Analytical Model for Regular Dense Arrays of Planar Dipole Scatterers

Abstract

An analytical boundary condition for modeling the electromagnetic properties of planar regular dense arrays of dipole particles for oblique incidence of plane waves is developed. The regular array is assumed to be dense which means that the dipole particles are close to each other. The interaction between the dipole particles is taken into account by interaction constant. The expression for the interaction constant is written in analytical form and is used for developing a transmission-line model for arrays of planar dipole scatterers. The regular dense array is modeled as a shunt impedance which is different for TM and TE polarizations. 1 Introduction 2 Theory 3 Imaginary Part of β 4 Impedance and Reflection Dyadic 5 Conclusion Appendix A. References

Analytical Model of a Metasurface Consisting of a Regular Array of Sub-Wavelength Circular Holes in a Metal Sheet

“…Using the same set of the equations for the grid impedance of regular metallic strips, in fact, the effective width can be straightforwardly evaluated for the different unit-cells, leading to an easy, fast, and accurate design of different metasurfaces. It is worth mentioning also that the methods based on the polarizability of the unit-cell particle, though accurate, need the evaluation of special functions, as reported for the circular case in [16], and, thus, are not readily applicable for a fast design, as our proposed method does.…”

“…For a further validation, we compare our model to the one presented in [16] for a complementary structure, i.e., an array of disks, after a proper application of Babinet's principle (dot-line).…”

“…According to [23], we have simulated just one unit-cell using proper boundary conditions. As a further reference, we consider also the results given by other accurate analytical models available in the open technical literature and based on the polarizability of the inclusions [16].…”

“…By defining an average value of the tangential electric field and of the surface current density on the array plane, in fact, it is possible to introduce an effective grid impedance Z g describing the electrical properties of the structure [16][17][18][19][20].…”

A New Accurate Model of High-Impedance Surfaces Consisting of Circular Patches

“…The shape of the patch element affects the value of the capacitive reactance that need to be properly defined for the geometry under study, i.e., circular in this case. It is possible to find two different approaches in the open technical literature: the first considers the dense array as an frequency selective surfaces (FSSs) in long-wavelength regime [21], and the latter defines the electrically small individual patches in terms of an electric dipoles represented through its electric polarizability [22,23]. Both define a lumped impedance, that in the case of an array of perfect conducting metallic disks, is capacitive.…”