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Optical phonons that are Raman active can also interact indirectly with light, through Raman scattering. Optical phonons are often abbreviated as LO and TO phonons, for the longitudinal and transverse modes respectively; the splitting between LO and TO frequencies is often described accurately by the Lyddane–Sachs–Teller relation.
The separation between LO and TO phonon frequencies near the Γ-point (small wave vectors) is described by the LST relation. Note this plot shows much higher wavevectors than considered below, and the scale cannot not show the hybridization of the TO branch with light (which would be confined extremely close to Γ).
Phonons take on both labels such that transverse acoustic and optical phonons are denoted TA and TO, respectively; likewise, longitudinal acoustic and optical phonons are denoted LA and LO. The type of surface phonon can be characterized by its dispersion in relation to the bulk phonon modes of the crystal.
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.
A polariton is the result of the combination of a photon with a polar excitation in a material. The following are types of polaritons: Phonon polaritons result from coupling of an infrared photon with an optical phonon
In another example, for the far IR regions where the optical phonons are involved, the dielectric function (ε e,ω) are calculated as ,, = +,,,, where LO and TO denote the longitudinal and transverse optical phonon modes, j is all the IR-active modes, and γ is the temperature-dependent damping term in the oscillator model.
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where is the characteristic length of the system and represents the fraction of specularly scattered phonons. The p {\displaystyle p} parameter is not easily calculated for an arbitrary surface. For a surface characterized by a root-mean-square roughness η {\displaystyle \eta } , a wavelength-dependent value for p {\displaystyle p} can be ...