On linear waveguides of zigzag honeycomb lattice

Abstract

An analysis of the scalar linear waves in infinite honeycomb lattice strips with discrete Dirichlet and Neumann boundary conditions, as well as the periodic boundary condition, is presented for the zigzag orientation. The dispersion relations and the associated wave modes in these waveguides are provided in the paper; the former in terms of the Chebyshev polynomials. It is found that the localized propagating waves, addressed as surface wave modes, occur in case of certain boundary conditions only; for which the details are provided separately. The dispersion relations and wave modes for certain even and odd symmetry are also discussed in the paper, wherever applicable. Graphical illustrations of the dispersion curves for all waveguides are included. Applications include the transmission of phononic, electronic, magnetic, and photonic waves in nanostructures of carbon-like constituents. The analytical results are directly applicable for the out-of-plane phonons assuming only nearest-neighbor interactions in graphene nanoribbons on certain substrates, as well as the counterparts in the single orbital nearest neighbor tight-binding model for the electrons.