{{Note|Small values of inductance may result in the divergence of the FDTD numerical scheme. To avoid this problem, you need to increase the mesh resolution and adopt a higher mesh density. This, of course, may lead to a much longer computation time.}}
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===Defining Ports===
[[Image:FDTD48.png|thumb|200px250px|The Port Definition dialog]]
Ports are used to order and index sources for circuit parameter calculations like S/Y/Z [[parameters]]. That is why they are defined in the '''Observables''' section of Navigation Tree. In [[EM.Cube]]'s [[FDTD Module]], you can define ports at the location of '''Lumped Sources''', '''Waveguide Sources''' and '''Distributed Sources'''. In other words, ideal sources or other types of sources cannot be used to define ports or calculate port characteristics.
Ports are defined in the '''Observables''' section of the Navigation Tree. Right click on the '''Port Definition''' item of the Navigation Tree and select '''Insert New Port Definition...''' from the contextual menu. The Port Definition Dialog opens up, showing the default port assignments. If you have N sources in your physical structure, then N default ports are defined, with one port assigned to each source according to their order on the Navigation Tree.
[[Image:FDTD49.png|thumb|250px350px|Reassigning sources to ports and defining coupled ports.]]
You can define any number of ports equal to or less than the total number of sources in your project. The Port List of the dialog shows a list of all the ports in ascending order, with their associated sources and the port's characteristic impedance, which is 50O by default. You can delete any port by selecting it from the Port List and clicking the '''Delete '''button of the dialog. Keep in mind that after deleting a port, you will have a source in your project without any port assignment. Make sure that is what you intend. When you delete one or more ports in your project, their associated sources become free and "available" for either defining new ports or reassignment to the other ports. To define a new port, click the '''Add '''button of the Port Definition dialog to open the "Add Port" dialog. On the left side of this dialog, you will see a table containing all the available sources. Select one or more ports and use the right arrow ('''--->''') button to move them to the table on the right side, labeled "Associated". These ports are now associated with the new port being defined. You can move sources from the "Associated" table back to the "Available" table on the left using the left arrow ('''<---''') button of the dialog. You can associate more than one source with the same port. In that case, you will have coupled sources, collectively representing a coupled port.
===Plane Wave Source===
In [[EM.Cube]]'s [[FDTD ModuleTempo]], 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.Cube]]'s [[FDTD ModuleTempo]] provides the following polarization options:
* TMz
* RCPz
The direction of incidence is defined through the θ and φ angles of the unit propagation vector in the spherical coordinate system. The values of these angles are set in degrees in the boxes labeled '''Theta''' and '''Phi'''. The default incidence angles are θ = 180° and φ = 0° representing a normally incident plane wave propagating along the -Z direction with a +X-polarized E-vector. You select the polarization from the five radio buttons in the "Polarization" section of the dialog. In the TM<sub>z</sub> and TE<sub>z</sub> polarization cases, the magnetic and electric fields are parallel to the XY plane, respectively. The components of the unit propagation vector and normalized E- and H-field vectors are displayed in the source dialog. This way of defining a plane wave source is more convenient when the structure is laid out along the XY plane and Z-axis such as layered and periodic structures. In the more general case of custom linear polarization, besides the incidence angles, you have to enter the components of the unit electric '''Field Vector'''. However, two requirements must be satisfied: '''ê . ê''' = 1 and '''ê à k''' = 0 . This can be enforced using the '''Validate''' button at the bottom of the dialog. If these conditions are not met, an error message is generated. The left-hand (LCP) and right-hand (RCP) circular polarization cases are restricted to normal incidences only (θ = 180°).
Since the FDTD technique EM.Tempo requires a finite simulation domain, it also needs 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. To create a new plane wave source, follow these steps: * Right click on the '''Plane Waves''' item in the '''Sources''' section of the Navigation Tree and select '''Insert New Source...''' The Plane wave Dialog opens up.* 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 grid the world coordinate system (GCSWCS).* In the Field Definition section of the dialog, you can enter the '''Amplitude''' of the incident electric field in V/m and its '''Phase''' in degrees. The default field Amplitude is 1 V/m with a zero Phase.* The direction of the Plane Wave is determined by the incident '''Theta''' and '''Phi''' angles in degrees. You can also set the '''Polarization''' of the plane wave and choose from the five options described earlier. A plane wave box placed around a PEC sphere object. The trident at the corner of the box shows the propagation vector as well as the E-field and H-field polarization vectors.
===Gaussian Beam Source===
[[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 w<sub>0</sub>; 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 θ = λ<sub>0</sub>/(π.ω<sub>0</sub>) (λ<sub>0</sub> is the free-space wavelength).
{{note|The beam radius has Similar to be at least λthe plane wave source, a Gaussian beam is define by spherical angles of incidence Theta and Phi in degrees. You can also set the '''Polarization''' of the Gaussian Beam and choose from the three options: '''TM<sub>0z</sub>''', '''TE<sub>z</π; otherwisesub>''' and '''User Defined'''. A default Excitation Box three cells away from the bounding box of the geometry is initially suggested, strong fields appear outside i.e. the radio button '''Size: Default''' is selected by default. The radio button '''Size: Custom''' allows you to set the excitation box}}manually by modifying the coordinates of '''Corner 1''' (front lower left) and '''Corner 2''' (back upper right) of the box in the world coordinate system (WCS). The Gaussian beam box is displayed in the project workspace as a green wireframe box enclosing the structure. A translucent green circle normal to the direction propagation shows the footprint of Gaussian beam at its focal (waist) point.
The Unlike plane waves, a Gaussian beam box is displayed a localized field. Therefore, you need to specify the '''Beam Properties'''. This includes the coordinates of the beam's '''Focus''', which is the beam's waist center in the project workspace world coordinate system as well as a green wireframe box enclosing the structurebeam's '''Radius''' in project units. To define a new Gaussian Beam source, follow these steps:
* Right click on the '''Gaussian Beam''' item in the '''Sources''' section of the Navigation Tree and select '''Insert New Source...''' This opens up the Gaussian Beam Dialog.* Similar to the plane wave, a default Excitation Box three cells away from the bounding box of the geometry is suggested, i.e. the radio button '''Size: Default''' is selected by default. {{note|The radio button '''Size: Custom''' allows you beam radius has to set the excitation box manually by modifying the coordinates of '''Corner 1''' (front lower left) and '''Corner 2''' (back upper right) of the box in the grid coordinate system (GCS).* In the Field Definition section of the dialog, you can enter the Amplitude of incident electric field in V/m. The default field '''Amplitude''' is 1 V/m. Note that you do not specify the phase of a Gaussian beam because the beam focus already contains the phase information.* The direction of the Gaussian Beam is determined by the incident '''Theta''' and '''Phi''' angles in degrees. You can also set the '''Polarization''' of the Gaussian Beam and choose from the three options: '''TMbe at least λ<sub>z0</sub>''', '''TE<sub>z</sub>''' and '''User Defined'''.* Unlike plane wavesπ; otherwise, a Gaussian beam is a localized field. Therefore, you need to specify strong fields appear outside the '''Beam Properties'''. This includes the coordinates of the beam's '''Focus''', which is the beam's waist center in the world coordinate system as well as the beam's '''Radius''' in project units. A Gaussian beam excitation box placed around a horizontal PEC plate. The trident at the corner of the box shows the propagation vector as well as the E-field and H-field polarization vectors. The titled transparent green circle shows the footprint of Gaussian beam at its focal (waist) point.}}
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