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Multi-phonon Transitions

Definition: transitions between electronic levels of atoms or ions in solid media, involving the emission of multiple phonons

German: Multiphononen-Übergänge

Category: physical foundations

How to cite the article; suggest additional literature

The upper-state lifetime in a solid-state gain medium, or more generally the lifetime of a metastable electronic state of a dopant ion in such a medium, can be strongly reduced by decay processes which involve the simultaneous emission of several phonons. Such a process is called a multi-phonon transition, multiphonon relaxation or multiphonon quenching. Multiple phonons are typically required for such transitions because the energy of a single phonon is not sufficient to match the difference in level energies.

The rate of multi-phonon transitions decreases exponentially with increasing number of phonons required. As a consequence, a certain metastable state may exhibit a very strong reduction in its lifetime by multi-phonon emission if the host medium supports phonons with relatively high energy, whereas the same process may be negligible for a host medium with lower phonon energies. For that reason, many upconversion lasers work only with gain media which have small phonon energies, such as heavy metal glasses, so that sufficient lifetimes of certain energy levels are achieved. In other cases, however, high enough phonon energies are important if these are required for facilitating certain non-radiative transitions, which are needed e.g. to populate the upper laser level or to depopulate the lower laser level.

Multiphonon emission can already occur at low temperatures, where phonon modes of the material are hardly populated. However, the multi-phonon transition rate can increase with temperature due to stimulated emission of phonons, involving thermally populated phonon modes [1]. This happens when kBT is not much smaller than the energy of the involved phonons. As a consequence, metastable level lifetimes can be reduced at increasing temperatures.

Some examples of the importance of multi-phonon processes in laser gain media are:


[1]L. A. Riseberg and H. W. Moos, “Multiphonon orbit–lattice relaxation of excited states of rare earth ions in crystals”, Phys. Rev. 174 (2), 429 (1968)
[2]C. B. Layne et al., “Multiphonon relaxation of rare earth ions in oxide glasses”, Phys. Rev. B 16 (1), 10 (1977)
[3]Y. V. Orlovskii et al., “Multiple-phonon nonradiative relaxation: experimental rates in fluoride crystals doped with Er”, Phys. Rev. B 49 (6), 3821 (1994)
[4]Y. V. Orlovskii et al., “Temperature dependencies of excited states lifetimes and relaxation rates of 3–5 phonon (4–6 μm) transitions in the YAG, LuAG and YLF crystals doped with trivalent holmium, thulium, and erbium”, Opt. Materials 18, 355 (2002)
[5]Z. Burshtein, “Radiative, nonradiative, and mixed-decay transitions of rare-earth ions in dielectric media”, Opt. Eng. 49, 091005 (2010)

(Suggest additional literature!)

See also: gain media, rare-earth-doped gain media, upconversion lasers, fluoride fibers, quenching, non-radiative transitions, multiphonon absorption
and other articles in the category physical foundations

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