Definition: excited states (particularly electronic states in laser gain media) which have a relatively long lifetime due to slow radiative and non-radiative decay
German: metastabile Zustände
Category: physical foundations
Author: Dr. Rüdiger Paschotta
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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 does 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. Is a result, level lifetimes can then be much longer than usual, for example several milliseconds instead of a few nanoseconds.
Metastable States of Solid-state Gain Media
Solid-state gain media usually have a metastable electronic state as 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 multi-phonon transitions or quenching caused by certain impurities.
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 multi-phonon 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 multi-phonon processes are much stronger. Therefore, silica fibers are not usable for such upconversion lasers.
Trapping of Laser-active Atoms or Ions in Metastable States
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 can also not 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 in Gas Lasers
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.
Lasers Without Metastable States
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 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.
See also: upper-state lifetime, forbidden transitions, Q switching, Q-switched lasers, spiking
Questions and Comments from Users
Can you obtain the laser without metastable state?
The author's answer:
Yes, there are laser gain media which do not have metastable states. This applies to semiconductor gain media and to laser dyes, for example.
Why are there non-radiative transitions to metastable state in lasers?
The author's answer:
See the article on non-radiative transitions.
Why can't we pump electrons directly from ground state to a metastable state?
The author's answer:
You can, only the transition rate will be very low for a moderate amount of pump power.
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What causes the existence of meta-stable state?
The author's answer:
It is just the lack of efficient processes for depopulating a certain level. For example, spontaneous emission may be prohibited by selection rules, i.e., by certain symmetries of wavefunctions.