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Saturation Energy

Definition: a measure of the incident optical pulse energy required for achieving significant saturation of an absorber or a gain medium

German: Sättigungsenergie

Category: physical foundations

Formula symbol: Esat

Units: J

How to cite the article; suggest additional literature

The saturation energy of a laser gain medium is the pulse energy of an incident short signal pulse which leads to a reduction in the gain to 1/e (≈ 37%) of its initial value. Similarly, the saturation energy of a saturable absorber is defined.

Usually, the gain or loss is assumed to be small, i.e. input and output pulse energies are similar. (In the case of large gain, the quantity can be related to the input or output pulse energy; the latter is more common for amplifiers.) The pulse duration is assumed to be so short (typically shorter than the upper-state lifetime) that both spontaneous emission and the addition of energy from the pump source are negligible.

saturation of laser gain by a short pulse
Figure 1: Dependence of laser gain after amplification of a pulse on the incident pulse energy, relative to the saturation energy. When the pulse energy equals the saturation energy, the gain is reduced to ≈ 37% of the initial value.

The saturation fluence is the saturation energy per unit area.

For a low-gain laser amplifier, saturation fluence and energy can be calculated according to

saturation fluence and energy

where h ν is the photon energy at the signal wavelength, σem and σabs are the emission and absorption cross sections at the emission wavelength, and A is the mode area. The quantity σabs is zero for four-level gain media (exhibiting no reabsorption on the laser transition) but should not be forgotten for quasi-three-level gain media.

Calculator for the Saturation Energy

Transition cross section:
Beam radius:
Saturation energy: calc

Enter input values with units, where appropriate. After you have modified some inputs, click the "calc" button to recalculate the output.

When N passes of a pulse through an amplifier medium are arranged, an effective saturation energy can be defined, which is reduced by a factor N.

These quantities can be defined in an analogous way for saturable absorbers. For example, a pulse with a fluence equal to the saturation fluence reduces the saturable loss of a SESAM to 1/e of its initial value.

Note that the saturation fluence of a saturable absorber does not depend on the thickness of the absorber layer, unless the thickness is so large that the fluence is reduced substantially within the device.

Importance of the Saturation Energy

The saturation energy plays an important role in various areas of laser physics and laser design. Some examples are:

See also: gain saturation, saturable absorbers, saturation power, transition cross sections, gain
and other articles in the category physical foundations

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