Polariton

A polariton is a quasi-particle physics, in the strong interaction ( coupling) of an electromagnetic field with the excited state arises ( for example, a phonon or exciton in a solid body ), which has a dipole moment.

A typical example is the coupling of a mechanical collective lattice vibration ( phonon frequencies in the optical range and the transverse polarization) of a solid body of an electromagnetic wave ( photon).

The polaritons should not be confused with the polarons. The latter one has to do with fermionic quasiparticles, eg with an electron plus " entrained polarization cloud " while representing the polariton bosonic quasiparticles.

Polaritons in a solid body

In a solid body, a polariton is formed in the interaction of an elementary excitation (eg, phonon, exciton or plasmon ) with photons. The underlying physical phenomena are absorption, reflection or dispersion of electromagnetic radiation through the solid.

In the case of strong coupling of the photons in the solid state to other elementary excitations, the effect can not be described by perturbation theory. Photon and the elementary excitation instead form a new quasi-particles - the polariton. The strong coupling is found when it cut the dispersion curves of the photon and the excitation, that is, if the energy and momentum of the interaction partners practically coincide.

Regarding the quasi-particles involved, a distinction in detail between phonon - polariton, exciton - polariton or plasmon polaritons.

The phonon - polariton

The phonon - polariton can be in crystals with ionic bonding (eg NaCl) find. Figuratively speaking, calls an electromagnetic wave polarization

And thus a lattice distortion produced. Conversely, a transversal wave optical grating grid is accompanied by an electromagnetic wave. Here, two different types of polarization play an important role:

• Ion polarization due to the displacement of the ions of an ion crystal lattice in the electric field.
• The electronic polarization can be regarded as a displacement of the electron cloud with respect to the nuclei.

Both of which can be described by the oscillator model. Thus, considering an ion pair, one obtains for each ion, the differential equation of the damped harmonic oscillator, the external disturbance, the electric field acts. For the dielectric constant is obtained using the Lyddane -Sachs -Teller relation following important relationship:

Description of the variables introduced:

• : Resonance frequency of the vibratory system, that is, the ion
• : Dielectric constant of the material under consideration at frequencies well below the resonance frequency ( "static" )
• : Dielectric constant of the material under consideration at frequencies well above the resonant frequency
• : Damping constant of the harmonic oscillator

Assuming a plane wave, is obtained with the aid of Maxwell's equations, the general dispersion relation of electromagnetic waves in the medium ( with the wave number k )

Substituting in this the derived equation, we obtain ( with ) the dispersion relation of polaritons:

The exciton - polariton

The exciton is formed polariton as phonon polariton from the interaction between matter and electromagnetic waves, for example, when excited at the photoluminescence spectroscopy. Electromagnetic radiation generated in the solid state polarization (see above):

This means that the matter is partially polarized. Electromagnetic waves are polarized transversely in vacuo. In matter however, also forms a longitudinal polarization.

Send excitons in recombination of electromagnetic radiation. This radiation interacts with the solid or its polarization. It " creates " the exciton - polariton. Electromagnetic waves and excitons have a dispersion. During the interaction of these two particles, the polariton, which is described by the exciton Polaritondispersion (see picture: exciton - polariton dispersion).

Longitudinal and transverse polarization, or in accordance with the longitudinal and transverse polariton, split on energy. In the picture of the course of the uncoupled Exzitondispersion (dashed lines) is shown, however, already in the longitudinal and transverse splitting, as it contributes as a proportion to the exciton Polaritondispersion. The dispersion of photons in vacuum ( uncoupled / without interaction) is shown in red.

With the interaction of the longitudinal exciton - polariton () bends the origin starting () call and asymptotically approaches the uncoupled dispersion of the photons ( UPB and its history in blue). In the transverse branch, the exciton - polariton bends the course of the photons with the coupling (interaction ) and asymptotically approaches the dispersion of the transverse exciton () at (LPB and its history in blue). The splitting can be seen in the origin between UPB and LPB as the difference of the dashed lines, which corresponds to an energy as

In the experiment, this difference is apparent. Excitons are formed of an electron from the conduction band and a hole from the valence band, where there are three valence bands, which are energetically Descending A, B and C mentioned. These are, for example, to see in the schema image of photoluminescence spectroscopy. All excitons split LT. Thus, each exciton splits. Trade shows can be this splitting of the exciton in photoluminescence with very good resolution. In this case, all the radiating events appear as peaks as well as the exciton events. In the measurement, then each two peaks, instead of one, to see the distance on the energy scale then corresponds to the splitting (see picture: LT polariton splitting ).

The splitting can, for example, in zinc oxide (ZnO ) is hardly measurable (about 0.2 MeV: at one of the A- valence band exciton - polaritons ) or measurable ( about 10 meV: at one of the B- valence - exciton be polaritons ).