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6.4 Materials

Currently, Angora only supports isotropic materials. Anisotropic materials may also be supported in the future. Please send any comments, suggestions, and requests to help@angorafdtd.org.

Global variable: list Materials

The properties of a certain material type are specified in the Materials list (see section Lists).

 
Materials:
(
    {
        material_tag = "this_material";
        rel_permittivity = 2.0;
        rel_permeability = 1.0;
        electric_conductivity = 0.0;
        magnetic_conductivity = 0.0;
        drude_pole_frequency = 0.0;
        drude_pole_relaxation_time = 0.0;
        transparent = false;
    },
    {
        …
        …
    }
);

In this example, two materials are defined in two respective unnamed groups; only the first being shown in complete detail.

Sub-variable of Materials: string material_tag

This string variable assigns a name to the particular material, so it can be referred to later in the configuration file.

Sub-variable of Materials: floating-point rel_permittivity (default: 1.0)

This variable specifies the relative permittivity (or the dielectric constant) of the material. In SI units, the absolute permittivity of the material is this variable multiplied by the permittivity of free space (8.85418782E-12 F/m).

Sub-variable of Materials: floating-point rel_permeability (default: 1.0)

This variable specifies the relative permeability (or the magnetic constant) of the material. In SI units, the absolute permeability of the material is this variable multiplied by the permeability of free space (4piE-7).

Sub-variable of Materials: floating-point electric_conductivity (units: S/m) (default: 0)

This variable specifies the electric conductivity (in Siemens/m or Mho/m) of the material.

Sub-variable of Materials: floating-point magnetic_conductivity (units: Ohm/m) (default: 0)

This variable specifies the magnetic conductivity (in Ohm/m) of the material.

Sub-variable of Materials: floating-point drude_pole_frequency (units: radians) (default: 0)

This variable specifies the Drude pole frequency (in radians) of the material (see Drude Dispersion).

Sub-variable of Materials: floating-point drude_pole_relaxation_time (units: sec) (default: 0)

This variable specifies the Drude pole relaxation time (in seconds) of the material (see Drude Dispersion).

Sub-variable of Materials: boolean transparent (default: false)

If set to false, any unspecified constitutive parameter is set to its default value. If set to true, unspecified constitutive parameters become transparent, meaning that when an object made up of this material is placed in the grid, the unspecified constitutive parameters are kept unchanged.


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6.4.1 Drude Dispersion

Angora supports frequency-dependent permittivities described by a Drude dispersion model with a single pole. The relative permittivity of a material with a single Drude pole is given by the expression

\begin{displaymath}
\epsilon_r = \epsilon_{r_{\infty}}-{{\omega_p^2}\over{\omega^2-j\omega/\tau_p}}
\end{displaymath}

where $
\omega
$ is the radian frequency, $
\omega_p
$ is the Drude pole frequency (also known as the plasma frequency) of the material, and $
\tau_p
$ is the Drude pole relaxation time of the material.

Currently, Drude dispersion cannot be used for materials extending into the PML (see Perfectly-Matched Layer (PML)). Consequently, the plane-wave injector (see Plane Waves) and the near-field-to-far-field transformer (see Near-Field-to-Far-Field Transformer) cannot handle planar layers with Drude dispersion. This feature may be added in the future.


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