Light transport and localization in a quasi-one-dimensional graphene-like photonic lattice

Photonic analogs of graphene (waveguide lattices that imitate the electronic properties of graphene in the optical range) demonstrate the presence of special topological states (flat bands) due to the presence of conical Dirac points, which form a linear dispersion relation. Using the coupled-mode method for a graphene-like photonic lattice formed by a periodically repeating cell of six waveguides and taking into account the interaction of each waveguide with its nearest neighbors, with each other, and between lattice cells, we derive a dispersion relation and analytical expressions for the amplitudes of propagating waves. This allows the emergence of light localization to be accurately predicted as a functions of the values of the coupling constants that describe highly localized radiation propagating without transverse diffraction along the graphene-like lattice. It is shown that the spectrum of linear waves in the system (in the strong coupling approximation) consists of four dispersion bands and two flat bands.