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Phonons

According to quantum mechanics, microscopic vibrations (sound waves) in solid media are quantized. This means that vibration energy can only be exchanged in the form of so-called phonons, which have an energy which is Planck's constant <$h$> multiplied by the phonon frequency.

Different kinds of vibration modes exist, involving very different frequencies and thus phonon energies:

• Acoustic phonons are associated with long-wavelength vibrations, where neighbored particles oscillate nearly in phase. They have relatively low frequencies, e.g. in the gigahertz region.
• Optical phonons are associated with vibrations where neighbored particles oscillate nearly in anti-phase. The frequencies of optical phonons are in the terahertz region (leading to much higher phonon energies than for acoustic phonons), and in ionic crystals or glasses they can be involved in the absorption of infrared light. Note that due to the opposite electrical charges of neighbored ions, such kind of vibrations can couple to the electromagnetic field through their electrical dipole moment.

Phonons are important for infrared optics and for the physics of solid-state lasers:

• As mentioned above, absorption processes can directly generate optical phonons – either a single phonon per absorbed photon or multiple phonons (multiphonon absorption) (but in that case with lower probability). Due to the requirement of momentum conservation and the very small momentum of photons of light (with wavelengths much longer than the lattice constant), photons can couple only to optical phonons with quite small wave numbers.
• They lead to very fast transitions between different sublevels of Stark level manifolds, and therefore to fast thermalization of Stark level manifolds and to significant lifetime broadening. Particularly in vibronic lasers, they can strongly increase the gain bandwidth.
• Phonons are involved in multi-phonon transitions between closely spaced Stark level manifolds. Such processes are essential for laser operation in many cases, but can also be very detrimental in other cases, and may thus enforce the use of a different host glass or crystal.
• Phonons are also involved in Raman scattering (with optical phonons) and Brillouin scattering (with acoustic phonons), where an incident photon is transformed into a photon with slightly lower energy and a phonon carrying away the difference of photon energies.

See also: multi-phonon transitions, quenching, Raman scattering, Brillouin scattering, solid-state lasers, vibronic lasers, gain bandwidth, photons