Changes

{{Note|You can import external objects only to '''[[CubeCAD]]'''. You need to move the imported objects form [[CubeCAD]] to EM.Tempo as described above.}}

====Perfect Conductors====

EM.Tempo offers two types of perfect conductors:

PEC and PMC materials do not have any constitutive material properties that you can modify except for their color or texture.

[[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_m):

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.

[[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_m'''), are all tensorial in nature. Each constitutive parameter in this case is represented by a 3×3 matrix:

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.

[[File:FDTD7.png|thumb|250px|Debye Add Pole Dialog]]

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.

Coming soon...

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Once you define a source, you can always changes its [[parameters]] later from its property dialog, which can be accessed from its right-click contextual menu. You can also delete sources.

An ideal source acts as a voltage source in series with an internal resistance that can be placed between any two adjacent mesh grid nodes anywhere in the computational domain. The ideal source is displayed as a small orange arrow in the project workspace. By default, [[EM.Tempo]] creates a +Z-directed ideal source located at the origin of coordinates (0, 0, 0). You can change the direction of the ideal source to ±X, ±Y or ±Z.

A lumped source is the most commonly used way of exciting a structure in [[EM.Tempo]]. A lumped source is indeed an ideal source that must be placed on a line object that is parallel to one of the three principal axes and shows up as a small red arrow on the host line. Lumped sources are typically used to define ports and compute the port characteristics like S/Y/Z [[parameters]]. Lumped sources can also be place on line arrays. The property dialog of a lumped source has a drop-down list that contains the name of all the legitimate line objects (i.e. lines that are parallel to one of the principal axes) and line arrays. The '''Offset''' parameter of a lumped source is its distance from the start point of the host line. A lumped source by default is placed at the center of its host line. In other words, the default offset value is equal to half the length of the host line object.

{{Note|In order to create a lumped source, you must have at least one line object or line array in the project workspace.}}

A real waveguide structure is usually excited using some type of strategically located probe mechanism. EM.Tempo also provides the '''Waveguide Source''', a special type of source that excites a prescribed TE₁₀ modal field distribution in a hollow rectangular waveguide structure. The scattering [[parameters]] are calculated from knowledge of incident and reflected fields at designated waveguide ports. Waveguide sources typically provide more accurate results for scattering [[parameters]] compared to lumped ports as they represent the actual dominant propagating modes at the transmission line ports.

A waveguide source must be placed across a rectangular waveguide which is oriented along one of the three principal axes. In other words, the plane of the waveguide source must be parallel to one of the principal (XY, YZ or ZX) coordinate planes. The property dialog of the waveguide source provides a drop-down list containing the name of all the legitimate box objects or box arrays. The waveguide source is displayed as an orange rectangle with a cross and a perpendicular small orange arrow across the host box object. The '''Offset''' parameter of a waveguide source is its distance from the base of the host box. A waveguide source by default is placed at the center of its host box. In other words, the default offset value is equal to half the longitudinal dimension of the host box object.

Waveguide sources are a special case of distributed sources in [[EM.Tempo]]. A Distributed Source is defined in a rectangular plane of finite extents, parallel to one of the three principal coordinate planes. An impressed electric field component is assumed across the specified rectangular area, which pumps energy into the computational domain. The current version of [[EM.Tempo]] provides three spatial field profiles for a distributed source:

In the '''Excitation Plane''' section of the dialog, first you have to select the orientation of the source plane. The dropdown list labeled '''Direction''' gives three options: '''X, Y''' and '''Z''', which create planes parallel to the YZ, ZX and XY principal planes, respectively. Depending on the choice of the plane orientation, another dropdown list labeled '''Field Dir''' gives four options for the direction of the source field component. For example, the default plane orientation is X (parallel to the YZ-Plane) and the available field directions are +Y, -Y, +Z and -Z. Next, you have to enter the coordinates of two opposite corners of the source plane: the lower left and upper right corners. You can type in values for the X, Y, Z coordinates or you can use the spin buttons to slide the default source planes in the project workspace.

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[[Image:FDTD45.png|thumb|250px| EM.Tempo's Distributed Source dialog]]

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In [[EM.Tempo]], you can excite a structure with an arbitrary incident plane wave and compute its scattering pattern or bi-static radar cross section. A plane wave excitation is defined by its propagation vector indicating the direction of incidence and its polarization. [[EM.Tempo]] provides the following polarization options:

EM.Tempo requires a finite plane wave incidence surface to calculate the excitation. When you create a plane wave source, a plane wave box is created as part of its definition. A trident symbol on the box shows the propagation vector as well as the E-field and H-field polarization vectors. The time domain plane wave excitation is calculated on the surface of this box and injected into the computational domain. The plane wave box is displayed in the project workspace as a purple wireframe box enclosing the structure. Initially, the radio button '''Size: Default''' is selected. With this option, the boundaries of the excitation box always have a distance of three cells from the bounding box of the geometry and cannot be changed. The radio button '''Size: Custom''' allows you to set the excitation box manually. The values for the coordinates of '''Corner 1''' and '''Corner 2''' can now be changed. Corner 1 is the front lower left corner and Corner 2 is the rear upper right corner of the box. The box has to be defined in the world coordinate system (WCS).

[[EM.Cube]] gives you an option to illuminate objects with a focused beam instead of a uniform plane wave. The focused beam is a Gaussian beam, which is a solution of the paraxial approximation to the Helmholtz equation. The fundamental Gaussian beam is rotationally-symmetric about its propagation axis, and its transverse field distribution follows a Gaussian function profile. The critical parameter is the beam radius w₀; it is the point where the field drops by 1/e from its value at the center. The beam opens up into a cone along the propagation direction, with a cone angle of tan &theta; = &lambda;₀/(&pi;.&omega;₀) (&lambda;₀ is the free-space wavelength).

{{note|The beam radius has to be at least &lambda;₀/&pi;; otherwise, strong fields appear outside the excitation box}}

Coming soon...

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==Running FDTD Simulations==