Design of printed disk artificial materials

In general, the characterization of a periodic structure with conducting or dielectric inclusions requires the calculation of its band structure. However, when the dimensions of the basic cell are much smaller then the radiation wavelength, we may avoid the computational burden of calculating the resonating frequencies of the periodic structure, and use instead a quasi-static analysis. To circumvent the problem of a full wave rigorous analysis, we recently proposed a periodic Green function based method (see Silveirinha, M. and Fernandes, C., 2001 AP-S Symp. Boston, vol.1, p.312). This method requires only the discretization of the inclusions´ surface, being the periodicity (which accounts for the interaction between obstacles), implicitly imposed by the crystal Green function. We consider a composite medium synthesized by stacking dielectric slabs, where the PEC inclusions are parallel disks. The PEC disks are printed using a conventional lithography process. We describe a formalism to compute the effective permittivity and permeability of a printed disk artificial medium.