[[Image:MORE.png|40px]] Click here to learn more about '''[[Data Visualization and Processing]]''' in [[EM.Cube]].
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==Modeling 3D Periodic Structures in EM.Tempo==
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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.
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[[Image:MORE.png|40px]] Click here to learn more about the theory of '''[[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===
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A periodic structure is one that repeats itself infinitely along one, two or three directions. In this release of [[EM.Tempo]], 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.
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To define a periodic structure, follow these steps:
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* Select '''Menu > Simulate > Computational Domain > Periodicity Settings...''' or right click on the '''Periodicity''' item in the '''Computational Domain''' section of the Navigation Tree and select '''Periodicity Settings...''' from the contextual menu. This open up the Periodicity Settings Dialog.
* Check the box labeled '''Periodic Structure''' and click the '''Apply''' button of this dialog. The default domain box initially shrinks to the edges of the physical structure in the project workspace. The default periods along the X and Y axes appear in the dialog, which are equal to the dimensions of the structure's bounding box.
* Enter new values for '''X Spacing''' and '''Y Spacing '''in project units and close the dialog.
* 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.
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===Exciting Periodic Structures as Radiators===
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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.
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[[Image:MORE.png|40px]] Click here to learn more about '''[[Modeling Infinite Phased Arrays]]'''.
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[[Image:FDTD139.png|thumb|320px|Placing a field probe above a periodic structure excited by an obliquely incident plane wave source.]]
===Exciting Periodic Structures Using Plane Waves===
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Using a plane wave source to excite a periodic structure in [[EM.Tempo]], you can model frequency selective surfaces, electromagnetic band-gap (EBG) structures, metamaterials, etc. Exciting periodic structures with plane wave sources requires careful attention. [[EM.Tempo]]'s FDTD simulation engine uses the direct spectral domain FDTD or constant transverse wavenumber method for analyzing periodic structures. In this technique, instead of a plane wave box, one defines a plane wave surface parallel to the X-Y plane. At the end of the FDTD simulation of a periodic structure with plane wave excitation, the reflection and transmission coefficients of the structure are calculated and saved into ASCII data files.
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One of the pitfalls of the direct spectral FDTD method is the possibility of horizontal resonances, which may lead to indefinite oscillation or even divergence of field values during the time marching loop. This happens in the case of oblique plane wave incidence when θ > 0°. [[EM.Tempo]]'s FDTD engine automatically detects such cases and avoids those resonances by shifting the modulation frequency of the modulated Gaussian pulse waveform away from the resonant frequency. However, in some cases, the size of oscillations may still remain large after a large number of time steps. Occasionally, a late-time diverging behavior may appear. To avoid situations like these, it is highly recommended that you place a time-domain field probe above your structure and monitor the temporal field behavior during the time marching loop as shown in the figure below.
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[[Image:MORE.png|40px]] Click here to learn more about '''[[Reflection & Transmission Characteristics of Periodic Structures]]'''.
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