Abstract: This work analyzed polarization modes of lattice waves at various wave vectors in two-dimensional honeycomb lattices, which can provide new insights for teaching lattice vibrations in Solid State Physics. The dynamical matrix of the lattice vibration and its eigenvalue equation can be obtained through analyzing the lattice motion, from which the phonon dispersion and polarization can be solved. Symmetry analysis indicates that the vibration modes at high-symmetry wave vectors M and K have linear and circular polarizations, respectively. A perturbation theory from Quantum Mechanics can be used to solve lattice waves at wave vectors near K, which are found to exhibit elliptical polarizations. 

Key words: lattice wave, lattice vibration, honeycomb lattice, polarization mode