==Modeling 3D Periodic Structures Using FDTDin EM.Tempo==
EM.Tempo allows you to simulate doubly periodic structures with periodicities along the X and Y directions. Many interesting structures such as frequency selective surfaces (FSS), electromagnetic band-gap (EBG) structures and metamaterial structures can be modeled using periodic geometries. In the case of an infinitely extended periodic structure, it is sufficient to analyze only a unit cell. In the FDTD method, this is accomplished by applying periodic boundary conditions (PBC) at the side walls of the computational domain.
Click here to learn more about [[Time Domain Simulation of Periodic Structures]].
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[[Image:FDTD134.png|thumb|320px|EM.Tempo's Periodicity Settings dialog]]
===Setting Up A Periodic Unit Cell===
Using [[EM.Cube]]'s [[FDTD Module]], you can simulate complex 3D periodic structures. A periodic structure is one that repeats itself infinitely along one, two or three directions. In this release of [[EM.Cube]]'s [[FDTD ModuleTempo]], the periodicity is limited to the X-Y plane. In other words, the periodic structure repeats itself along the X- and Y-axes, but not along the Z-axis. By default, your physical structure is not periodic, and you have to instruct [[EM.Cube]] to turn it into a periodic structure through [[FDTD Module]]'s Periodicity Dialog. By designating a structure as periodic, you enforce periodic boundary conditions (PBC) on the side walls of its computational domain. Your structure in the project workspace then turns into a periodic unit cell. The periodic side walls are displayed with dashed blues lines. [[Image:FDTD134.png|250px|thumb|[[FDTD Module]]'s Periodicity Settings dialog]]
To define a periodic structure, follow these steps:
* Periodic boundary conditions (PBC) are established on the ±X and ±Y faces of the domain box. You still have to designate the boundary conditions on the ±Z faces of the computational domain. These are CPML by default. But you can change them to PEC or PMC.
===Exciting A Periodic Structure As An Infinite Phased ArrayStructures===Â In [[EM.Tempo]], a periodic structure can be excited using various source types. Exciting the unit cell structure using a lumped source, a waveguide source, an ideal source or a distributed source, you can model an infinite periodic antenna array. For most practical antenna types, you will excite your periodic structure with a lumped source or waveguide source. In this case, you can define a port for the lumped source or waveguide source and calculate the S<sub>11</sub> parameter or input impedance of the periodic antenna array. You can also compute the near-field and far-field data.
In Click here to learn more about [[EM.CubeModeling Infinite Phased Arrays]]'s [[FDTD Module]], a periodic structure can be excited using various source types. Exciting the unit cell structure using a lumped source, a waveguide source, an ideal source or a distributed source, you can model an infinite periodic antenna array. For most practical antenna types, you will excite your periodic structure with a lumped source or waveguide source. In this case, you can define a port for the lumped source or waveguide source and calculate the S<sub>11</sub> parameter or input impedance of the periodic antenna array. You can also compute the near-field and far-field data.
[[EM.Cube]]'s periodic FDTD simulator uses periodic boundary conditions (PBC) to model an infinite periodic array. All the periodic replicas of the unit cell structure are excited. In this case, you can impose a phase progression across the infinite array to steer its beam. You can do this from the property dialog of the lumped source or waveguide source. At the bottom of the '''Lumped Source Dialog''' or '''Waveguide Source Dialog''', there is a section titled '''Periodic Beam Scan Angles'''. This section is grayed out when the project structure is not periodic. You can enter desired beam scan angle values for both '''Theta''' and '''Phi''' in degrees. At the end of the periodic FDTD simulation, the radiation pattern of the unit cell is calculated and stored in a radiation data file with a '''.RAD''' file extension. The 3D radiation patterns that you normally visualize in [[EM.Cube]], in this case, correspond to the single unit cell, not the infinite array. Therefore, they do not show the beam scanning even if you have entered nonzero values for the θ and/or φ scan angles. For this purpose, you have to define a finite-sized array factor. You do this in the "Impose Array Factor" section of the '''Radiation Pattern Dialog'''. In the case of a periodic structure, when you define a new far field item in the Navigation Tree, the values of element spacing along the X and Y directions are automatically set equal to the values of the periodic lattice spacing along those directions. Set the number of elements along the X and Y directions to any desired values. [[EM.Cube]] will then compute the radiation pattern of the specified finite-sized periodic array, and the beam scanning will appear in the radiation pattern plots, if any.