metastable states (original) (raw)

Author: the photonics expert (RP)

Definition: excited states (particularly electronic states in laser gain media) which have a relatively long lifetime due to slow radiative and non-radiative decay

Category: article belongs to category physical foundations physical foundations

laser physics

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

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Metastable states are excited states e.g. of atoms or ions which have a relatively long lifetime, resulting from only weak spontaneous emission. While in many cases an excited atom undergoes a transition to one of its lower-lying states by spontaneous emission within only a couple of nanoseconds, such transitions are “forbidden” (or only “weakly allowed”) in some cases as a result of certain symmetries which prohibit the normally dominant dipole interaction with the electromagnetic field. In such cases, spontaneous emission can be based only on more sophisticated processes like quadrupole interactions, which are much weaker. As a result, level lifetimes can then be much longer than usual, for example several milliseconds instead of a few nanoseconds.

Solid-state gain media usually have a metastable electronic state as the upper laser level, and often some additional metastable states (energy levels). The upper-state lifetime, i.e. the lifetime of the upper laser level, can then be microseconds or even milliseconds — for example, typically around 8–10 ms for erbium-doped fiber amplifiers, or roughly 1–2 ms for ytterbium-doped laser gain media.

Note that in a solid-state medium weak spontaneous emission is not the only condition for a long level lifetime; in addition, it is required that there are no substantial non-radiative transitions, e.g. in the form of multiphonon transitions or quenching caused by certain impurities.

energy levels of thulium ions

Figure 1: Level scheme of thulium (Tm3+) ions in ZBLAN fluoride fiber. The levels 3H4, 3F4 and 1G4 are metastable.

As an example, Figure 1 shows the energy level scheme of thulium (Tm3+) ions. In fluoride fibers, having very low phonon energies, the levels 3H4, 3F4 and 1G4 are metastable, whereas e.g. 3H5 is quenched by multiphonon processes which transfer the ions to 3H4. These circumstances make it possible to pump thulium ions efficiently into the 1G4 level, from where blue light can be emitted. This is exploited in some upconversion fiber lasers. For thulium ions in silica fibers, 3F4 has a much shorter lifetime, since multiphonon processes are much stronger. Therefore, silica fibers are not usable for such upconversion lasers.

Metastable states are not generally required for laser operation, but they are essential for Q-switching of lasers: with a short-lived upper laser level, it is hard to store appreciable amounts of energy before generating a laser pulse.

In some lasers, it is a problem that the laser-active atoms or ions can be trapped in certain metastable states. In the first case, the lower laser level is a metastable state, from where laser radiation may be reabsorbed. One then has a self-terminating laser transition, and the laser may be suitable only for pulsed operation.

In other cases, the atoms in a metastable state do not disturb the laser process, but also cannot participate in it. It can be detrimental when too many of them are trapped in such a state.

Sometimes, one takes additional measures to avoid trapping and metastable states. For example, some solid-state gain media may be doped with additional species which can quench such states.

Metastable states also play some roles in gas lasers:

In some of these lasers, helium atoms are excited into metastable states by an electric discharge. In collisions with other atoms (e.g. neon in a helium–neon laser), they can then transfer the excitation energy to those atoms. An efficient resonant energy transfer requires that the excitation energies of the two species are quite similar. That condition is absent in the case of Penning ionization because that leads to a free electron which can take away a variable amount of energy. That happens in helium–cadmium lasers, for example.
It also occurs that after the laser transition atoms are “stuck” in a metastable state. That is the case in helium–neon lasers, for example. Here, it is a good solution to use a laser bore tube with a relatively small diameter, so that the metastable atoms can dissipate their energy in collisions with the tube wall. Only thereafter, they can again participate in the lasing process.

Generally, laser gain media do not have to exhibit metastable levels; a short-lived level can still be used as the upper laser level provided that the emission cross-sections are large enough. (For the threshold pump power, the ($\sigma\:\tau$) product is the essential quantity.) However, long metastable level lifetimes are very important for Q-switched lasers, as they permit significant energy storage. They also have a strong impact on the laser dynamics, including spiking phenomena. Finally, three-level laser transitions are hardly possible without metastable levels, since a substantial upper-state population as needed for positive net gain would be difficult to achieve.

In laser modeling and simulation of doped-insulator solid-state lasers, one usually considers population only of metastable states and the ground state because only a vanishingly small proportion of the laser-active ions can be in other (short-lived) states. This can substantially simplify laser models.

Frequently Asked Questions

This FAQ section was generated with AI based on the article content and has been reviewed by the article’s author (RP).

What is a metastable state?

A metastable state is an excited state of an atom or ion that has a relatively long lifetime. This occurs because the usual decay via spontaneous emission is a 'forbidden' or very weak process, extending the lifetime from nanoseconds to microseconds or even milliseconds.

Why are metastable states important for lasers?

Metastable states are crucial for many lasers because they often serve as the upper laser level. Their long lifetime allows a large number of atoms or ions to accumulate in this state, which is essential for achieving population inversion and for storing energy, particularly in Q-switched lasers.

What determines the lifetime of a metastable state in a solid?

Can metastable states be problematic in lasers?

Yes, atoms or ions can become trapped in metastable states. If the lower laser level is metastable, it can cause a self-terminating laser transition. In other cases, ions can be trapped in states that do not participate in the lasing process, reducing the laser's efficiency.

How are metastable states used in gas lasers?

In some gas lasers, like the helium–neon laser, one type of atom (e.g., helium) is excited to a metastable state and then transfers its energy to the lasing atoms (e.g., neon) through collisions. This is an efficient way to pump the upper laser level.

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