Effective medium theory applied to photonic crystals composed of cubic or square cylinders

Using the effective medium theory, I interpret the band-gap opening in photonic crystals with simple geometries as an interference effect between alternating layers of high and low optical indices and introduce the interesting concept of multidimensional quarter-wave stacks. The interpretation provides a simple insight into band-gap opening processes. For several simple crystal geometries, I analyze the variations of the gap width and depth with respect to the light polarization, the incident angle, and contrast inversion. For two- and three-dimensional structures composed of cubic and square cylinders, I show that the effective medium theory can be used to predict accurately the gap width, the central wavelength, and the attenuation at the central wavelength. The validity domain of the effective medium theory predictions is checked with results from rigorous computations.