- There are a single or multiple higher-lying energy levels in a suitable distance above an excited level, i.e., fitting to the photon energy according to the wavelength of the incident light.
- There is some population in the excited starting level. (ESA may be largely suppressed if there cannot be a significant population in the starting level, e.g. because it is very short-lived.)
The second condition is obviously more easily fulfilled if the starting level is a metastable state, i.e., a level with a substantial lifetime.
Detrimental Effects of ESA in Lasers and Amplifiers
In solid-state laser gain media, for example, it can occur that the population in the upper laser level does not only lead to amplification by stimulated emission, but also to absorption processes for the pump or laser radiation where laser ions are excited to a higher-lying energy level. For example, that happened when erbium-doped fiber amplifiers where pumped with laser diodes emitting at 808 nm (Figure 1). Pumping at that wavelength did not only lead to the population in the upper laser level, but also to the useless excitation of higher-lying levels through ESA. The problem was later solved by pumping with laser diodes which emit around 975 nm, where ESA is largely avoided.
For a laser, such additional losses by ESA can raise the threshold pump power and reduce the slope efficiency. Of course, excited-state absorption may not only occur with pump light, but also with laser or signal light. It may thus degrade the gain and efficiency of an amplifier for certain ranges of signal wavelength, or cause a laser to operate at somewhat different wavelengths where it can largely escape excited-stayed absorption.
ESA is a common problem particularly for broadband laser gain media such as transition-metal-doped crystals, but less so for rare-earth-doped crystals with their relatively narrow-bandwidth transitions. Of course, ESA is more likely to be relevant for laser ions with multiple electronic levels, such as erbium or thulium, whereas it is not possible for ytterbium.
ESA is also common in various saturable absorber materials such as Cr4+:YAG. Here, the ground state absorption can be fully bleached, but what remains even at rather high optical intensities is the excited-state absorption, which recovers much more rapidly. In effect, ESA causes nonsaturable losses (at least for nanosecond pulses), which may amount to a significant fraction of the saturable losses.
ESA in Upconversion Lasers
Although excited-state absorption is in most cases a detrimental effect, it can also be useful for upconversion pumping, where the excitation of higher-lying energy levels is required. This is exploited e.g. in some thulium-doped lasers (Figure 2), and also in other upconversion lasers. Rate equation models require the values of ESA cross-sections (see below), in addition to the lifetimes of intermediate energy levels.
Calculating Effects of ESA
In some cases, it is relatively simple to include ESA in a laser model. For example, pump or signal ESA may simply lead to an additional absorption term, if ESA leads ions to levels from where they quickly relax to the upper laser level. In more complicated situations, such as the thulium level scheme discussed above, rate equation modeling may be applied.
Measurement of ESA Cross-sections
The measurement of excited-state absorption is more difficult than that for ground-state absorption. A common technique is based on the use of a modulated pump beam, creating a modulated population in a certain electronic level, and monitoring the transmission of the sample with a monochromator, a photodetector, and a lock-in amplifier. The spectra obtained essentially show the difference in laser gain and ESA, but can also contain contributions from other levels.
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