Phonon polariton
In condensed matter physics, a phonon polariton is a type of quasiparticle that can form in a diatomic ionic crystal due to coupling of transverse optical phonons and photons.
Phonon polariton spectra have traditionally been studied using Raman spectroscopy.
[2] 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.
[3] A phonon polariton is a type of quasiparticle that can form in some crystals due to the coupling of photons and lattice vibrations.
They have properties of both light and sound waves, and can travel at very slow speeds in the material.
They are useful for manipulating electromagnetic fields at nanoscale and enhancing optical phenomena.
The dispersion relations will therefore never cross each other, resulting in a lack of coupling.
Optical phonons, by contrast, have a non-zero angular frequency at
The behavior of the phonon polaritons can be described by the dispersion relation.
This dispersion relation is most easily derived for diatomic ion crystals with optical isotropy, for example sodium chloride and zinc sulfide.
Since the atoms in the crystal are charged, any lattice vibration which changes the relative distance between the two atoms in the unit cell will change the dielectric polarization of the material.
To describe these vibrations, it is useful to introduce the parameter w, which is given by: Where Using this parameter, the behavior of the lattice vibrations for long waves can be described by the following equations:[5] Where For the full coupling between the phonon and the photon, we need the four Maxwell's equations in matter.
Solving the resulting equations for ω and k, the magnitude of the wave vector, yields the following dispersion relation, and furthermore an expression for the optical dielectric constant:[6] With
The coupling of the phonon and the photon is the most promininent in the region where the original transverse disperion relations would have crossed.
The physical interpretation of this effect is that the frequency becomes too high for the ions to partake in the vibration, causing them to be essentially static.
This results in a dispersion relation resembling one of a regular photon in a crystal.
The lower branch in this region behaves, because of their low phase velocity compared to the photons, as regular transverse lattice vibrations.
yields: This equation gives the ratio of the frequency of the longitudonal optical phonon (
) in diatomic cubic ionic crystals, and is known as the Lyddane-Sachs-Teller relation.
They are similar to surface plasmon polaritons, although studied to a far lesser extent.
[9] The applications are far ranging from materials with negative index of refraction to high-density IR data storage.
Although optical phonons themselves do not have a high thermal conductivity, SPhPs do seem to have this.
If the correct wavelength is chosen, this laser can induce the formation of a polariton on the sample.
[2] The induction of polaritons is very similar to that in Raman experiments, with a few differences.
With the extremely high spatial resolution of SNOM, one can induce polaritons very locally in the sample.
In the case of CW polaritons, standing waves will be created, which will again be detected by the AFM tip.
Whether one is observing on the bulk surface or close to an edge, the signal is in temporal form.
In this field phonon polaritons are used for high speed signal processing and terahertz spectroscopy.
[15] The real-space imaging of phonon polaritons was made possible by projecting them onto a CCD camera.
