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EM.Picasso

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/* Working with EM.Picasso Simulation Data */

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== Modeling Periodic Planar Structures in EM.Picasso ==

[[EM.Picasso]] allows you to simulate doubly periodic planar structures with periodicities along the X and Y directions. Once you designate your planar structure as periodic, [[EM.Picasso]]'s Planar MoM simulation engine uses a spectral domain solver to analyze it. In this case, the dyadic Green's functions of periodic planar structure take the form of doubly infinite summations rather than integrals.

[[Image:Info_icon.png|40px]] Click here to learn more about the theory of '''[[Planar_Method_of_Moments#Periodic_Planar_MoM_Simulation| Periodic Green's functions]]'''.

{{Note| [[EM.Picasso]] can handle both regular and skewed periodic lattices.}}

[[Image:PMOM99.png|thumb|300px|EM.Picasso's Periodicity Settings dialog.]]

[[Image:image122.png|thumb|400px|Modeling a periodic screen using two different types of unit cell.]]

=== Defining a Periodic Structure in EM.Picasso ===

An infinite periodic structure in [[EM.Picasso]] is represented by a "'''Periodic Unit Cell'''". To define a periodic structure, you must open [[EM.Picasso]]'s Periodicity Settings Dialog by right clicking the '''Periodicity''' item in the '''Computational Domain''' section of the navigation tree and selecting '''Periodicity Settings...''' from the contextual menu or by selecting '''Menu''' '''>''' '''Simulate > 'Computational Domain > Periodicity Settings...''' from the menu bar. In the Periodicity Settings Dialog, check the box labeled '''Periodic Structure'''. This will enable the section titled''"''Lattice Properties". You can define the periods along the X and Y axes using the boxes labeled '''Spacing'''. In a periodic structure, the virtual domain is replaced by a default blue periodic domain that is always centered around the origin of coordinates. Keep in mind that the periodic unit cell must always be centered at the origin of coordinates. The relative position of the structure within this centered unit cell will change the phase of the results.

In many cases, your planar structure's traces or embedded objects are entirely enclosed inside the periodic unit cell and do not touch the boundary of the unit cell. [[EM.Picasso]] allows you to define periodic structures whose unit cells are interconnected. The interconnectivity applies only to PEC, PMC and conductive sheet traces, and embedded object sets are excluded. Your objects cannot cross the periodic domain. In other words, the neighboring unit cells cannot overlap one another. However, you can arrange objects with linear edges such that one or more flat edges line up with the domain's bounding box. In such cases, [[EM.Picasso]]'s planar MoM mesh generator will take into account the continuity of the currents across the adjacent connected unit cells and will create the connection basis functions at the right and top boundaries of the unit cell. It is clear that due to periodicity, the basis functions do not need to be extended at the left or bottom boundaries of the unit cell. As an example, consider a periodic metallic screen as shown in the figure on the right. The unit cell of this structure can be defined as a rectangular aperture in a PEC ground plane (marked as Unit Cell 1). In this case, the rectangle object is defined as a slot trace. Alternatively, you can define a unit cell in the form of a microstrip cross on a metal trace. In the latter case, however, the microstrip cross should extend across the unit cell and connect to the crosses in the neighboring cells in order to provide current continuity.

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<td> [[Image:pmom_per5_tn.png|thumb|300px|The PEC cross unit cell.]] </td>

<td> [[Image:pmom_per6_tn.png|thumb|300px|Planar mesh of the PEC cross unit cell. Note the cell extensions at the unit cell's boundaries.]] </td>

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=== Exciting Periodic Structures as Radiators in EM.Picasso ===

When a periodic planar structure is excited using a gap or probe source, it acts like an infinite periodic phased array. All the periodic replicas of the unit cell structure are excited. You can even impose a phase progression across the infinite array to steer its beam. You can do this from the property dialog of the gap or probe source. At the bottom of the '''Gap Source Dialog''' or '''Probe Source Dialog''', there is a section titled '''Periodic Beam Scan Angles'''. You can enter desired values for '''Theta''' and '''Phi''' beam scan angles in degrees. To visualize the radiation patterns of a beam-steered antenna array, you have to define a finite-sized array factor in the Radiation Pattern dialog. You do this in the '''Impose Array Factor''' section of this dialog. The values of '''Element Spacing''' along the X and Y directions must be set equal to the value of '''Periodic Lattice Spacing''' along those directions.

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<td> [[Image:Period5.png|thumb|350px|Setting periodic scan angles in EM.Picasso's Gap Source dialog.]] </td>

<td> [[Image:Period6.png|thumb|350px|Setting the array factor in EM.Picasso's Radiation Pattern dialog.]] </td>

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<td> [[Image:Period7.png|thumb|360px|Radiation pattern of an 8Ã8 finite-sized periodic printed dipole array with 0° phi and theta scan angles.]] </td>

<td> [[Image:Period8.png|thumb|360px|Radiation pattern of a beam-steered 8Ã8 finite-sized periodic printed dipole array with 45° phi and theta scan angles.]] </td>

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=== Exciting Periodic Structures Using Plane Waves in EM.Picasso ===

When a periodic planar structure is excited using a plane wave source, it acts as a periodic surface that reflects or transmits the incident wave. [[EM.Picasso ]] calculates the reflection and transmission coefficients of periodic planar structures. If you run a single-frequency plane wave simulation, the reflection and transmission coefficients are reported in the Output Window at the end of the simulation. Note that these periodic characteristics depend on the polarization of the incident plane wave. You set the polarization (TMz or TEz) in the '''Plane Wave Dialog''' when defining your excitation source. In this dialog you also set the values of the incident '''Theta''' and '''Phi''' angles. At the end of the planar MoM simulation of a periodic structure with plane wave excitation, the reflection and transmission coefficients of the structure are calculated and saved into two complex data files called "reflection.CPX" and "transmission.CPX".

{{Note|In the absence of any finite traces or embedded objects in the project workspace, [[EM.Picasso]] computes the reflection and transmission coefficients of the layered background structure of your project.}}

[[Image:PMOM102.png|thumb|400px|A periodic planar layered structure with slot traces excited by a normally incident plane wave source.]]

=== Running a Periodic MoM Analysis ===

You run a periodic MoM analysis just like an aperiodic MoM simulation from [[EM.Picasso]]'s Run Dialog. Here, too, you can run a single-frequency analysis or a uniform or adaptive frequency sweep, or a parametric sweep, etc. Similar to the aperiodic structures, you can define several observables for your project. If you open the Planar MoM Engine Settings dialog, you will see a section titled "Infinite Periodic Simulation". In this section, you can set the number of Floquet modes that will be computed in the periodic Green's function summations. By default, the numbers of Floquet modes along the X and Y directions are both equal to 25, meaning that a total of 2500 Floquet terms will be computed for each periodic MoM simulation.

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[[Image:PMOM98.png|thumb|600px|Changing the number of Floquet modes from the Planar MoM Engine Settings dialog.]]

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You learned earlier how to use [[EM.Cube]]'s powerful, adaptive frequency sweep utility to study the frequency response of a planar structure. Adaptive frequency sweep uses rational function interpolation to generate smooth curves of the scattering parameters with a relatively small number of full-wave simulation runs in a progressive manner. Therefore, you need a port definition in your planar structure to be able to run an adaptive frequency sweep. This is clear in the case of an infinite periodic phased array, where your periodic unit cell structure must be excited using either a gap source or a probe source. You run an adaptive frequency sweep of an infinite periodic phased array in exactly the same way to do for regular, aperiodic, planar structures.

[[EM.Cube]]'s Planar Modules also allows you to run an adaptive frequency sweep of periodic surfaces excited by a plane wave source. In this case, the planar MoM engine calculates the reflection and transmission coefficients of the periodic surface. Note that you can conceptually consider a periodic surface as a two-port network, where Port 1 is the top half-space and Port 2 is the bottom half-space. In that case, the reflection coefficient R is equivalent to S<sub>11</sub> parameter, while the transmission coefficient T is equivalent to S<sub>21</sub> parameter. This is, of course, the case when the periodic surface is illuminated by the plane wave source from the top half-space, corresponding to 90Â°< θ = 180Â°. You can also illuminate the periodic surface by the plane wave source from the bottom half-space, corresponding to 0Â° = θ < 90Â°. In this case, the reflection coefficient R and transmission coefficient T are equivalent to S<sub>22</sub> and S<sub>12</sub> parameters, respectively. Having these interpretations in mind, [[EM.Cube]] enables the "'''Adaptive Frequency Sweep'''" option of the '''Frequency Settings Dialog''' when your planar structure has a periodic domain together with a plane wave source.

=== Modeling Finite-Sized Periodic Arrays ===

[[Image:Info_icon.png|40px]] Click here to learn about '''[[Modeling Finite-Sized Periodic Arrays Using NCCBF Technique]]'''.

Kazem Sabet

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