Homogenization of periodic structures: One layer is "bulk"

In homogenization theories of periodic electromagnetic structures, such as photonic crystals or metamaterials, it is commonly assumed that the accuracy of the effective medium representation is affected by the thickness of the sample in two different ways. The first factor is the optical length (OL) of wave propagation within the sample. For a large OL, minor deviations in the wave number may strongly affect transmission and reflection. The second factor is the putative convergence to bulk characteristics (CB), once the number of layers in the sample has approached or passed a certain threshold. The theoretical analysis and numerical examples of this letter show that, while the OL influence is real, CB is not actually relevant; in a sense, one layer is already "bulk". Copyright (C) 2022 EPLA