==Defining The Physical Structure==
[[Image:FDTD1.png|thumb|left|200px|[[FDTD Module]]'s Navigation Tree.]]
In [[EM.Cube]]'s [[FDTD Module]], a physical structure consists of sets of objects that are grouped together and identified by their material types. Materials are divided into seven categories that are listed under the '''Physical Structure''' node at the top of the Navigation Tree:
Under each material node, you can create new material groups of the same type/category but with different properties (color, texture, or electric and magnetic constitutive [[parameters]]). These material groups are used to organize the CAD objects you draw in the project workspace or import from external model files. When you create a new geometrical object such as a Box or a Sphere, it is inserted under the currently active material type. There is only one material group that is active at any time. It is recommended that you first create material groups, and then draw new objects as part of the active material group. However, if you start a new EM.Tempo project from scratch, and start drawing a new object without having previously defined any material groups, a new default PEC group is created and added to the navigation tree to hold your new CAD object.
{| border="0"To define a new material group, follow these steps:|-| valign="top"|* Right click on the name of the desired material in the navigation tree and select '''Insert New Material...''' from the contextual menu. A material dialog opens up.[[Image:FDTD1* Specify a '''Label''' and '''Color''' (and optional Texture) for the material group being created.png|thumb|left|200px|* Either accept the default values of the available material [[FDTD Moduleparameters]]or enter new values.* Click the 's Navigation Tree''OK''' button of the dialog to accept the changes and close it.]]|-|}Once a new material node has been created on the navigation tree, it becomes the "Active" material group of the project workspace. You can now draw objects in the project workspace, and they will be added under the active node. All the objects belonging to the same material group share the same color and material properties. You can also move objects among different material groups using their contextual menu. Â
===Perfect Conductors===
# '''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.
PEC and PMC materials do not have any constitutive material properties that you can modify except for their color or texture. Note that [[FDTD Module]]'s PMC materials are different in nature than the PMC traces you will find in [[EM.Cube]]'s [[Planar Module]]. In the latter, the PMC term is applied to slot traces, which represent finite-sized cut-out objects (areas) from an infinite horizontal PEC ground plane. [[FDTD Module]]'s PMC objects, by contrast, can be arbitrarily oriented [[Surface Objects|surface objects]] or impenetrable [[Solid Objects|solid objects]] of finite extents. To define a new PEC or PMC material, follow these steps: * Right click on either the '''PEC''' or '''PMC''' items in Navigation Tree and select '''Insert New PEC/PMC...''' from the contextual menu.* Specify a '''Label''' and '''Color''' (and optional Texture) for the PEC or PMC material being created.* Click the '''OK''' button of the dialog to accept the changes and close it. Once a PEC or PMC node has been created on the Navigation Tree, you can draw objects in the project workspace, and they will be added under that node. In other words, all the CAD objects belonging to a PEC or PMC group have the same color or texture.
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===Dielectric Materials===
In [[EM.Cube]]'s [[FDTD ModuleTempo]], 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]]
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.
To define a new Dielectric material, follow these steps:Â * Right click on the '''Dielectric''' item of the Navigation Tree and select '''Insert New Dielectric...''' from the contextual menu.* Specify a '''Label''', '''Color''' (and optional Texture) and the electromagnetic properties of the dielectric material to be created: '''Relative Permittivity''' (ε<sub>r</sub>), '''Relative Permeability''' (μ<sub>r</sub>), '''Electric Conductivity''' (σ) and '''Magnetic Conductivity''' (σ<sub>m</sub>).* You may also choose from a 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.* Click the '''OK''' button of the dielectric material dialog to accept the changes and close it.Â
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[[Image:FDTD6.png|thumb|250px|[[FDTD Module]]'s Anisotropic Material dialog]]
[[EM.Cube]]'s [[FDTD ModuleTempo]] 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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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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To define a new Anisotropic material, follow these steps:
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* Right click on the '''Anisotropic''' item of the Navigation Tree and select '''Insert New Anisotropic...''' from the contextual menu.
* Specify a '''Label''' and '''Color''' (and optional Texture) for the anisotropic material being created.
* By default, the box labeled '''Uniaxial Material''' is checked. This means that all the constitutive matrices are diagonal. The off-diagonal elements of '''ε''', '''μ''', '''σ''' and ''' σ<sub>m</sub>''' matrices are all set to zero and greyed out. You need to enter values for the diagonal elements of these matrices. To set values for the off-diagonal elements of the constitutive matrices, you have to remove the "Anisotropic" check mark first.
* Click the '''OK''' button of the dialog to accept the changes and close it.
===Dispersive Materials===
[[#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 three four types of dispersive material:
# Debye Material
# Drude Material (Unmagnetized Plasma)
# Lorentz Material
# Left-handed Metamaterial
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.
===Geometrical Rules & Material Hierarchy===
[[Image:fdtd14_tn.png|theumb|400px|Geometric construction of a dielectric-coated metallic cylinder.]]The following rules apply to the definition of materials and objects in [[EM.Cube]]'s [[FDTD ModuleTempo]]:
* Under the [[#Perfect Conductors|PEC]] and [[#Perfect Conductors|PMC]] material categoriescategory, you can define all types of solid , and surface and [[Surface Curve Objects|surface curve objects]].* Under the [[#Perfect Conductors|PMC]] category, you can define only define rectangle strip objects parallel to the principal planes.
* Under the [[#Dielectric Materials|Dielectric]], [[#Anisotropic Materials|Anisotropic]] and [[#Dispersive Materials|Dispersive]] material categories, you can define only [[Solid Objects|solid objects]].
* Under the [[#Perfect Conductors|PEC]] material Inhomogeneous Material category, you can also only import a Cartesian ".CAR" data file.* Under the Thin Wire category, you can only define [[Curve Objects|curve line objects]] such as lines, polylines, etc. parallel to model wire structuresthe principal axes.
[[EM.Cube]]'s [[FDTD ModuleTempo]] allows overlapping objects, although it is generally recommended that object overlaps be avoided in favor of clearly defined geometries and object boundaries. If two or more objects of the same material type and group overlap, they are merged using the Boolean union operation during the mesh generation process. If two overlapping objects belong to two different material categories, then the material properties of the FDTD cells in the overlap region will follow the [[FDTD Module]]EM.Tempo's material priority hierarchy rule. In that case, the overlap area cells will always be regarded as having the material type of the higher priority. According to this rule, the material types are ordered from the highest priority to the lowest in the following manner:
# [[#Perfect Conductors|PEC]]
# [[#Dielectric Materials|Dielectric]]
It is therefore recommended to avoid overlapping objects belonging to different material groups within the same material category. To overlap two PEC objects with different colors does not matter. But to overlap two dielectric solids with different permittivity will create ambiguity. In that caseIf planned carefully, the FDTD simulation will run and complete successfully, but you will not be clear as to which permittivity value was used for the cells of the overlap region. Sometimes taking advantage of [[FDTD Module]]EM.Tempo's material priority hierarchy rule makes would make the construction of complex objects easier. For example, a dielectric coated metallic cylinder can be modeled by two concentric cylinders: an inner PEC of smaller radius and an outer dielectric of larger radius as shown in the illustration below. The portion of the dielectric cylinder that overlaps the inner PEC cylinder is ignored by the FDTD engine because the PEC cylinder takes precedence over the dielectric in the material hierarchy. Alternatively, you can model the same structure by an inner solid PEC cylinder enclosed by an outer hollow pipe-shaped dielectric cylinder. The hollow solid can be built by extruding a planar ring or by subtracting two concentric cylinders. The first configuration utilizing material hierarchy is, of course, much easier to construct. {{isoimg|fdtd14_tn.png|Geometric construction of a dielectric-coated metallic cylinder.}}
===Moving Objects Among Material Groups===