Effective medium theory of symmetric two-dimensional subwavelength periodic structures

Recent experimental and theoretical investigations have shown that periodic subwavelength structured surfaces with periods small compared to the illumination wavelength behave as homogeneous medium, and have suggested interesting applications, such as fabrication of anti-reflection coatings1,2,3, quarter wave plates4, polarizers5, and graded-phase diffractive elements6. The replacement of the periodic structure by a homogeneous medium is often referred as homogenization or effective medium theory (EMT). EMT can be applied to a large variety of physical material properties, such as diffusion constant, magnetic permeability, thermal conductivity, etc. To facilitate the design and fabrication of artificial dielectric elements, one must be able to relate the effective index of the subwavelength structured surface in a simple way.