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

Abstract

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. Index Terms-Antenna arrays, electromagnetic radiation, electromagnetic scattering, Green's function, integral equation, perfectly matched layer (PML), periodic structures, method of moments (MoM), stationary phase method.

Efficient Computation of 1-D Periodic Layered Mixed Potentials for the Analysis of Leaky-Wave Antennas With Vertical Elements

“…Suitable applications of such periodic printed LWAs include low-cost beam-scanning radiators, Guido novel sensors, and smart antennas. With the combination of the fabrication advantages and the plenitude of applications, it is clear that the development of appropriate computational modeling tools for the fast and accurate design of periodic printed LWAs has become necessary [9]- [15]. As is well known, radiation phenomena in LWAs are due to the excitation of leaky waves with complex wavenumbers that dominate the aperture field and determine the radiation pattern [16].…”

An Efficient 1-D Periodic Boundary Integral Equation Technique to Analyze Radiation onto Straight and Meandering Microstrip Lines

“…Upon knowledge of the Green's function, the BIE can be solved by the Method of Moments (MoM) [11]. An overview of techniques is provided in [12]. Additionally, a new interesting method based on fast periodic interpolations is reported in [13].…”

“…As the PML-based periodic Green's functions can be constructed in an elegant and natural way, it is very beneficial to implement them within a BIEMoM scheme. This technique has been successfully applied in [12] to analyze the scattering and radiation from/by 1-D periodic microstrip antenna arrays. However, the technique presented in [12] can only be applied to antenna arrays as a completely arbitrary shape of the metallization within one unit cell was not allowed.…”

“…This technique has been successfully applied in [12] to analyze the scattering and radiation from/by 1-D periodic microstrip antenna arrays. However, the technique presented in [12] can only be applied to antenna arrays as a completely arbitrary shape of the metallization within one unit cell was not allowed. In contrast, the method presented in this paper allows to rapidly evaluate the current density on arbitrary 1-D periodic microstrip metallizations, illuminated by a plane wave.…”

“…The mth unit cell is denoted S uc,m = {ρ ≡ xx + yŷ + dẑ : mb ≤ x < (m+1)b , −∞ < y < ∞}, m ∈ Z. In contrast to our previous work [12], which only allowed the analysis of antenna arrays, here the metallization extends across the borders of the unit cells, allowing a continuous current flow in the x-direction. A plane wave E PW (r ≡ xx+yŷ+zẑ) = E 0 e −jk0k·r illuminates the structure.…”