multiphonon transitions (original) (raw)

Author: the photonics expert (RP)

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

Alternative terms: multi-phonon transitions, multiphonon decay, multiphonon relaxation

Category: article belongs to category physical foundations physical foundations

laser physics

DOI: 10.61835/3dk Cite the article: BibTex BibLaTex plain text HTML Link to this page! LinkedIn

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What are Multiphonon Transitions?

Ions in solids such as laser gain media (for example) have different energy levels, and transitions between those can be caused by absorption of light, by spontaneous or stimulated emission, and by various non-radiative mechanisms. An example of the latter possibility are multiphonon transitions, where multiple phonons (quanta of lattice vibrations) are simultaneously emitted and carry away the difference of the excitation energies of the two levels. That way, transitions with a larger energy difference are possible, compared with the emission of a single phonon.

Transition rates of multiphonon transitions decrease rapidly (exponentially) with increasing order (i.e., number of emitted phonons). With only two or three phonons required, transitions can be very rapid, while for five phonons, for example, they may be negligibly slow.

Importance of Maximum Phonon Energy

An important parameter is the maximum phonon energy of a material because it determines the minimum number of required phonons for a multiphonon transition between two levels with a given difference in excitation energy. There are cases where very strong multiphonon transition rates occur for ions in a high phonon energy glass such as fused silica, while that rate is negligible for a low phonon energy glass, e.g. ZBLAN, a fluoride glass containing heavy metals.

Temperature Dependence

Multiphonon emission can already occur at low temperatures, where phonon modes of the material are hardly populated. However, the multiphonon transition rate can increase with temperature due to stimulated emission of phonons, involving thermally populated phonon modes [1]. This happens when ($k_\textrm{B}T$) is not much smaller than the energy of the involved phonons. As a consequence, metastable level lifetimes can be reduced at increasing temperatures.

Multiphonon processes are relevant for solid-state laser gain media, and this in several ways:

They can play an essential role in the function of a laser by providing useful transitions. For example, in neodymium-doped laser gain media, one typically pumps ions from their ground state to an excited state above the upper laser level. From there, multiphonon transitions quickly take them to the upper laser level (4F3/2). Also, the lower laser level of most four-level solid-state gain media is rapidly depopulated by multiphonon emission; that is important because otherwise one could have reabsorption losses on the laser transition.
On the other hand, it can be very detrimental if the laser transition itself is bypassed by multiphonon processes, or if other important metastable states are depopulated. Therefore, many mid-infrared laser sources, e.g. 3-μm erbium-doped fiber lasers, need to be realized with low phonon energy glasses. (Low phonon energies are also important for transparency in the mid-infrared wavelength region.) Also, some upconversion lasers based on erbium-doped or thulium-doped glass require heavy metal glasses (e.g. fluoride glasses) as host media, since high phonon energy glasses such as silica would lead to insufficient lifetimes of required metastable levels.

Frequently Asked Questions

What is a multiphonon transition?

A multiphonon transition is a non-radiative process where an ion in a solid changes its energy level by simultaneously emitting multiple phonons (quanta of lattice vibrations). This process allows the ion to release energy corresponding to a gap larger than a single phonon energy.

Why is the maximum phonon energy of a material important?

A material's maximum phonon energy determines the minimum number of phonons needed to bridge a given energy gap. Materials with high phonon energy, like fused silica, have much faster multiphonon transition rates than low-phonon-energy materials, such as ZBLAN fluoride glass.

Are multiphonon transitions helpful or harmful for lasers?

They can be both. They are helpful for rapidly populating the upper laser level or depopulating the lower laser level in a four-level laser system. However, they are harmful when they cause the upper laser level to decay non-radiatively, which reduces efficiency and is a problem for many mid-infrared laser sources.

How does temperature affect multiphonon transitions?

The rate of multiphonon transitions typically increases with temperature. This is caused by the stimulated emission of phonons, which becomes more likely as phonon modes become thermally populated, resulting in shorter lifetimes of metastable states.

Bibliography

[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); doi:10.1103/PhysRev.174.429
[2]	C. B. Layne et al., “Multiphonon relaxation of rare earth ions in oxide glasses”, Phys. Rev. B 16 (1), 10 (1977); doi:10.1103/PhysRevB.16.10
[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); doi:10.1103/PhysRevB.49.3821
[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); doi:10.1016/S0925-3467(01)00174-4
[5]	Z. Burshtein, “Radiative, nonradiative, and mixed-decay transitions of rare-earth ions in dielectric media”, Opt. Eng. 49, 091005 (2010); doi:10.1117/1.3483907

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