion-dependent
The pole relaxation time coefficient	$\gamma_p$	~	Real number, $\gamma_p\geq0$	0	Coefficient of pole relaxation time, dispersion-dependent

Material Setting #

In the Materials library window, you can add a Debye material model by selecting Add material>Add new material>Add debye material, and modify the material parameters of the Debye model in the pop-up editing interface to create the desired Debye material model.

Drude Material #

Drude materials are used to describe metallic dispersive material models that are represented using the permittivity $\varepsilon_{total}(f)$. For a Drude material with a single pole ($p = 1$), the relation between the permittivity $\varepsilon_{total}$ and the frequency $f$ is expressed as:

$$\varepsilon_{total}(f) = \varepsilon + \frac{\omega_p^2}{-(2\pi f)^2 + j2\pi f\gamma_p}$$

Wherein, $\varepsilon$ represents the permittivity;

Name	Symbol	Units	Range	Default	Description
Permittivity	$\varepsilon$	~	Real number, $\varepsilon\geq1$	1	Real part of the permittivity $\varepsilon_{total}$, dispersion-free
Drude pole frequency	$\omega_p$	$rad/s$	Real number, $\omega_p \geq0$	0	Angular frequency at the Drude pole, dispersion-dependent
Inverse of the pole relaxation time	$\gamma_p$	$rad/s$	Real number, $\gamma_p\geq0$	0	Reciprocal of the pole relaxation time coefficient, dispersion-dependent

Material Setting #

In the Materials library window, you can add a Drude material model by selecting Add material>Add new material>Add drude material, and modify the material parameters of the Drude model in the pop-up editing interface to create the desired Drude material model.

Lorentz Material #

Lorentz materials are typically used for dispersive material models that are represented as $\varepsilon_{total}(f)$. For a Lorentz material with a single pole ($p = 1$), the relation between the permittivity $\varepsilon_{total}$ and the frequency $f$ is expressed as:

$$\varepsilon_{total}(f) = \varepsilon + \frac{\varepsilon_p\cdot\omega_p^2}{\omega_p^2 + 4\pi j\gamma_p\cdot f - (2\pi f)^2}$$

Wherein, $\varepsilon$ represents the permittivity;
$\varepsilon_p$ represents the Lorentz permittivity;
$\omega_p$ represents the angular frequency at the Lorentz pole;
and $\gamma_p$ represents the Lorentz damping coefficient.

Name	Symbol	Units	Range	Default	Description
Permittivity	$\varepsilon$	~	Real number, $\varepsilon\geq1$	1	Real part of the permittivity $\varepsilon_{total}$, dispersion-free
Lorentz permittivity	$\varepsilon_p$	~	Real number, $\varepsilon_p \geq0$	0	Permittivity at the Lorentz pole, dispersion-dependent
Lorentz pole frequency	$\omega_p$	$rad/s$	Real number, $\omega_p \geq0$	0	Angular frequency at the Lorentz pole, dispersion-dependent
Lorentz damping coefficient	$\gamma_p$	~	Real number, $\gamma_p\geq0$	0	Lorentz damping coefficient ($\omega_p>\gamma_p$)

Material Setting #

In the Materials library window, you can add a Lorentz material model by selecting Add material>Add new material>Add lorentz material, and modify the material parameters of Lorentz model in the pop-up editing interface to create the desired Lorentz material model.