Click here to learn more about [[FDTD Material Types]].
====Perfect Conductors====
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EM.Tempo offers two types of perfect conductors:
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# '''Perfect Electric Conductor (PEC) Objects:''' The tangential electric field on the surface of this type of perfect conductor is zero. The electric and magnetic fields are assumed to vanish inside the volume of a PEC object. A PEC material is characterized by an infinite electric conductivity (σ = ∞). You can draw solid, surface and [[Curve Objects|curve objects]] as part of a PEC group.
# '''Perfect Magnetic Conductor (PMC) Planes:''' The tangential magnetic field on the surface of this type of perfect conductor is zero. The electric and magnetic fields are assumed to vanish inside the volume of a PMC object. A PMC material is characterized by an infinite magnetic conductivity (σ<sub>m</sub> = ∞). EM.Tempo currently allows only PMC plates (rectangle strips objects) parallel to one of the three principal axes.
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PEC and PMC materials do not have any constitutive material properties that you can modify except for their color or texture.
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====Dielectric Materials====
[[Image:FDTD5.png|thumb|450px|[[EM.Cube]]'s material list]]
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>):
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:<math> \mathbf{D} = \epsilon \mathbf{E}, \quad \quad \mathbf{J} = \sigma \mathbf{E} </math>
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:<math> \mathbf{B} = \epsilon \mathbf{H}, \quad \quad \mathbf{M} = \sigma_m \mathbf{H} </math>
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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.
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You may also choose from [[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.
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==== Anisotropic Materials ====
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[[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:
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[[File:FDTD16.png|600px]]
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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.
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====Dispersive Materials====
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[[File:FDTD7.png|thumb|250px|Debye Add Pole Dialog]]
[[#Perfect Conductors|PEC]], [[#Perfect Conductors|PMC]], [[#Dielectric Materials|dielectric]] and [[#Anisotropic Materials|anisotropic]] materials are non-dispersive. In other words, their constitutive [[parameters]] do not vary with frequency. Most of the materials used in the design of RF and microwave circuits, antennas and systems fall into this frequency-independent category. However, there are other types of materials whose constitutive [[parameters]] exhibit frequency-dependent behaviors. [[EM.Cube]]'s [[FDTD Module]] currently offers four types of dispersive material:
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# Debye Material
# Drude Material (Unmagnetized Plasma)
# Lorentz Material
# Left-handed Metamaterial
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The FDTD simulation engine uses the Auxiliary Differential Equation (ADE) method to model dispersive materials. [[EM.Cube]] allows you to define an arbitrary number of poles for each of the above dispersive material types. Keep in mind that all the objects belonging to the same dispersive material group have the same dispersion properties.
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The complex permittivity of a Debye material with N poles is given by:
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:<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]]-->
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where <math>\varepsilon_{\infty}</math> is the value of the permittivity at infinite frequency, <math>\tau_p</math> is the relaxation time corresponding to the p''th'' pole having the unit of seconds, and <math>\varepsilon_{sp}</math> is the value of the static permittivity (at DC) corresponding to the p''th'' pole. <math>\Delta \varepsilon_p = \varepsilon_{sp} - \varepsilon_{\infty}</math> represents the change in permittivity due to the p''th'' pole.
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Unmagnetized plasmas are typically modeled as Drude materials. The complex permittivity of a Drude material with N poles is given by:
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:<math> \varepsilon(\omega) = \varepsilon_{\infty} - \sum_{p=1}^N \dfrac{{\omega_p}^2}{\omega^2 - j\omega \nu_p} </math>
<!--[[Image:FDTD19(1).png]]-->
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where <math>\omega_p</math> and <math>\nu_p</math> are the angular plasma frequency and angular collision frequency corresponding to the p''th'' pole, respectively, and both are expressed in rad/s. For an unmagnetized plasma, <math>\varepsilon_{\infty} = 1</math>.
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The complex permittivity of a Lorentz material with N poles is given by:
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:<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]]-->
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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.
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==== Inhomogeneous Materials ====
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Coming soon...
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==== Thin Wires ====
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Coming soon...
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{| border="0"
|-
| valign="top"|
[[Image:FDTD2.png|thumb|250px|EM.Tempo's PEC Dialog]]
| valign="top"|
[[Image:FDTD3.png|thumb|250px|EM.Tempo's PMC Dialog]]
| valign="top"|
[[Image:FDTD4.png|thumb|250px|Dielectric Material dialog]]
| valign="top"|
[[Image:FDTD6.png|thumb|250px|[[FDTD Module]]'s Anisotropic Material dialog]]
| valign="top"|
[[Image:FDTD8.png|thumb|250px|Debye Material Dialog]]
|-
|}
===Geometrical Rules & Material Hierarchy===