Some formulae for evaluation of the polariton and plasmon frequencies, in materials

We present new relations for calculation of phonon polaritons, plasmons and plasmon polaritons frequencies, which differ from the standard relations. So, we study the frequency of phonon polaritons in a two dimensional lattice with applications to CuO2 lattice. Next, we evaluate plasmon frequencies in graphene and in Cu2D and Cu3D metals. Further, we evaluate the frequency of surface plasmon polaritons at the Cu2D/air and Cu3D/air interfaces. The obtained results are in a good agreement with experimental data. Also, we present a correspondence between the potential vector and the displacement of an oscillator. It is well known that the commutation relations of the operators in second quantization originate from the simple harmonic oscillators that are used to quantize the electromagnetic field. Finally, we present a comparison between photons, phonons and plasmons.