lower-state lifetime (original) (raw)

Definition: the lifetime of the population in the lower laser level in the absence of radiation

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What is a Lower-state Lifetime?

In a laser gain medium, both stimulated and spontaneous emission bring laser-active ions or atoms into the lower laser level. If a significant population can accumulate in that level because it is not sufficiently quickly depleted, laser radiation can be reabsorbed, bringing the ions or atoms back to the upper laser level. Even though the absorbed energy is not strictly lost, this process is detrimental because it effectively reduces the laser gain. Consequently, the threshold pump power can be increased and the power efficiency reduced.

Cases with Moderately Large Lower-state Lifetime

In many solid-state laser gain media (particularly in four-level gain media), the population in the lower laser level can never be large because that level is too far above the ground state to have a significant population in thermal equilibrium, and because that equilibrium is quickly reached e.g. by multiphonon transitions. Typical values of the lifetime of the lower laser level (called lower-state lifetime, lower level lifetime, or terminal level lifetime) are between a few picoseconds and tens of nanoseconds, while pumping and lasing processes typically work on microsecond or even millisecond time scales.

For continuous-wave lasers, such small values of the lower-state lifetime (far below the upper-state lifetime) effectively suppress any reabsorption on the laser transition. However, significant reabsorption effects can still occur when energy is very quickly extracted from the gain medium. This may be the case in Q-switched lasers, where the phenomenon can cause the formation of satellite pulses [1, 4], and in particular in amplifiers for ultrashort pulses (e.g. regenerative amplifiers based on Ti:sapphire or rare-earth-doped laser gain media), where significant amounts of energy are extracted from the gain medium within a few picoseconds or even less. A clear signature for this effect is the reduction in the amplifier gain and efficiency for short durations of the amplified pulses. A possible countermeasure is the selection of a host crystal (or glass) with a smaller lower-state lifetime. (Unfortunately, measured data are sparse.) Also, chirped-pulse amplification effectively solves this problem because it strongly increases the pulse duration within the amplifier.

In mode-locked lasers, a lower-state lifetime in the picosecond or even nanosecond regime usually has no significant effect, even if the pulse duration is far below the lower-state lifetime. This is because the circulating pulse energy is usually very small compared with the saturation energy, so that only a very small fraction of the upper-state population is transferred to the lower laser level during the amplification of a pulse.

Cases with Long Lower-state Lifetime

A few solid-state gain media have laser transitions where the lower-state lifetime is really large — sometimes even several milliseconds, possibly larger than the upper-state lifetime. An example of this situation is the 2.7-μm transition (4I11/2 → 4I13/2) of Er3+ in fluoride fibers. Here, there are no multiphonon processes depopulating the lower laser level, and the pump radiation also cannot affect this population. In that case, the laser transition is usually self-terminating. A method for avoiding this is to exploit cooperative lasing.

Frequently Asked Questions

What is the lower-state lifetime in a laser medium?

The lower-state lifetime is the average time a laser-active ion or atom remains in the lower energy level of the laser transition before it is depopulated, for example through multiphonon transitions.

Why is a long lower-state lifetime problematic for a laser?

A long lower-state lifetime allows a significant population to accumulate in the lower laser level. This leads to reabsorption of the laser radiation, which effectively reduces the net gain, increases the pump threshold, and lowers the power efficiency.

In which laser systems is the lower-state lifetime particularly critical?

The lower-state lifetime is most critical in systems with rapid energy extraction, such as Q-switched lasers and amplifiers for ultrashort pulses. It is less of a concern in most continuous-wave or mode-locked lasers with low pulse energy.

What is a self-terminating laser transition?

A self-terminating laser transition is one where the lower-state lifetime is very long, sometimes even longer than the upper-state lifetime. This causes population to get trapped in the lower level, which quickly terminates the laser action.

Bibliography

[1]	T. Y. Fan, “Effect of finite lower level lifetime on Q-switched lasers”, IEEE J. Quantum Electron. 24 (12), 2345 (1988); doi:10.1109/3.14358
[2]	C. Bibeau et al., “Direct measurements of the terminal laser level lifetime in neodymium-doped crystals and glasses”, J. Opt. Soc. Am. B 12 (10), 1981 (1995); doi:10.1364/JOSAB.12.001981
[3]	C. Bibeau et al., “Pulse length and terminal-level lifetime dependence of energy extraction for neodymium-doped phosphate amplifier glass”, IEEE J. Quantum Electron. 32 (8), 1487 (1996); doi:10.1109/3.511562
[4]	S. P. Ng, “Satellite pulse generation in diode-pumped Q-switched Nd:GdVO4 lasers”, IEEE J. Quantum Electron. 42 (7), 625 (2006); doi:10.1109/JQE.2006.875866

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