A series of phonon-polaritons in a diatomic ionic crystal

• The Hamiltonian of a diatomic ionic crystal in the Kun Huang model is proposed.
• The local field is taken into account by introducing of an effective charge.
• A perturbation theory in the introduced self-consistently small interaction is build.
• A statistical operator for the electromagnetic field in ionic crystal is constructed.
• The new series of long-wave upper phonon-polaritons is obtained.

The interaction between the harmonics of the optical phonon and the transverse wave of the electromagnetic field in ionic crystals with two atoms in the unit cell is considered. The Kun Huang model is used to describe the point charges sublattices that oscillate with a frequency ω0ω0. The thermal motion of charges sublattices surrounding thermostat is taken into account. The local field is taken into account as well by introducing of an effective charge. A statistical operator of the system in a perturbation theory is introduced self-consistently small interaction is constructed. The new series of long-wave phonon-polaritons as the eigenwaves of the transverse electromagnetic field is obtained. The approximation is valid for a small ratio of the standard thermal deviation to the wavelength that allows to limit only the second and the third phonon harmonics in the dispersion equation at plotting the graph. A frequency line 2ω02ω0 restricts the top of the first upper phonon-polariton graph and the bottom of the second upper phonon-polariton graph for the used example of cesium bromide crystal. The rest of the phonon-polaritons have graphs in the form of stairs with a slope, asymptotically approaching to the photon graph in this crystal, and with a height ω0ω0.