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[[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.

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

=== 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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