In [[EM.Tempo]], a dielectric material represents a general isotropic, homogeneous material with both electric and magnetic properties. The constitutive [[parameters]] of a dielectric material include permittivity (ε), permeability (μ), electric conductivity (σ) and magnetic conductivity (σ<sub>m</sub>):
[[Image:FDTD17.png|300px]]<math> \mathbf{D} = \epsilon \mathbf{E}, \quad \quad \mathbf{J} = \sigma \mathbf{E} </math>Â :<math> \mathbf{B} = \epsilon \mathbf{H}, \quad \quad \mathbf{M} = \sigma_m \mathbf{H} </math>
where '''E''' and '''H''' are the electric and magnetic fields, respectively, '''D''' is the electric flux density, also known as the electric displacement vector, '''B''' is the magnetic flux density, also known as the magnetic induction vector, and '''J '''and '''M '''are the electric and magnetic current densities, respectively. For example, an imperfect metal can be represented by a dielectric material that has a large, finite, electric conductivity. PEC and PMC, therefore, are the limiting cases of an isotropic dielectric material when σ → ∞ or σ<sub>m</sub> → ∞, respectively.
You may also choose from a [[EM.Cube]]'s list of preloaded material types. Click the button labeled '''Material''' to open [[EM.Cube]]'s Material List dialog. Select the desired material from the list or type the first letter of a material to find it. For example, typing '''V''' selects '''Vacuum '''in the list. Once you close the dialog by clicking '''OK''', the selected material properties fill the parameter fields automatically.
[[FileImage:FDTD5.png|thumb|left|350px|[[EM.Cube]]'s material list]]
=== Anisotropic Materials ===
[[EM.Tempo]] allows you to define a general anisotropic material, whose constitutive [[parameters]], i.e. permittivity ('''ε'''), permeability ('''μ'''), electrical conductivity ('''σ''') and magnetic conductivity ('''σ<sub>m</sub>'''), are all tensorial in nature. Each constitutive parameter in this case is represented by a 3Ã3 matrix:
{|
|[[Image:FDTD16.png|thumb|500px|]]
|}
A "'''Uniaxial'''" material is a special case of an anisotropic material whose constitutive [[parameters]] are all diagonal matrices. Specifying an anisotropic material as <u>'''Uniaxial'''</u> in the [[FDTD Module]] has a very important computational implication. There are six field update equations for uniaxial materials at each time steps: three for the electric field and three for the magnetic field. In this respect, a uniaxial material is similar to an isotropic dielectric material. On the other hand, a fully anisotropic material with non-zero off-diagonal constitutive matrix elements requires twelve update equations at each time step: three equations for the three components of each of the four vector fields '''E''', '''D''', '''H''' and '''B'''. As a result, the time loop for fully anisotropic materials takes much longer time than uniaxial materials.
where <math>\omega _p</math> and <math>\delta_p</math> 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, <math>\Delta \varepsilon_p = \varepsilon_{sp} - \varepsilon_{\infty}</math> represents the change in permittivity due to the p''th'' pole.
[[File:FDTD7.png|thumb|left|200px250px|Debye Add Pole Dialog]]
===Geometrical Rules & Material Hierarchy===
[[Image:fdtd14_tn.png|theumbthumb|400px|Geometric construction of a dielectric-coated metallic cylinder.]]
The following rules apply to the definition of materials and objects in [[EM.Tempo]]: