Phonon polaritons

Phonon polaritons are a type of quasiparticle that can form in a diatomic ionic crystal due to coupling of transverse optical phonons and photons. They are particular type of polariton, which behave like bosons. Phonon polaritons occur in the region where the wavelength and energy of phonons and photons are similar, as to adhere to the avoided crossing principle. Phonon polariton spectra have traditionally been studied using Raman spectroscopy. The recent advances in (scattering-type) scanning near-field optical microscopy((s-)SNOM) and atomic force microscopy(AFM) have made it possible to observe the polaritons in a more direct way. Phonon polaritons only result from coupling of transverse optical phonons, this is due to the particular form of the dispersion relation of the phonon and photon and their interaction. Photons consist of electromagnetic waves, which are always transverse. Therefore, they can only couple with transverse phonons in crystals. Near the dispersion relation of an acoustic phonon can be approximated as being linear, with a particular gradient giving a dispersion relation of the form , with the speed of the wave, the angular frequency and k the absolute value of the wave vector . The dispersion relation of photons is also linear, being also of the form , with c being the speed of light in vacuum. The difference lies in the magnitudes of their speeds, the speed of photons is many times larger than the speed for the acoustic phonons. The dispersion relations will therefore never cross each other, resulting in a lack of coupling. The dispersion relations touch at , but since the waves have no energy, no coupling will occur. Optical phonons, by contrast, have a non-zero angular frequency at and have a negative slope, which is also much smaller in magnitude to that of photons. This will result in the crossing of the optical phonon branch and the photon dispersion, leading to their coupling and the forming of a phonon polariton. The behavior of the phonon polaritons can be described by the dispersion relation.