In the case of an infinite periodic planar structure, the field equations can be written in the following form:
:<math>\mathbf{E(r) = E^{inc}(r)} + \sum_{m=-\infty}^{\infty} \sum_{n=-\infty}^{\infty}\bigg[\iiint_V \mathbf{ \overline{\overline{G}}_{EJ}(r|r') \cdot J_{mn}(r') } \, d\nu' + \iiint_V \mathbf{ \overline{\overline{G}}_{EM}(r|r') \cdot M_{mn}(r') } \, d\nu'\bigg]</math>Â Â :<math>\mathbf{H(r) = H^{inc}(r)} + \sum_{m=-\infty}^{\infty} \sum_{n=-\infty}^{\infty}\bigg[\iiint_V \mathbf{ \overline{\overline{G}}_{HJ}(r|r') \cdot J_{mn}(r') } \, d\nu' + \iiint_V \mathbf{ \overline{\overline{G}}_{HM}(r|r') \cdot M_{mn}(r') } \, d\nu'\bigg]</math><!--[[File:PMOM94.png]]-->
where
[[File:PMOM95<math>\mathbf{J_{mn}(1r).png]]= J_{mn}}(x,y,z) = \mathbf{J_{00}}(x+m S_x, y+n S_y, z) e^{j(m k_{x00} S_x + n k_{y00} S_y)}</math>
In the above equations, '''J:<sub>00</submath>\mathbf{M_{mn}(r)''' and '''M<sub>= M_{mn}}(x,y,z) = \mathbf{M_{00</sub>}}(r)''' are the periodic unit cell's electric and magnetic currents that are repeated everywhere in space on a rectangular lattice with periods S<sub>x</sub> and S<sub>+m S_x, y</sub> along the X and Y directions+n S_y, respectively. k<sub>z) e^{j(m k_{x00</sub> and k<sub>} S_x + n k_{y00} S_y)}</submath> are the periodic propagation constants along the X and Y directions, respectively, and they are given by:
and :<math> -\infty < m, n < \infty </math><!--[[File:PMOM95(1).png]]--> In the above equations, <math>\mathbf{J_{00}(r)}</math> and <math>\mathbf{M_{00}(r)}</math> are the periodic unit cell's electric and magnetic currents that are repeated everywhere in space on a rectangular lattice with periods S<sub>x</sub> and S<sub>y</sub> along the X and Y directions, respectively. <math>k_{x00}</math> and <math>k_{y00}</math> are the periodic propagation constants along the X and Y directions, respectively, and they are given by: :<math> k_{x00} = k_0 \sin\theta \cos\phi </math> :<math> k_{y00} = k_0 \sin\theta \sin\phi </math><!--[[File:PMOM96(1).png]]-->
where θ and φ are the beam scan angles in the case of periodic excitation of lumped sources, or they are the spherical angles of incidence in the case of a plane wave source illuminating the periodic structure. Using the infinite summations, one can define periodic dyadic Green's functions in the spectral domain in the following manner:
:<math>\mathbf{ \overline{\overline{G}}_{\mu \nu}^{PER} (r|r') } =\frac{1}{S_x S_y} \sum_{m=-\infty}^{\infty} \sum_{n=-\infty}^{\infty}\mathbf{ \tilde{\overline{\overline{G}}}_{\mu \nu} } (k_x, k_y, z|z')e^{-j[k_{xm}(x-x') + k_{yn}(y-y')]}</math>Â where:<math>k_{xm} = k_{x00} + \frac{2\pi m}{S_x} \quad \text{and} \quadk_{ym} = k_{y00} + \frac{2\pi m}{S_y}</math><!--[[File:PMOM97.png]]-->
The above doubly infinite periodic Green's functions are said to be expressed in terms of "Floquet Modes". The exact formulation involves an infinite set of these periodic Floquet modes. During the MoM matrix fill process for a periodic structure, a finite number of Floquet modes are calculated. By default, EM.Cube's planar MoM engine considers M<sub>x</sub> = M<sub>y</sub> = 25. This implies a total of 51 modes along the X direction and a total of 51 modes along the Y direction, or a grand total of 51<sup>2</sup> = 2,601 Floquet modes. You can increase the number of Floquet modes for your project from the Planar MoM Engine Settings Dialog. In the section titled "Periodic Simulation", you can change the values of '''Number of Floquet Modes''' in the two boxes designated X and Y.