Effective properties of cylinders in a square lattice

Abstract

Periodic subwavelength structures on a boundary can enhance the transmission through the boundary. While rigorous methods are accurate for designing these structures, recent methods could benefit from an improved effective medium approximation. In this work, a modified Rayleigh mixture formula is used to approximate the effective properties of periodic cylinders in a square lattice for transverse electromagnetic plane waves. The modified Rayleigh mixture formula outperforms the Maxwell Garnett formula where the height is greater than the diameter. A comparison is shown for completeness.