Scattering and Radiation from/by 1-D Periodic Metallizations Residing in Layered Media

An efficient technique is proposed to compute the scattering or radiation from/by 1-D periodic structures residing in a layered background medium. The technique is based on a mixed potential integral equation (MPIE) combined with the method of moments (MoM), solving for the unknown current density flowing within a unit cell of the periodic structure. The formalism requires the knowledge of the pertinent layered medium Green´s functions with 1-D periodicity. Here, these Green´s functions are derived in closed-form by invoking the perfectly matched layer (PML)-paradigm. The stationary phase method is applied to determine the far field of the infinite, periodic structure, leading to a series of Floquet modes. In addition, approximating this series leads to an efficient technique to estimate the scattering or radiation from/by large, but finite, periodic structures with a 1-D periodic character. The theory is illustrated and validated by means of various examples, stemming from scattering and radiation applications from/by antenna arrays residing on microstrip substrates. The efficiency of the method is also demonstrated.