Something of Discrete Photonics: Discrete Diffraction and Optical Flat Bands in Waveguide Arrays

Abstract

The one- and two dimensional waveguide arrays in the case of the electromagnetic wave propagating only along the waveguide are discussed. The waveguide array consists of alternating waveguides of positive and negative refraction indexes. On some particular examples it is shown that the features of the spectrum are depended on number of waveguides per unit cell. For example, the spectrum contains frequency gaps in the case of the unit cell contains two waveguides. If the unit cell contains the three waveguides then the additional pseudo flat band is appeared in 1D array. The coupled electromagnetic waves propagating in 2D array, which consists of alternating waveguides of positive and negative refraction indexes, are discussed. In the case of the array having cross section in the form of face-centered square lattice the flat band takes place.